Metrics for Falkner and Boettcher, Equation (22+)

analyze6.0ms (0.1%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	50%	0%	0%	50%	0%	3
50%	25%	25%	0%	0%	50%	0%	4
75%	37.5%	12.5%	0%	0%	50%	0%	5
87.5%	43.7%	6.2%	0%	0%	50%	0%	6
93.8%	46.9%	3.1%	0%	0%	50%	0%	7
96.9%	48.4%	1.6%	0%	0%	50%	0%	8
98.4%	49.2%	0.8%	0%	0%	50%	0%	9
99.2%	49.6%	0.4%	0%	0%	50%	0%	10
99.6%	49.8%	0.2%	0%	0%	50%	0%	11
99.8%	49.9%	0.1%	0%	0%	50%	0%	12

Compiler

Compiled 22 to 17 computations (22.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

Operation ival-mult, time spent: 1.0ms, 33.0% of total-time

Operation ival-sqrt, time spent: 1.0ms, 33.0% of total-time

Operation ival-pi, time spent: 0.0ms, 0.0% of total-time

Operation ival-sub, time spent: 0.0ms, 0.0% of total-time

Operation ival-div, time spent: 0.0ms, 0.0% of total-time

Operation const, time spent: 0.0ms, 0.0% of total-time

sample1.7s (38.8%)

Results

1.5s	8255×	256	valid
1.0ms	11×	256	invalid
0.0ms	1×	256	valid

Precisions

Click to see histograms. Total time spent on operations: 926.0ms

Operation ival-mult, time spent: 546.0ms, 59.0% of total-time

Operation ival-sqrt, time spent: 123.0ms, 13.0% of total-time

Operation ival-sub, time spent: 107.0ms, 12.0% of total-time

Operation ival-div, time spent: 71.0ms, 8.0% of total-time

Operation ival-pi, time spent: 48.0ms, 5.0% of total-time

Operation const, time spent: 32.0ms, 3.0% of total-time

Bogosity

preprocess384.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

1294×	`fma-define`
1188×	`times-frac`
946×	`fma-neg`
880×	`unsub-neg`
856×	`distribute-lft-in`

FPErrors

Click to see full error table

Overpredictions	Example	Example	Subexpression
0	-	-	`(PI.f64)`
0	-	-	`(.f64 (.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v)))`
0	-	-	`(-.f64 1 (*.f64 v v))`
1	(7.89762087926163e-163)	-	`(.f64 6 (.f64 v v))`
0	-	-	`v`
0	-	-	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
0	-	-	`(-.f64 2 (.f64 6 (.f64 v v)))`
0	-	-	`6`
0	-	-	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
0	-	-	`(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))`
0	-	-	`4`
0	-	-	`3`
0	-	-	`(*.f64 v v)`
0	-	-	`(*.f64 3 (PI.f64))`
0	-	-	`2`
0	-	-	`1`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	31	292
1	91	272
2	210	252
3	706	248
4	2204	248
5	5036	236
6	7676	236

Stop Event

1×	node limit

Calls

Call 1

Inputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 (neg.f64 v) (neg.f64 v)))))))
(neg.f64 (/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 (neg.f64 v) (neg.f64 v))))))))

Outputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v)))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v)))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 (neg.f64 v) (neg.f64 v)))))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v)))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
(neg.f64 (/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 (neg.f64 v) (neg.f64 v)))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 (neg.f64 v) (neg.f64 v))))))))
(/.f64 -4 (.f64 (.f64 3 (PI.f64)) (.f64 (-.f64 1 (.f64 v v)) (sqrt.f64 (+.f64 2 (.f64 -6 (.f64 v v)))))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (neg.f64 (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))))
(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (fma.f64 (.f64 v v) -6 2)))
(/.f64 (/.f64 (/.f64 4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Symmetry

(abs v)

Compiler

Compiled 195 to 122 computations (37.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 112.0ms

Operation ival-mult, time spent: 52.0ms, 46.0% of total-time

Operation ival-sqrt, time spent: 24.0ms, 21.0% of total-time

Operation ival-sub, time spent: 23.0ms, 20.0% of total-time

Operation const, time spent: 7.0ms, 6.0% of total-time

Operation ival-div, time spent: 4.0ms, 4.0% of total-time

Operation ival-pi, time spent: 3.0ms, 3.0% of total-time

eval2.0ms (0%)

Compiler: Compiled 89 to 59 computations (33.7% saved)

prune2.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
▶	98.5%	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Status

Accuracy

Program

▶

100.0%

(/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (*.f64 v v)))) (sqrt.f64 (+.f64 2 (*.f64 (*.f64 v v) -6))))

▶

98.5%

(/.f64 4 (*.f64 (*.f64 (*.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v))) (sqrt.f64 (-.f64 2 (*.f64 6 (*.f64 v v))))))

Compiler

Compiled 40 to 30 computations (25% saved)

localize253.0ms (5.8%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	100.0%	(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
✓	100.0%	(.f64 (PI.f64) (-.f64 1 (.f64 v v)))
✓	99.7%	(.f64 (.f64 v v) -6)
✓	98.5%	(/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v))))
✓	100.0%	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	100.0%	(.f64 (.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v)))
✓	99.7%	(.f64 6 (.f64 v v))
✓	98.5%	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Compiler

Compiled 155 to 89 computations (42.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 98.0ms

Operation ival-mult, time spent: 37.0ms, 38.0% of total-time

Operation ival-sqrt, time spent: 22.0ms, 22.0% of total-time

Operation ival-sub, time spent: 20.0ms, 20.0% of total-time

Operation ival-div, time spent: 7.0ms, 7.0% of total-time

Operation const, time spent: 6.0ms, 6.0% of total-time

Operation ival-add, time spent: 5.0ms, 5.0% of total-time

Operation ival-pi, time spent: 1.0ms, 1.0% of total-time

series30.0ms (0.7%)

Counts

8 → 96

Calls

24 calls:

Time	Variable		Point	Expression
4.0ms	v	@	0	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
3.0ms	v	@	inf	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
3.0ms	v	@	0	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
2.0ms	v	@	inf	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
2.0ms	v	@	0	(.f64 (PI.f64) (-.f64 1 (.f64 v v)))

rewrite317.0ms (7.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1046×	`prod-diff`
772×	`log1p-expm1-u`
372×	`associate-r`
234×	`associate-l`
174×	`expm1-log1p-u`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	29	311
1	432	287
2	5802	287

Stop Event

1×	node limit

Counts

8 → 206

Calls

Call 1

Inputs
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(.f64 6 (.f64 v v))
(.f64 (.f64 3 (PI.f64)) (-.f64 1 (*.f64 v v)))
(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
(/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v))))
(.f64 (.f64 v v) -6)
(.f64 (PI.f64) (-.f64 1 (.f64 v v)))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))

Outputs
(-.f64 (exp.f64 (log1p.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 1)
(.f64 4 (/.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2) (.f64 3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))))
(.f64 1 (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 4/3 (/.f64 (/.f64 1 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 4/3 (/.f64 1 (.f64 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 4/3 (.f64 (/.f64 1 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2)))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2))
(.f64 (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1)
(.f64 (cbrt.f64 (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))) 2)) (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))) 2)) (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (/.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2)))
(.f64 (sqrt.f64 (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) (sqrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (/.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2)))
(.f64 (/.f64 -4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (/.f64 1 (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 -4 (/.f64 1 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (neg.f64 (.f64 3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))))))
(.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2) (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))))
(.f64 (/.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) -1/2) (.f64 3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 4)
(.f64 (/.f64 1 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (/.f64 1 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)))
(.f64 (/.f64 4/3 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (/.f64 (/.f64 1 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (/.f64 4/3 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) (/.f64 (/.f64 1 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) 1) (/.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) (/.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)))
(.f64 (/.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 1) (/.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (/.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (/.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(pow.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 2)
(pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (.f64 (-.f64 1 (pow.f64 v 2)) (/.f64 (PI.f64) 4/3))) -1)
(neg.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(neg.f64 (/.f64 -4 (.f64 (.f64 3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(neg.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
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(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) 1) (/.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (/.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 2) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) (/.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)))
(.f64 (/.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) 1) (/.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (/.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (/.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))))) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(pow.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1)
(pow.f64 (cbrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3)
(pow.f64 (pow.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 2)
(pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (.f64 (-.f64 1 (pow.f64 v 2)) (/.f64 (PI.f64) 4/3))) -1)
(neg.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (neg.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(neg.f64 (/.f64 -4 (.f64 (.f64 3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(neg.f64 (/.f64 (/.f64 -4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(sqrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2))) 2)) (fma.f64 (pow.f64 v 2) -6 2)))
(log.f64 (exp.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(cbrt.f64 (pow.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3))
(cbrt.f64 (/.f64 (pow.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) 3) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2)))
(expm1.f64 (log1p.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(log1p.f64 (expm1.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(exp.f64 (log.f64 (/.f64 (/.f64 4/3 (*.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(exp.f64 (.f64 (log.f64 (/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (pow.f64 v 2)))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1))

eval169.0ms (3.9%)

Compiler: Compiled 8107 to 6589 computations (18.7% saved)

prune28.0ms (0.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	299	3	302
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	299	5	304

Accuracy

100.0%

Counts

304 → 5

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
▶	99.4%	(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
✓	98.5%	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
▶	97.9%	(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
▶	97.9%	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 75 to 61 computations (18.7% saved)

localize237.0ms (5.4%)

Localize:

Found 8 expressions with local error:

New	Accuracy	Program
✓	100.0%	(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
✓	99.7%	(.f64 (.f64 v v) -6)
✓	98.4%	(/.f64 4/3 (PI.f64))
✓	100.0%	(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
✓	100.0%	(.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
✓	99.7%	(.f64 6 (.f64 v v))
✓	98.5%	(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	98.4%	(/.f64 (sqrt.f64 1/2) (PI.f64))

Compiler

Compiled 118 to 75 computations (36.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

Operation ival-mult, time spent: 90.0ms, 62.0% of total-time

Operation ival-sqrt, time spent: 26.0ms, 18.0% of total-time

Operation ival-div, time spent: 12.0ms, 8.0% of total-time

Operation ival-sub, time spent: 6.0ms, 4.0% of total-time

Operation const, time spent: 5.0ms, 3.0% of total-time

Operation ival-add, time spent: 4.0ms, 3.0% of total-time

Operation ival-pi, time spent: 1.0ms, 1.0% of total-time

series19.0ms (0.4%)

Counts

8 → 72

Calls

18 calls:

Time	Variable		Point	Expression
5.0ms	v	@	inf	(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
1.0ms	v	@	0	(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
1.0ms	v	@	inf	(.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
1.0ms	v	@	0	(.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
1.0ms	v	@	-inf	(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

rewrite155.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

909×	`log1p-expm1-u`
758×	`prod-diff`
757×	`expm1-log1p-u`
274×	`associate-r`
174×	`associate-l`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	192
1	360	170
2	4595	170

Stop Event

1×	node limit

Counts

8 → 183

Calls

Call 1

Inputs
(/.f64 (sqrt.f64 1/2) (PI.f64))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(.f64 6 (.f64 v v))
(.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
(sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))
(/.f64 4/3 (PI.f64))
(.f64 (.f64 v v) -6)
(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))

Outputs
(-.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)))) 1)
(*.f64 (sqrt.f64 1/2) (/.f64 1 (PI.f64)))
(*.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 1)
(*.f64 1 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(*.f64 (cbrt.f64 1/2) (/.f64 (cbrt.f64 (sqrt.f64 1/2)) (PI.f64)))
(.f64 (cbrt.f64 1/2) (.f64 (cbrt.f64 (sqrt.f64 1/2)) (/.f64 1 (PI.f64))))
(*.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (cbrt.f64 (/.f64 1/2 (pow.f64 (PI.f64) 2))))
(*.f64 (cbrt.f64 (/.f64 1/2 (pow.f64 (PI.f64) 2))) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(*.f64 (pow.f64 1/2 1/4) (/.f64 (pow.f64 1/2 1/4) (PI.f64)))
(.f64 (pow.f64 1/2 1/4) (.f64 (pow.f64 1/2 1/4) (/.f64 1 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) (sqrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(*.f64 (neg.f64 (sqrt.f64 1/2)) (/.f64 1 (neg.f64 (PI.f64))))
(*.f64 (/.f64 1 (PI.f64)) (sqrt.f64 1/2))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (sqrt.f64 1/2) (cbrt.f64 (PI.f64))))
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (/.f64 (sqrt.f64 1/2) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (cbrt.f64 1/2) 1) (/.f64 (cbrt.f64 (sqrt.f64 1/2)) (PI.f64)))
(*.f64 (/.f64 (cbrt.f64 1/2) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (cbrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(*.f64 (/.f64 (cbrt.f64 1/2) (sqrt.f64 (PI.f64))) (/.f64 (cbrt.f64 (sqrt.f64 1/2)) (sqrt.f64 (PI.f64))))
(*.f64 (/.f64 (pow.f64 1/2 1/4) 1) (/.f64 (pow.f64 1/2 1/4) (PI.f64)))
(*.f64 (/.f64 (pow.f64 1/2 1/4) (pow.f64 (cbrt.f64 (PI.f64)) 2)) (/.f64 (pow.f64 1/2 1/4) (cbrt.f64 (PI.f64))))
(pow.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 1)
(pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) 3)
(pow.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) 2)
(pow.f64 (/.f64 (PI.f64) (sqrt.f64 1/2)) -1)
(neg.f64 (/.f64 (sqrt.f64 1/2) (neg.f64 (PI.f64))))
(neg.f64 (/.f64 (neg.f64 (sqrt.f64 1/2)) (PI.f64)))
(sqrt.f64 (/.f64 1/2 (pow.f64 (PI.f64) 2)))
(log.f64 (exp.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)))))
(cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 1/2) (PI.f64)) 3))
(cbrt.f64 (/.f64 (*.f64 1/2 (sqrt.f64 1/2)) (pow.f64 (PI.f64) 3)))
(expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(exp.f64 (log.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))))
(exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 1/2) (PI.f64))) 1))
(-.f64 (exp.f64 (log1p.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))) 1)
(.f64 4 (/.f64 1/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(*.f64 (/.f64 4/3 (PI.f64)) (/.f64 1 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 1 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(.f64 (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (PI.f64) 2)) (fma.f64 (pow.f64 v 2) -6 2))))
(.f64 (cbrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (PI.f64) 2)) (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(.f64 (sqrt.f64 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(.f64 -4 (/.f64 1 (.f64 -3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(.f64 (/.f64 1/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 4)
(pow.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(pow.f64 (cbrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 3)
(pow.f64 (pow.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 2)
(pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (/.f64 (.f64 (PI.f64) 3) 4)) -1)
(neg.f64 (/.f64 -4 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(sqrt.f64 (/.f64 (/.f64 16/9 (pow.f64 (PI.f64) 2)) (fma.f64 (pow.f64 v 2) -6 2)))
(log.f64 (exp.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))))
(cbrt.f64 (pow.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(expm1.f64 (log1p.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(log1p.f64 (expm1.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(exp.f64 (log.f64 (/.f64 4/3 (*.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(exp.f64 (.f64 (log.f64 (/.f64 4/3 (.f64 (PI.f64) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 6 (pow.f64 v 2)))) 1)
(-.f64 0 (*.f64 6 (pow.f64 v 2)))
(pow.f64 (*.f64 6 (pow.f64 v 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 6 (pow.f64 v 2))) 3)
(pow.f64 (*.f64 (pow.f64 (pow.f64 v 2) 3) 216) 1/3)
(pow.f64 (*.f64 v (sqrt.f64 -6)) 2)
(neg.f64 (*.f64 6 (pow.f64 v 2)))
(sqrt.f64 (*.f64 (pow.f64 v 4) 36))
(log.f64 (pow.f64 (exp.f64 (pow.f64 v 2)) 6))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 6 (pow.f64 v 2)))))
(log.f64 (/.f64 1 (pow.f64 (exp.f64 (pow.f64 v 2)) 6)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 v 2) 3) 216))
(expm1.f64 (log1p.f64 (*.f64 6 (pow.f64 v 2))))
(log1p.f64 (expm1.f64 (*.f64 6 (pow.f64 v 2))))
(exp.f64 (log.f64 (*.f64 6 (pow.f64 v 2))))
(exp.f64 (.f64 (log.f64 (.f64 6 (pow.f64 v 2))) 1))
(-.f64 (exp.f64 (log1p.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))) 1)
(pow.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(pow.f64 (cbrt.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 3)
(pow.f64 (pow.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3) 1/3)
(pow.f64 (sqrt.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 2)
(sqrt.f64 (.f64 (fma.f64 (pow.f64 v 2) -6 2) (.f64 (pow.f64 (PI.f64) 2) 9)))
(log.f64 (pow.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (*.f64 (PI.f64) 3)))
(log.f64 (+.f64 1 (expm1.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))))
(cbrt.f64 (pow.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(cbrt.f64 (.f64 (pow.f64 (.f64 (PI.f64) 3) 3) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2)))
(cbrt.f64 (.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2) (pow.f64 (.f64 (PI.f64) 3) 3)))
(expm1.f64 (log1p.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(log1p.f64 (expm1.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(exp.f64 (log.f64 (.f64 (PI.f64) (.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) (*.f64 3 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 1))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(*.f64 1 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(*.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(/.f64 (sqrt.f64 (+.f64 4 (*.f64 (pow.f64 v 4) 36))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(/.f64 (sqrt.f64 (-.f64 8 (.f64 (pow.f64 (pow.f64 v 2) 3) 216))) (sqrt.f64 (+.f64 (+.f64 4 (.f64 (pow.f64 v 4) 36)) (*.f64 12 (pow.f64 v 2)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (pow.f64 v 2) 3) 216) 8)) (sqrt.f64 (-.f64 (+.f64 4 (.f64 (pow.f64 v 4) 36)) (*.f64 12 (pow.f64 v 2)))))
(pow.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/2)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1))
(exp.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))
(-.f64 (exp.f64 (log1p.f64 (/.f64 4/3 (PI.f64)))) 1)
(.f64 4 (/.f64 1 (.f64 (PI.f64) 3)))
(*.f64 4/3 (/.f64 1 (PI.f64)))
(*.f64 (/.f64 4/3 (PI.f64)) 1)
(*.f64 1 (/.f64 4/3 (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2) (cbrt.f64 (/.f64 4/3 (PI.f64))))
(*.f64 (sqrt.f64 (/.f64 4/3 (PI.f64))) (sqrt.f64 (/.f64 4/3 (PI.f64))))
(*.f64 -4/3 (/.f64 1 (neg.f64 (PI.f64))))
(*.f64 (/.f64 1 (PI.f64)) 4/3)
(pow.f64 (/.f64 4/3 (PI.f64)) 1)
(pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 3)
(pow.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 4/3 (PI.f64))) 2)
(pow.f64 (*.f64 (PI.f64) 3/4) -1)
(neg.f64 (/.f64 -4/3 (PI.f64)))
(sqrt.f64 (/.f64 16/9 (pow.f64 (PI.f64) 2)))
(log.f64 (exp.f64 (/.f64 4/3 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 4/3 (PI.f64)))))
(cbrt.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3))
(expm1.f64 (log1p.f64 (/.f64 4/3 (PI.f64))))
(log1p.f64 (expm1.f64 (/.f64 4/3 (PI.f64))))
(exp.f64 (log.f64 (/.f64 4/3 (PI.f64))))
(exp.f64 (*.f64 (log.f64 (/.f64 4/3 (PI.f64))) 1))
(-.f64 (exp.f64 (log1p.f64 (*.f64 6 (pow.f64 v 2)))) 1)
(-.f64 0 (*.f64 6 (pow.f64 v 2)))
(pow.f64 (*.f64 6 (pow.f64 v 2)) 1)
(pow.f64 (cbrt.f64 (*.f64 6 (pow.f64 v 2))) 3)
(pow.f64 (*.f64 (pow.f64 (pow.f64 v 2) 3) 216) 1/3)
(pow.f64 (*.f64 v (sqrt.f64 -6)) 2)
(neg.f64 (*.f64 6 (pow.f64 v 2)))
(sqrt.f64 (*.f64 (pow.f64 v 4) 36))
(log.f64 (pow.f64 (exp.f64 (pow.f64 v 2)) 6))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 6 (pow.f64 v 2)))))
(log.f64 (/.f64 1 (pow.f64 (exp.f64 (pow.f64 v 2)) 6)))
(cbrt.f64 (*.f64 (pow.f64 (pow.f64 v 2) 3) 216))
(expm1.f64 (log1p.f64 (*.f64 6 (pow.f64 v 2))))
(log1p.f64 (expm1.f64 (*.f64 6 (pow.f64 v 2))))
(exp.f64 (log.f64 (*.f64 6 (pow.f64 v 2))))
(exp.f64 (.f64 (log.f64 (.f64 6 (pow.f64 v 2))) 1))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(*.f64 1 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(*.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4))
(*.f64 (pow.f64 1 1/2) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(/.f64 (sqrt.f64 (+.f64 4 (*.f64 (pow.f64 v 4) 36))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(/.f64 (sqrt.f64 (-.f64 8 (.f64 (pow.f64 (pow.f64 v 2) 3) 216))) (sqrt.f64 (+.f64 (+.f64 4 (.f64 (pow.f64 v 4) 36)) (*.f64 12 (pow.f64 v 2)))))
(/.f64 (sqrt.f64 (+.f64 (.f64 (pow.f64 (pow.f64 v 2) 3) 216) 8)) (sqrt.f64 (-.f64 (+.f64 4 (.f64 (pow.f64 v 4) 36)) (*.f64 12 (pow.f64 v 2)))))
(pow.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/2)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1))
(exp.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))

eval122.0ms (2.8%)

Compiler: Compiled 4431 to 3772 computations (14.9% saved)

prune31.0ms (0.7%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	253	2	255
Fresh	0	0	0
Picked	1	2	3
Done	0	2	2
Total	254	6	260

Accuracy

100.0%

Counts

260 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
✓	99.4%	(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
▶	99.4%	(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))
▶	99.4%	(/.f64 (.f64 (/.f64 1 (PI.f64)) 4/3) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) -6))))
✓	98.5%	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	97.9%	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 82 to 68 computations (17.1% saved)

localize133.0ms (3%)

Localize:

Found 3 expressions with local error:

New	Accuracy	Program
✓	98.4%	(/.f64 4/3 (PI.f64))
✓	100.0%	(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
✓	99.7%	(.f64 (.f64 v v) -6)

Compiler

Compiled 67 to 46 computations (31.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 62.0ms

Operation ival-mult, time spent: 28.0ms, 45.0% of total-time

Operation ival-sqrt, time spent: 13.0ms, 21.0% of total-time

Operation ival-div, time spent: 12.0ms, 19.0% of total-time

Operation ival-add, time spent: 4.0ms, 6.0% of total-time

Operation const, time spent: 3.0ms, 5.0% of total-time

Operation ival-pi, time spent: 1.0ms, 2.0% of total-time

series10.0ms (0.2%)

Counts

3 → 24

Calls

6 calls:

Time	Variable		Point	Expression
7.0ms	v	@	0	(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
1.0ms	v	@	inf	(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
1.0ms	v	@	-inf	(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
1.0ms	v	@	0	(.f64 (.f64 v v) -6)
1.0ms	v	@	-inf	(.f64 (.f64 v v) -6)

rewrite113.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1428×	`unpow-prod-down`
776×	`log-prod`
745×	`log1p-expm1-u`
745×	`expm1-log1p-u`
326×	`prod-diff`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	169	47
2	2093	47

Stop Event

1×	node limit

Counts

3 → 126

Calls

Call 1

Inputs
(.f64 (.f64 v v) -6)
(sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6)))
(/.f64 4/3 (PI.f64))

Outputs
(+.f64 0 (*.f64 (pow.f64 v 2) -6))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2))) (cbrt.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2))))) (log.f64 (cbrt.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2)))))
(+.f64 (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2)))) (log.f64 (sqrt.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2)))))
(-.f64 (exp.f64 (log1p.f64 (*.f64 (pow.f64 v 2) -6))) 1)
(pow.f64 (*.f64 (pow.f64 v 2) -6) 1)
(pow.f64 (cbrt.f64 (*.f64 (pow.f64 v 2) -6)) 3)
(pow.f64 (pow.f64 (*.f64 (pow.f64 v 2) -6) 3) 1/3)
(pow.f64 (*.f64 v (sqrt.f64 -6)) 2)
(sqrt.f64 (*.f64 (pow.f64 v 4) 36))
(log.f64 (pow.f64 (exp.f64 -6) (pow.f64 v 2)))
(log.f64 (+.f64 1 (expm1.f64 (*.f64 (pow.f64 v 2) -6))))
(cbrt.f64 (pow.f64 (*.f64 (pow.f64 v 2) -6) 3))
(expm1.f64 (log1p.f64 (*.f64 (pow.f64 v 2) -6)))
(log1p.f64 (expm1.f64 (*.f64 (pow.f64 v 2) -6)))
(exp.f64 (fma.f64 2 (log.f64 v) (log.f64 -6)))
(exp.f64 (*.f64 (fma.f64 2 (log.f64 v) (log.f64 -6)) 1))
(exp.f64 (.f64 (log.f64 (cbrt.f64 (.f64 (pow.f64 v 2) -6))) 3))
(exp.f64 (.f64 (.f64 3 (fma.f64 2 (log.f64 v) (log.f64 -6))) 1/3))
(exp.f64 (.f64 (log.f64 (.f64 v (sqrt.f64 -6))) 2))
(+.f64 0 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))) (log.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) (log.f64 (sqrt.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))))
(-.f64 (exp.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 1)
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(*.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (log.f64 (exp.f64 1)))
(*.f64 1 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(*.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 2))
(*.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4))
(*.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/2) (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))
(*.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2) (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/2))
(.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2) (pow.f64 (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/2))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(*.f64 (pow.f64 1 1/3) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 2) (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2)) 1) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1))
(.f64 (pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 1/2) (pow.f64 (.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/2))
(*.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(.f64 (pow.f64 (fma.f64 (pow.f64 (pow.f64 v 2) 3) -216 8) 1/2) (pow.f64 (/.f64 1 (fma.f64 (.f64 (pow.f64 v 2) -6) (fma.f64 (pow.f64 v 2) -6 -2) 4)) 1/2))
(.f64 (pow.f64 (-.f64 4 (.f64 (pow.f64 v 4) 36)) 1/2) (pow.f64 (/.f64 1 (+.f64 2 (*.f64 6 (pow.f64 v 2)))) 1/2))
(.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 1/2) (pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 1/2))
(.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/2) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/2))
(*.f64 (pow.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/2) 1) (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2) 1))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 3) (pow.f64 (cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 3))
(.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(.f64 (pow.f64 (pow.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 2) 1/3) (pow.f64 (.f64 (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/3))
(.f64 (pow.f64 (.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 1/3) (pow.f64 (*.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2)) 1/3))
(.f64 (pow.f64 (.f64 (fma.f64 (pow.f64 v 2) -6 2) (cbrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/3) (pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/3))
(.f64 (pow.f64 (.f64 (fma.f64 (pow.f64 v 2) -6 2) (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 1/3) (pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 2) (pow.f64 (sqrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4)) 2))
(/.f64 (sqrt.f64 (-.f64 4 (.f64 (pow.f64 v 4) 36))) (sqrt.f64 (+.f64 2 (.f64 6 (pow.f64 v 2)))))
(/.f64 (sqrt.f64 (fma.f64 (pow.f64 (pow.f64 v 2) 3) -216 8)) (sqrt.f64 (fma.f64 (*.f64 (pow.f64 v 2) -6) (fma.f64 (pow.f64 v 2) -6 -2) 4)))
(pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/2)
(pow.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1)
(pow.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2) 1/3)
(pow.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 1/4) 2)
(fabs.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))
(log.f64 (exp.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log.f64 (+.f64 1 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))))
(cbrt.f64 (pow.f64 (fma.f64 (pow.f64 v 2) -6 2) 3/2))
(expm1.f64 (log1p.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(log1p.f64 (expm1.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))))
(exp.f64 (*.f64 (log.f64 (fma.f64 (pow.f64 v 2) -6 2)) 1/2))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 (fma.f64 (pow.f64 v 2) -6 2)))) 3))
(exp.f64 (.f64 (.f64 3/2 (log.f64 (fma.f64 (pow.f64 v 2) -6 2))) 1/3))
(exp.f64 (.f64 (.f64 1/4 (log.f64 (fma.f64 (pow.f64 v 2) -6 2))) 2))
(+.f64 0 (/.f64 4/3 (PI.f64)))
(+.f64 (log.f64 (*.f64 (cbrt.f64 (exp.f64 (/.f64 4/3 (PI.f64)))) (cbrt.f64 (exp.f64 (/.f64 4/3 (PI.f64)))))) (log.f64 (cbrt.f64 (exp.f64 (/.f64 4/3 (PI.f64))))))
(+.f64 (log.f64 (sqrt.f64 (exp.f64 (/.f64 4/3 (PI.f64))))) (log.f64 (sqrt.f64 (exp.f64 (/.f64 4/3 (PI.f64))))))
(-.f64 (exp.f64 (log1p.f64 (/.f64 4/3 (PI.f64)))) 1)
(*.f64 4/3 (/.f64 1 (PI.f64)))
(*.f64 (/.f64 4/3 (PI.f64)) 1)
(*.f64 (/.f64 4/3 (PI.f64)) (log.f64 (exp.f64 1)))
(*.f64 1 (/.f64 4/3 (PI.f64)))
(*.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2))
(*.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) (pow.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2) 1/3))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2) (cbrt.f64 (/.f64 4/3 (PI.f64))))
(*.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 2))
(*.f64 (sqrt.f64 (/.f64 4/3 (PI.f64))) (sqrt.f64 (/.f64 4/3 (PI.f64))))
(*.f64 -4/3 (/.f64 1 (neg.f64 (PI.f64))))
(*.f64 -4/3 (pow.f64 (/.f64 1 (neg.f64 (PI.f64))) 1))
(*.f64 (/.f64 1 (PI.f64)) 4/3)
(*.f64 (/.f64 1 (PI.f64)) (log.f64 (exp.f64 4/3)))
(*.f64 (/.f64 1 (pow.f64 (cbrt.f64 (PI.f64)) 2)) (pow.f64 (/.f64 (cbrt.f64 (PI.f64)) 4/3) -1))
(*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (pow.f64 (/.f64 (sqrt.f64 (PI.f64)) 4/3) -1))
(*.f64 (pow.f64 1 1/3) (/.f64 4/3 (PI.f64)))
(*.f64 (pow.f64 (cbrt.f64 4/3) 3) (pow.f64 (cbrt.f64 (/.f64 1 (PI.f64))) 3))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2)) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 3))
(*.f64 (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 3) (pow.f64 (cbrt.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 3))
(.f64 (pow.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) (cbrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))))) 3) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 3))
(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 3))
(*.f64 (pow.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2) 1/3) (cbrt.f64 (/.f64 4/3 (PI.f64))))
(.f64 (pow.f64 (.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (/.f64 4/3 (PI.f64)))) 1/3) (pow.f64 (*.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (/.f64 4/3 (PI.f64)))) 1/3))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3)) 1/3) (pow.f64 (sqrt.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2) 4/3) 1/3) (pow.f64 (/.f64 1 (PI.f64)) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2) (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2)) 1/3) (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 1/3))
(.f64 (pow.f64 (.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2) (sqrt.f64 (/.f64 4/3 (PI.f64)))) 1/3) (pow.f64 (sqrt.f64 (/.f64 4/3 (PI.f64))) 1/3))
(*.f64 (pow.f64 (sqrt.f64 4/3) 2) (pow.f64 (sqrt.f64 (/.f64 1 (PI.f64))) 2))
(*.f64 (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 2)) 2) (pow.f64 (sqrt.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 2))
(*.f64 (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 2) (pow.f64 (sqrt.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 2))
(.f64 (pow.f64 (.f64 (cbrt.f64 (.f64 (PI.f64) 3/4)) (cbrt.f64 (.f64 (PI.f64) 3/4))) -1) (cbrt.f64 (/.f64 4/3 (PI.f64))))
(pow.f64 (/.f64 4/3 (PI.f64)) 1)
(pow.f64 (cbrt.f64 (/.f64 4/3 (PI.f64))) 3)
(pow.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3) 1/3)
(pow.f64 (sqrt.f64 (/.f64 4/3 (PI.f64))) 2)
(pow.f64 (*.f64 (PI.f64) 3/4) -1)
(pow.f64 (/.f64 (*.f64 (PI.f64) 3/4) 1) -1)
(neg.f64 (/.f64 -4/3 (PI.f64)))
(sqrt.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 2))
(log.f64 (exp.f64 (/.f64 4/3 (PI.f64))))
(log.f64 (+.f64 1 (expm1.f64 (/.f64 4/3 (PI.f64)))))
(cbrt.f64 (pow.f64 (/.f64 4/3 (PI.f64)) 3))
(expm1.f64 (log1p.f64 (/.f64 4/3 (PI.f64))))
(log1p.f64 (expm1.f64 (/.f64 4/3 (PI.f64))))
(exp.f64 (log.f64 (/.f64 4/3 (PI.f64))))
(exp.f64 (*.f64 (log.f64 (/.f64 4/3 (PI.f64))) 1))
(exp.f64 (*.f64 (log.f64 (cbrt.f64 (/.f64 4/3 (PI.f64)))) 3))
(exp.f64 (.f64 (.f64 3 (log.f64 (/.f64 4/3 (PI.f64)))) 1/3))
(exp.f64 (*.f64 (log.f64 (sqrt.f64 (/.f64 4/3 (PI.f64)))) 2))
(exp.f64 (.f64 (log.f64 (.f64 (PI.f64) 3/4)) -1))

eval191.0ms (4.4%)

Compiler: Compiled 2803 to 2464 computations (12.1% saved)

prune23.0ms (0.5%)

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	0	0
Picked	0	2	2
Done	0	4	4
Total	150	6	156

Accuracy

100.0%

Counts

156 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
✓	99.4%	(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
✓	99.4%	(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))
✓	99.4%	(/.f64 (.f64 (/.f64 1 (PI.f64)) 4/3) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) -6))))
✓	98.5%	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
✓	97.9%	(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Compiler

Compiled 173 to 133 computations (23.1% saved)

regimes13.0ms (0.3%)

Counts

7 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 (.f64 (/.f64 1 (PI.f64)) 4/3) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) -6))))
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Outputs
(/.f64 (/.f64 4/3 (.f64 (PI.f64) (-.f64 1 (.f64 v v)))) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))

Calls

4 calls:

4.0ms	v
4.0ms	(*.f64 v v)
2.0ms	(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))
2.0ms	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Results

Accuracy	Segments	Branch
100.0%	1	`v`
100.0%	1	`(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))`
100.0%	1	`(.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v)))))`
100.0%	1	`(*.f64 v v)`

Compiler

Compiled 46 to 33 computations (28.3% saved)

regimes9.0ms (0.2%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))
(/.f64 (.f64 (/.f64 1 (PI.f64)) 4/3) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) -6))))

Outputs
(/.f64 (.f64 (/.f64 1 (PI.f64)) 4/3) (sqrt.f64 (+.f64 2 (.f64 (*.f64 v v) -6))))

Calls

2 calls:

7.0ms	v
2.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
99.4%	1	`v`
99.4%	1	`(*.f64 v v)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes6.0ms (0.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))
(/.f64 4 (.f64 (.f64 3 (PI.f64)) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

Outputs
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 (+.f64 2 (.f64 (.f64 v v) -6))))

Calls

2 calls:

3.0ms	v
2.0ms	(*.f64 v v)

Results

Accuracy	Segments	Branch
99.4%	1	`v`
99.4%	1	`(*.f64 v v)`

Compiler

Compiled 6 to 3 computations (50% saved)

regimes3.0ms (0.1%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))

Outputs
(/.f64 (/.f64 4/3 (PI.f64)) (sqrt.f64 2))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
99.4%	1	`v`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Stop Event

1×

done

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Outputs
(*.f64 4/3 (/.f64 (sqrt.f64 1/2) (PI.f64)))

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.9%	1	`v`

Compiler

Compiled 63 to 53 computations (15.9% saved)

soundness354.0ms (8.1%)

Rules

1294×	`fma-define`
1188×	`times-frac`
946×	`fma-neg`
909×	`log1p-expm1-u`
880×	`unsub-neg`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	292
1	91	272
2	210	252
3	706	248
4	2204	248
5	5036	236
6	7676	236
0	27	192
1	360	170
2	4595	170

Stop Event

1×	node limit
1×	node limit

Compiler

Compiled 305 to 194 computations (36.4% saved)

end0.0ms (0%)

preprocess70.0ms (1.6%)

Remove: (abs v)
Compiler: Compiled 346 to 256 computations (26% saved)

analyze6.0ms (0.1%)

sample1.7s (38.8%)

preprocess384.0ms (8.8%)

eval2.0ms (0%)

prune2.0ms (0%)

localize253.0ms (5.8%)

series30.0ms (0.7%)

rewrite317.0ms (7.2%)

eval169.0ms (3.9%)

prune28.0ms (0.6%)

localize237.0ms (5.4%)

series19.0ms (0.4%)

rewrite155.0ms (3.5%)

eval122.0ms (2.8%)

prune31.0ms (0.7%)

localize133.0ms (3%)

series10.0ms (0.2%)

rewrite113.0ms (2.6%)

eval191.0ms (4.4%)

prune23.0ms (0.5%)

regimes13.0ms (0.3%)

regimes9.0ms (0.2%)

regimes6.0ms (0.1%)

regimes3.0ms (0.1%)

regimes5.0ms (0.1%)

soundness354.0ms (8.1%)

end0.0ms (0%)

preprocess70.0ms (1.6%)

Profiling