Metrics for sqrtexp (problem 3.4.4)

analyze185.0ms (3.9%)

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
50%	50%	50%	0%	0%	0%	0%	3
50%	50%	50%	0%	0%	0%	0%	4
50%	50%	50%	0%	0%	0%	0%	5
53.1%	53.1%	46.9%	0%	0%	0%	0%	6
54.7%	54.7%	45.3%	0%	0%	0%	0%	7
55.5%	55.4%	44.5%	0%	0%	0%	0%	8
55.9%	55.8%	44.1%	0%	0%	0%	0%	9
56.1%	56%	43.9%	0%	0%	0%	0%	10
56.2%	56.1%	43.8%	0%	0%	0%	0%	11
56.2%	56.2%	43.8%	0%	0%	0%	0%	12

Compiler

Compiled 14 to 12 computations (14.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 95.0ms

Operation ival-mult, time spent: 31.0ms, 33.0% of total-time

Operation ival-exp, time spent: 21.0ms, 22.0% of total-time

Operation ival-sub, time spent: 20.0ms, 21.0% of total-time

Operation ival-sqrt, time spent: 13.0ms, 14.0% of total-time

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

Operation const, time spent: 4.0ms, 4.0% of total-time

sample3.1s (64.9%)

Results

1.3s	4207×	1	valid
440.0ms	3215×	0	valid
316.0ms	2649×	0	unsamplable
636.0ms	789×	2	valid
5.0ms	44×	0	infinite
0.0ms	1×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 1.8s

Operation ival-exp, time spent: 1.0s, 57.0% of total-time

Operation ival-sub, time spent: 249.0ms, 14.0% of total-time

Operation ival-mult, time spent: 151.0ms, 9.0% of total-time

Operation ival-sqrt, time spent: 123.0ms, 7.0% of total-time

Operation ival-div, time spent: 102.0ms, 6.0% of total-time

Operation backward-pass, time spent: 102.0ms, 6.0% of total-time

Operation const, time spent: 40.0ms, 2.0% of total-time

Bogosity

preprocess714.0ms (15%)

Algorithm

1×	egg-herbie

Rules

1436×	`times-frac`
1340×	`fma-neg`
772×	`associate-/l*`
694×	`unswap-sqr`
588×	`div-sub`

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
172	0	-	-	`(-.f64 (exp.f64 (*.f64 2 x)) 1)`
172	0	-	-	`(-.f64 (exp.f64 x) 1)`
0	0	-	-	`x`
0	0	-	-	`(exp.f64 x)`
0	0	-	-	`(*.f64 2 x)`
0	1	(-55.86413251773741)	-	`(exp.f64 (*.f64 2 x))`
0	0	-	-	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`
0	0	-	-	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
0	0	-	-	`2`
0	0	-	-	`1`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	24	144
1	56	136
2	88	136
3	172	136
4	387	96
5	1260	80
6	6179	80

Stop Event

1×	node limit

Calls

Call 1

Inputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (neg.f64 x))) 1) (-.f64 (exp.f64 (neg.f64 x)) 1)))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (neg.f64 x))) 1) (-.f64 (exp.f64 (neg.f64 x)) 1))))

Outputs
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (*.f64 1 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x)))
(sqrt.f64 (*.f64 1 (+.f64 1 (exp.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (neg.f64 x))) 1) (-.f64 (exp.f64 (neg.f64 x)) 1)))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 (neg.f64 x))) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (/.f64 (expm1.f64 (*.f64 x -2)) (expm1.f64 (neg.f64 x))))
(sqrt.f64 (+.f64 1 (exp.f64 (neg.f64 x))))
(hypot.f64 1 (pow.f64 (exp.f64 x) -1/2))
(neg.f64 (sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 (neg.f64 x))) 1) (-.f64 (exp.f64 (neg.f64 x)) 1))))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 2 (neg.f64 x))) (expm1.f64 (neg.f64 x)))))
(neg.f64 (sqrt.f64 (/.f64 (expm1.f64 (*.f64 x -2)) (expm1.f64 (neg.f64 x)))))
(neg.f64 (sqrt.f64 (+.f64 1 (exp.f64 (neg.f64 x)))))
(neg.f64 (hypot.f64 1 (pow.f64 (exp.f64 x) -1/2)))

Compiler

Compiled 107 to 79 computations (26.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 363.0ms

Operation ival-div, time spent: 132.0ms, 36.0% of total-time

Operation ival-exp, time spent: 99.0ms, 27.0% of total-time

Operation ival-sub, time spent: 79.0ms, 22.0% of total-time

Operation ival-mult, time spent: 38.0ms, 10.0% of total-time

Operation const, time spent: 7.0ms, 2.0% of total-time

Operation ival-sqrt, time spent: 7.0ms, 2.0% of total-time

eval1.0ms (0%)

Compiler: Compiled 21 to 16 computations (23.8% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 6 to 5 computations (16.7% saved)

localize35.0ms (0.7%)

Localize:

Found 1 expressions with local error:

New	Accuracy	Program
✓	100.0%	(+.f64 1 (exp.f64 x))

Compiler

Compiled 15 to 9 computations (40% saved)

Precisions

Click to see histograms. Total time spent on operations: 8.0ms

Operation ival-add, time spent: 3.0ms, 39.0% of total-time

Operation ival-exp, time spent: 2.0ms, 26.0% of total-time

Operation ival-sqrt, time spent: 2.0ms, 26.0% of total-time

Operation const, time spent: 1.0ms, 13.0% of total-time

series2.0ms (0%)

Counts

1 → 4

Calls

3 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(+.f64 1 (exp.f64 x))
1.0ms	x	@	inf	(+.f64 1 (exp.f64 x))
1.0ms	x	@	-inf	(+.f64 1 (exp.f64 x))

rewrite328.0ms (6.9%)

Algorithm

1×	batch-egg-rewrite

Rules

500×	`unpow-prod-down`
322×	`log1p-expm1-u`
322×	`expm1-log1p-u`
310×	`add-exp-log`
297×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	79	14
2	909	14

Stop Event

1×	node limit

Counts

1 → 62

Calls

Call 1

Inputs
(+.f64 1 (exp.f64 x))

Outputs
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (+.f64 1 (exp.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(*.f64 (pow.f64 1 1/3) (+.f64 1 (exp.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2) 1/3) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 5)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(/.f64 1 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (+.f64 1 (exp.f64 (.f64 x 3))))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (cbrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) 2)) (sqrt.f64 (pow.f64 (-.f64 1 (exp.f64 x)) 2)))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) 2)) (sqrt.f64 (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) 2)))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (-.f64 1 (exp.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (*.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (exp.f64 x)))
(pow.f64 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))) -1)
(pow.f64 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (exp.f64 x)))) (sqrt.f64 (log1p.f64 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (exp.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (exp.f64 x))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 2))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (exp.f64 x) 1 1)
(fma.f64 (cbrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

940×	`fma-define`
820×	`hypot-define`
776×	`unswap-sqr`
532×	`distribute-lft-in`
500×	`log-prod`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	2500
1	430	2248
2	1193	2104
3	4692	2104

Stop Event

1×	node limit

Counts

66 → 102

Calls

Call 1

Inputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2))))
(+.f64 2 (+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 2)))))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(*.f64 (+.f64 1 (exp.f64 x)) (log.f64 (E.f64)))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(*.f64 (pow.f64 1 1/3) (+.f64 1 (exp.f64 x)))
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2) 1/3) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 5)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(/.f64 1 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (+.f64 1 (exp.f64 (.f64 x 3))))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (cbrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) 2)) (sqrt.f64 (pow.f64 (-.f64 1 (exp.f64 x)) 2)))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) 2)) (sqrt.f64 (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) 2)))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (-.f64 1 (exp.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (*.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(pow.f64 (E.f64) (log1p.f64 (exp.f64 x)))
(pow.f64 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))) -1)
(pow.f64 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))) -1)
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (exp.f64 x)))) (sqrt.f64 (log1p.f64 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(exp.f64 (log1p.f64 (exp.f64 x)))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (exp.f64 x))) 3))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (exp.f64 x))) 1/3))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 2))
(fma.f64 1 (exp.f64 x) 1)
(fma.f64 (exp.f64 x) 1 1)
(fma.f64 (cbrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1)
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)

Outputs
2
(+.f64 2 x)
(+.f64 2 (+.f64 x (*.f64 1/2 (pow.f64 x 2))))
(+.f64 2 (fma.f64 1/2 (pow.f64 x 2) x))
(+.f64 2 (+.f64 x (+.f64 (.f64 1/6 (pow.f64 x 3)) (.f64 1/2 (pow.f64 x 2)))))
(+.f64 2 (+.f64 x (fma.f64 1/6 (pow.f64 x 3) (*.f64 1/2 (pow.f64 x 2)))))
(+.f64 2 (+.f64 (fma.f64 1/2 (pow.f64 x 2) x) (*.f64 1/6 (pow.f64 x 3))))
(+.f64 2 (fma.f64 1/2 (pow.f64 x 2) (fma.f64 1/6 (pow.f64 x 3) x)))
(-.f64 (+.f64 1 (+.f64 1 (exp.f64 x))) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(-.f64 (/.f64 1 (-.f64 1 (exp.f64 x))) (/.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(*.f64 1 (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (+.f64 1 (exp.f64 x)) (log.f64 (E.f64)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 2) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) (hypot.f64 1 (sqrt.f64 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (/.f64 1 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(*.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 1/4) (pow.f64 (+.f64 2 (expm1.f64 x)) 3/4))
(*.f64 (pow.f64 1 1/3) (+.f64 1 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(.f64 (pow.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2) 1/3) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x)))))
(*.f64 (pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2) 1/3) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 5/2)) (pow.f64 (+.f64 2 (expm1.f64 x)) 1/6))
(.f64 (cbrt.f64 (pow.f64 (.f64 (+.f64 1 (exp.f64 x)) (cbrt.f64 (+.f64 1 (exp.f64 x)))) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4) 2)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (+.f64 1 (exp.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 8)) (cbrt.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x)))))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 5/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (cbrt.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 5/2)) (pow.f64 (+.f64 2 (expm1.f64 x)) 1/6))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/4))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3/2)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/4) (pow.f64 (+.f64 1 (exp.f64 x)) 3/4))
(*.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 1/4) (pow.f64 (+.f64 2 (expm1.f64 x)) 3/4))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 4)) (cbrt.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(*.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 5)) (pow.f64 (+.f64 1 (exp.f64 x)) 1/6))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (sqrt.f64 (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 5)))
(*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 1/6) (pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 5/2))
(*.f64 (pow.f64 (+.f64 2 (expm1.f64 x)) 1/6) (pow.f64 (cbrt.f64 (+.f64 2 (expm1.f64 x))) 5/2))
(/.f64 1 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 1 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) (+.f64 (pow.f64 (exp.f64 x) 2) (-.f64 1 (exp.f64 x))))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (neg.f64 (+.f64 1 (exp.f64 (*.f64 x 3)))) (neg.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (neg.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2))) (neg.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (cbrt.f64 (.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (+.f64 1 (exp.f64 (.f64 x 3))))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (pow.f64 (+.f64 2 (expm1.f64 x)) 2))) (cbrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (cbrt.f64 (*.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (cbrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (cbrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (cbrt.f64 (*.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (cbrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (cbrt.f64 (.f64 (neg.f64 (expm1.f64 (.f64 2 x))) (pow.f64 (+.f64 1 (exp.f64 x)) 2))) (cbrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (cbrt.f64 (.f64 (neg.f64 (expm1.f64 (.f64 2 x))) (pow.f64 (+.f64 2 (expm1.f64 x)) 2))) (cbrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (pow.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) 2)) (sqrt.f64 (pow.f64 (-.f64 1 (exp.f64 x)) 2)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(/.f64 (sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 (*.f64 x 3))) 2)) (sqrt.f64 (pow.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) 2)))
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (*.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (-.f64 1 (exp.f64 x)))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (*.f64 (neg.f64 (expm1.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (*.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (.f64 (-.f64 1 (exp.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (*.f64 (neg.f64 (expm1.f64 x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (exp.f64 (.f64 x 3))))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (pow.f64 (exp.f64 x) 3)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (pow.f64 (exp.f64 3) x)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 2 (expm1.f64 x)) (+.f64 1 (pow.f64 (exp.f64 x) 3)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 x)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 2 (expm1.f64 x)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 (.f64 x 3))) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (pow.f64 (exp.f64 x) 3)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (+.f64 1 (pow.f64 (exp.f64 3) x)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (+.f64 2 (expm1.f64 x)) (+.f64 1 (pow.f64 (exp.f64 x) 3)))) (sqrt.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (sqrt.f64 (*.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (+.f64 1 (exp.f64 x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (*.f64 (+.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 2) x)))) (sqrt.f64 (-.f64 1 (exp.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 1 (exp.f64 x)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(/.f64 (sqrt.f64 (.f64 (+.f64 2 (expm1.f64 x)) (neg.f64 (expm1.f64 (.f64 2 x))))) (sqrt.f64 (neg.f64 (expm1.f64 x))))
(pow.f64 (+.f64 1 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (cbrt.f64 (+.f64 1 (exp.f64 x))) 3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2) 1/2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3) 1/3)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (hypot.f64 1 (sqrt.f64 (exp.f64 x))) 2)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (E.f64) (log1p.f64 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(pow.f64 (/.f64 (fma.f64 (exp.f64 x) (expm1.f64 x) 1) (+.f64 1 (exp.f64 (*.f64 x 3)))) -1)
(*.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (/.f64 1 (fma.f64 (exp.f64 x) (expm1.f64 x) 1)))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 3) x)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(/.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)) (fma.f64 (exp.f64 x) (expm1.f64 x) 1))
(pow.f64 (/.f64 (-.f64 1 (exp.f64 x)) (-.f64 1 (pow.f64 (exp.f64 x) 2))) -1)
(/.f64 (-.f64 1 (pow.f64 (exp.f64 x) 2)) (-.f64 1 (exp.f64 x)))
(/.f64 (-.f64 1 (pow.f64 (exp.f64 2) x)) (-.f64 1 (exp.f64 x)))
(/.f64 (expm1.f64 (*.f64 2 x)) (expm1.f64 x))
(pow.f64 (exp.f64 (pow.f64 (cbrt.f64 (log1p.f64 (exp.f64 x))) 2)) (cbrt.f64 (log1p.f64 (exp.f64 x))))
(pow.f64 (exp.f64 (sqrt.f64 (log1p.f64 (exp.f64 x)))) (sqrt.f64 (log1p.f64 (exp.f64 x))))
(sqrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(log.f64 (exp.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(cbrt.f64 (pow.f64 (+.f64 1 (exp.f64 x)) 3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(log1p.f64 (expm1.f64 (+.f64 1 (exp.f64 x))))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(exp.f64 (log1p.f64 (exp.f64 x)))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(exp.f64 (.f64 (.f64 1/3 (log1p.f64 (exp.f64 x))) 3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(exp.f64 (.f64 (.f64 3 (log1p.f64 (exp.f64 x))) 1/3))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(exp.f64 (.f64 (.f64 1/2 (log1p.f64 (exp.f64 x))) 2))
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(fma.f64 1 (exp.f64 x) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(fma.f64 (exp.f64 x) 1 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(fma.f64 (cbrt.f64 (exp.f64 x)) (pow.f64 (cbrt.f64 (exp.f64 x)) 2) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(fma.f64 (pow.f64 (cbrt.f64 (exp.f64 x)) 2) (cbrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))
(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) 1)
(+.f64 (+.f64 2 (exp.f64 x)) -1)
(+.f64 2 (expm1.f64 x))
(+.f64 1 (exp.f64 x))

eval34.0ms (0.7%)

Compiler: Compiled 1464 to 1013 computations (30.8% saved)

prune90.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	100	3	103

Accuracy

100.0%

Counts

103 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	66.9%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
▶	73.4%	(sqrt.f64 2)

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize30.0ms (0.6%)

Compiler: Compiled 14 to 11 computations (21.4% saved)
Precisions: Click to see histograms. Total time spent on operations: 9.0ms
Operation ival-add, time spent: 4.0ms, 44.0% of total-time
Operation ival-sqrt, time spent: 4.0ms, 44.0% of total-time
Operation const, time spent: 1.0ms, 11.0% of total-time

eval0.0ms (0%)

Compiler: Compiled 1 to 1 computations (0% saved)

prune2.0ms (0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	0	0
Picked	2	2
Done	1	1
Total	3	3

Accuracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	66.9%	(sqrt.f64 (+.f64 2 x))
✓	100.0%	(sqrt.f64 (+.f64 1 (exp.f64 x)))
✓	73.4%	(sqrt.f64 2)

Compiler

Compiled 38 to 31 computations (18.4% saved)

regimes12.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))

Calls

3 calls:

7.0ms	x
2.0ms	(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))
2.0ms	(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))

Results

Accuracy	Segments	Branch
100.0%	1	`x`
100.0%	1	`(sqrt.f64 (/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1)))`
100.0%	1	`(/.f64 (-.f64 (exp.f64 (*.f64 2 x)) 1) (-.f64 (exp.f64 x) 1))`

Compiler

Compiled 27 to 22 computations (18.5% saved)

regimes3.0ms (0.1%)

Accuracy

Total -4.4b remaining (-25.6%)

Threshold costs -4.4b (-25.6%)

Counts

2 → 1

Calls

Call 1

Inputs
(sqrt.f64 2)
(sqrt.f64 (+.f64 2 x))

Outputs
(sqrt.f64 2)

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
73.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`1-exp`
2×	`+-commutative`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	18	23

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

Outputs
(sqrt.f64 (+.f64 1 (exp.f64 x)))
(sqrt.f64 2)

Compiler

Compiled 9 to 8 computations (11.1% saved)

soundness107.0ms (2.3%)

Rules

1436×	`times-frac`
1340×	`fma-neg`
772×	`associate-/l*`
694×	`unswap-sqr`
588×	`div-sub`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	24	144
1	56	136
2	88	136
3	172	136
4	387	96
5	1260	80
6	6179	80

Stop Event

1×	node limit

Compiler

Compiled 85 to 56 computations (34.1% saved)

end0.0ms (0%)

preprocess41.0ms (0.9%)

Compiler: Compiled 42 to 36 computations (14.3% saved)

analyze185.0ms (3.9%)

sample3.1s (64.9%)

preprocess714.0ms (15%)

eval1.0ms (0%)

prune1.0ms (0%)

localize35.0ms (0.7%)

series2.0ms (0%)

rewrite328.0ms (6.9%)

simplify83.0ms (1.7%)

eval34.0ms (0.7%)

prune90.0ms (1.9%)

localize30.0ms (0.6%)

eval0.0ms (0%)

prune2.0ms (0%)

regimes12.0ms (0.3%)

regimes3.0ms (0.1%)

simplify3.0ms (0.1%)

soundness107.0ms (2.3%)

end0.0ms (0%)

preprocess41.0ms (0.9%)

Profiling