Details

analyze0.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 10 to 6 computations (40% saved)

sample835.0ms (37.8%)

Results

422.0ms	4585×	body	256	valid
402.0ms	3671×	body	256	infinite

Bogosity

preprocess170.0ms (7.7%)

Algorithm

2×	egg-herbie

Rules

2428×	`fma-def`
1090×	`sub-neg`
988×	`distribute-rgt-in`
972×	`distribute-lft-in`
832×	`distribute-lft-out`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	38
1	28	38
2	49	38
3	105	38
4	272	38
5	810	38
6	2075	38
7	3821	38
8	5458	38
9	6039	38
10	6152	38
11	6266	38
12	6346	38
13	6346	38
14	7727	38
0	2	2

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (.f64 b b) (.f64 a a))

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (.f64 b b) (.f64 a a))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify160.0ms (7.3%)

Algorithm

1×	egg-herbie

Rules

2086×	`fma-def`
1386×	`distribute-lft-out`
998×	`distribute-lft-out--`
986×	`unsub-neg`
954×	`sub-neg`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	18	19
2	30	19
3	59	19
4	134	19
5	384	19
6	843	19
7	1706	19
8	3850	19
9	5508	19
10	6382	19
11	6751	19
12	6981	19
13	7095	19
14	7095	19

Stop Event

1×	node limit

Counts

1 → 2

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 a a (*.f64 b (neg.f64 b)))

eval0.0ms (0%)

Compiler: Compiled 16 to 8 computations (50% saved)

prune1.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Accurracy

96.9%

Counts

3 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	96.9%	(fma.f64 a a (*.f64 b (neg.f64 b)))
▶	92.6%	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 18 to 10 computations (44.4% saved)

localize22.0ms (1%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	93.2%	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 18 to 6 computations (66.7% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a	@	0	(-.f64 (.f64 a a) (.f64 b b))
0.0ms	b	@	0	(-.f64 (.f64 a a) (.f64 b b))
0.0ms	a	@	inf	(-.f64 (.f64 a a) (.f64 b b))
0.0ms	b	@	inf	(-.f64 (.f64 a a) (.f64 b b))
0.0ms	b	@	-inf	(-.f64 (.f64 a a) (.f64 b b))

rewrite67.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

1680×	`pow1`
1560×	`add-exp-log`
1560×	`log1p-expm1-u`
1560×	`expm1-log1p-u`
1522×	`add-log-exp`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	160	19
2	2247	19

Stop Event

1×	node limit

Counts

1 → 46

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(+.f64 (.f64 a a) (.f64 b (neg.f64 b)))
(+.f64 (.f64 a a) (.f64 (*.f64 b (neg.f64 b)) 1))
(+.f64 (.f64 a a) (+.f64 (.f64 b (neg.f64 b)) (fma.f64 (neg.f64 b) b (*.f64 b b))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (.f64 b (neg.f64 b)) 1 (.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 b b))) (cbrt.f64 (pow.f64 b 4)) (.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 1))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(+.f64 (.f64 b (neg.f64 b)) (.f64 a a))
(+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (-.f64 (.f64 a a) (*.f64 b b)) 1)
(.f64 1 (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (*.f64 b b)) 2)))
(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2)))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(*.f64 (+.f64 a b) (-.f64 a b))
(*.f64 (-.f64 a b) (+.f64 a b))
(/.f64 1 (/.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))) (-.f64 (pow.f64 a 6) (pow.f64 b 6))))
(/.f64 1 (/.f64 (fma.f64 a a (*.f64 b b)) (-.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6))) (neg.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (neg.f64 (fma.f64 a a (*.f64 b b))))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 (.f64 b (neg.f64 b)) 3)) (+.f64 (pow.f64 a 4) (-.f64 (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b))) (.f64 (.f64 a a) (*.f64 b (neg.f64 b))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) (pow.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 3)) (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))))
(/.f64 (-.f64 (pow.f64 a 4) (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b)))) (-.f64 (.f64 a a) (*.f64 b (neg.f64 b))))
(/.f64 (-.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b)))) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 1)
(pow.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 3)
(pow.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 2)
(sqrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2))
(log.f64 (pow.f64 (exp.f64 (+.f64 a b)) (-.f64 a b)))
(cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3))
(expm1.f64 (log1p.f64 (-.f64 (.f64 a a) (.f64 b b))))
(exp.f64 (log.f64 (-.f64 (.f64 a a) (.f64 b b))))
(log1p.f64 (expm1.f64 (-.f64 (.f64 a a) (.f64 b b))))
(fma.f64 a a (*.f64 b (neg.f64 b)))
(fma.f64 1 (.f64 a a) (.f64 b (neg.f64 b)))
(fma.f64 1 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (cbrt.f64 (pow.f64 a 4)) (pow.f64 (cbrt.f64 a) 2) (*.f64 b (neg.f64 b)))
(fma.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (+.f64 a b) (-.f64 a b) (fma.f64 (neg.f64 b) b (*.f64 b b)))

simplify53.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

1818×	`fma-def`
742×	`distribute-lft-in`
734×	`distribute-rgt-in`
422×	`cancel-sign-sub-inv`
340×	`unswap-sqr`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	128	2078
1	346	1964
2	1526	1810

Stop Event

1×	node limit

Counts

70 → 69

Calls

Call 1

Inputs
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (.f64 a a) (.f64 b (neg.f64 b)))
(+.f64 (.f64 a a) (.f64 (*.f64 b (neg.f64 b)) 1))
(+.f64 (.f64 a a) (+.f64 (.f64 b (neg.f64 b)) (fma.f64 (neg.f64 b) b (*.f64 b b))))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (.f64 b (neg.f64 b)) 1 (.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 b b))) (cbrt.f64 (pow.f64 b 4)) (.f64 b b)))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 1))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(+.f64 (.f64 b (neg.f64 b)) (.f64 a a))
(+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (-.f64 (.f64 a a) (*.f64 b b)) 1)
(.f64 1 (-.f64 (.f64 a a) (*.f64 b b)))
(.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (*.f64 b b)) 2)))
(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2)))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(*.f64 (+.f64 a b) (-.f64 a b))
(*.f64 (-.f64 a b) (+.f64 a b))
(/.f64 1 (/.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))) (-.f64 (pow.f64 a 6) (pow.f64 b 6))))
(/.f64 1 (/.f64 (fma.f64 a a (*.f64 b b)) (-.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6))) (neg.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (neg.f64 (fma.f64 a a (*.f64 b b))))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 (.f64 b (neg.f64 b)) 3)) (+.f64 (pow.f64 a 4) (-.f64 (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b))) (.f64 (.f64 a a) (*.f64 b (neg.f64 b))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) (pow.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 3)) (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))))
(/.f64 (-.f64 (pow.f64 a 4) (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b)))) (-.f64 (.f64 a a) (*.f64 b (neg.f64 b))))
(/.f64 (-.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b)))) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 1)
(pow.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 3)
(pow.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) 1/3)
(pow.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 2)
(sqrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2))
(log.f64 (pow.f64 (exp.f64 (+.f64 a b)) (-.f64 a b)))
(cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3))
(expm1.f64 (log1p.f64 (-.f64 (.f64 a a) (.f64 b b))))
(exp.f64 (log.f64 (-.f64 (.f64 a a) (.f64 b b))))
(log1p.f64 (expm1.f64 (-.f64 (.f64 a a) (.f64 b b))))
(fma.f64 a a (*.f64 b (neg.f64 b)))
(fma.f64 1 (.f64 a a) (.f64 b (neg.f64 b)))
(fma.f64 1 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (cbrt.f64 (pow.f64 a 4)) (pow.f64 (cbrt.f64 a) 2) (*.f64 b (neg.f64 b)))
(fma.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (+.f64 a b) (-.f64 a b) (fma.f64 (neg.f64 b) b (*.f64 b b)))

Outputs
(*.f64 -1 (pow.f64 b 2))
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 -1 (pow.f64 b 2))
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 -1 (pow.f64 b 2))
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (.f64 b (neg.f64 b)))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (.f64 (*.f64 b (neg.f64 b)) 1))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 a a) (+.f64 (.f64 b (neg.f64 b)) (fma.f64 (neg.f64 b) b (*.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (.f64 b (neg.f64 b)) 1 (.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 (cbrt.f64 (.f64 b b))) (cbrt.f64 (pow.f64 b 4)) (.f64 b b)))
(fma.f64 (+.f64 b a) (-.f64 a b) (fma.f64 (neg.f64 (cbrt.f64 (.f64 b b))) (cbrt.f64 (pow.f64 b 4)) (.f64 b b)))
(fma.f64 (neg.f64 (cbrt.f64 (*.f64 b b))) (cbrt.f64 (pow.f64 b 4)) (fma.f64 a a 0))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 1))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 b (neg.f64 b)) (.f64 a a))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (-.f64 (.f64 a a) (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(.f64 (-.f64 (.f64 a a) (*.f64 b b)) 1)
(-.f64 (.f64 a a) (.f64 b b))
(.f64 1 (-.f64 (.f64 a a) (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (*.f64 b b)) 2)))
(.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (*.f64 b b)) 2)))
(.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (*.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2)))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (+.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 (*.f64 b a) 2) (+.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 b a) 2))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 b b (*.f64 a a)))
(*.f64 (+.f64 a b) (-.f64 a b))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (-.f64 a b) (+.f64 a b))
(-.f64 (.f64 a a) (.f64 b b))
(/.f64 1 (/.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))) (-.f64 (pow.f64 a 6) (pow.f64 b 6))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (+.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 (*.f64 b a) 2) (+.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 b a) 2))))
(/.f64 1 (/.f64 (fma.f64 a a (*.f64 b b)) (-.f64 (pow.f64 a 4) (pow.f64 b 4))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (+.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 (*.f64 b a) 2) (+.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 b b (*.f64 a a)))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6))) (neg.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (+.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 (*.f64 b a) 2) (+.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 b a) 2))))
(/.f64 (neg.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4))) (neg.f64 (fma.f64 a a (*.f64 b b))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 b b (*.f64 a a)))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 (.f64 b (neg.f64 b)) 3)) (+.f64 (pow.f64 a 4) (-.f64 (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b))) (.f64 (.f64 a a) (*.f64 b (neg.f64 b))))))
(.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (/.f64 1 (+.f64 (+.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (.f64 b a) 2))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 (*.f64 b a) 2) (+.f64 (pow.f64 a 4) (pow.f64 b 4))))
(/.f64 (-.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (pow.f64 (*.f64 b a) 2))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) (pow.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 3)) (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (-.f64 (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) (pow.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) 3)) (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (-.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (-.f64 (.f64 a a) (.f64 b b))))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) (pow.f64 (.f64 0 (.f64 b b)) 3)) (fma.f64 (.f64 0 (.f64 b b)) (+.f64 (-.f64 (.f64 0 (.f64 b b)) (.f64 a a)) (.f64 b b)) (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)))
(/.f64 (+.f64 0 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3)) (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2))
(/.f64 (-.f64 (pow.f64 a 4) (.f64 (.f64 b (neg.f64 b)) (.f64 b (neg.f64 b)))) (-.f64 (.f64 a a) (*.f64 b (neg.f64 b))))
(.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (/.f64 1 (fma.f64 a a (.f64 b b))))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 a a (*.f64 b b)))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b)))) (-.f64 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b))))
(/.f64 (-.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (fma.f64 (neg.f64 b) b (.f64 b b)) (fma.f64 (neg.f64 b) b (.f64 b b)))) (-.f64 (.f64 a a) (+.f64 (.f64 b b) (fma.f64 (neg.f64 b) b (.f64 b b)))))
(/.f64 (+.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 0 (.f64 b b)) (.f64 0 (.f64 b b)))) (-.f64 (.f64 a a) (fma.f64 b b (.f64 0 (.f64 b b)))))
(/.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2) (-.f64 (.f64 a a) (.f64 b b)))
(pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 1)
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 3)
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3) 1/3)
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) 2)
(-.f64 (.f64 a a) (.f64 b b))
(sqrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2))
(-.f64 (.f64 a a) (.f64 b b))
(log.f64 (pow.f64 (exp.f64 (+.f64 a b)) (-.f64 a b)))
(-.f64 (.f64 a a) (.f64 b b))
(cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 3))
(-.f64 (.f64 a a) (.f64 b b))
(expm1.f64 (log1p.f64 (-.f64 (.f64 a a) (.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(exp.f64 (log.f64 (-.f64 (.f64 a a) (.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(log1p.f64 (expm1.f64 (-.f64 (.f64 a a) (.f64 b b))))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 a a (*.f64 b (neg.f64 b)))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 1 (.f64 a a) (.f64 b (neg.f64 b)))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 1 (-.f64 (.f64 a a) (.f64 b b)) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(fma.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) (.f64 0 (.f64 b b)))
(fma.f64 (cbrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (cbrt.f64 (pow.f64 (-.f64 (.f64 a a) (.f64 b b)) 2)) 0)
(fma.f64 (cbrt.f64 (pow.f64 a 4)) (pow.f64 (cbrt.f64 a) 2) (*.f64 b (neg.f64 b)))
(fma.f64 (cbrt.f64 (pow.f64 a 4)) (pow.f64 (cbrt.f64 a) 2) (neg.f64 (*.f64 b b)))
(-.f64 (.f64 (cbrt.f64 (pow.f64 a 4)) (pow.f64 (cbrt.f64 a) 2)) (.f64 b b))
(fma.f64 (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (sqrt.f64 (-.f64 (.f64 a a) (.f64 b b))) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 (+.f64 a b) (-.f64 a b) (fma.f64 (neg.f64 b) b (*.f64 b b)))
(-.f64 (.f64 a a) (.f64 b b))

localize27.0ms (1.2%)

Local Accuracy

Found 1 expressions with local accuracy:

New	Accuracy	Program
✓	96.9%	(fma.f64 a a (*.f64 b (neg.f64 b)))

Compiler

Compiled 18 to 6 computations (66.7% saved)

series2.0ms (0.1%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	a	@	-inf	(fma.f64 a a (*.f64 b (neg.f64 b)))
0.0ms	a	@	0	(fma.f64 a a (*.f64 b (neg.f64 b)))
0.0ms	a	@	inf	(fma.f64 a a (*.f64 b (neg.f64 b)))
0.0ms	b	@	0	(fma.f64 a a (*.f64 b (neg.f64 b)))
0.0ms	b	@	inf	(fma.f64 a a (*.f64 b (neg.f64 b)))

rewrite55.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

1434×	`pow1`
1304×	`add-exp-log`
1302×	`log1p-expm1-u`
1302×	`expm1-log1p-u`
1270×	`add-log-exp`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	179	13
2	2176	13

Stop Event

1×	node limit

Counts

1 → 22

Calls

Call 1

Inputs
(fma.f64 a a (*.f64 b (neg.f64 b)))

Outputs
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 (.f64 a a) 1) (*.f64 b b))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (+.f64 1 (pow.f64 (hypot.f64 a b) 2)) 1)
(*.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(*.f64 1 (pow.f64 (hypot.f64 a b) 2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)))
(*.f64 (hypot.f64 a b) (hypot.f64 a b))
(/.f64 (+.f64 (pow.f64 (.f64 a a) 3) (pow.f64 (.f64 b b) 3)) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (-.f64 (.f64 b (pow.f64 b 3)) (.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (pow.f64 b 3))) (pow.f64 (hypot.f64 a b) 2))
(pow.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 3)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3) 1/3)
(pow.f64 (hypot.f64 a b) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 2))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 2)))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a b) 2)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 a b) 2)))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a b) 2)))

simplify56.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1900×	`times-frac`
1800×	`fma-def`
1232×	`log-prod`
880×	`associate-r`
776×	`associate-l`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	59	1008
1	166	868
2	726	768
3	5567	768

Stop Event

1×	node limit

Counts

46 → 36

Calls

Call 1

Inputs
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(pow.f64 a 2)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(*.f64 -1 (pow.f64 b 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 (.f64 a a) 1) (*.f64 b b))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (+.f64 1 (pow.f64 (hypot.f64 a b) 2)) 1)
(*.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(*.f64 1 (pow.f64 (hypot.f64 a b) 2))
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2))
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)))
(*.f64 (hypot.f64 a b) (hypot.f64 a b))
(/.f64 (+.f64 (pow.f64 (.f64 a a) 3) (pow.f64 (.f64 b b) 3)) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (-.f64 (.f64 b (pow.f64 b 3)) (.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (pow.f64 b 3))) (pow.f64 (hypot.f64 a b) 2))
(pow.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 3)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3) 1/3)
(pow.f64 (hypot.f64 a b) 2)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 2))
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 2)))
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3))
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a b) 2)))
(exp.f64 (log.f64 (pow.f64 (hypot.f64 a b) 2)))
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a b) 2)))

Outputs
(*.f64 -1 (pow.f64 b 2))
(neg.f64 (*.f64 b b))
(*.f64 b (neg.f64 b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(pow.f64 a 2)
(*.f64 a a)
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 -1 (pow.f64 b 2))
(neg.f64 (*.f64 b b))
(*.f64 b (neg.f64 b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 -1 (pow.f64 b 2))
(neg.f64 (*.f64 b b))
(*.f64 b (neg.f64 b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (*.f64 -1 (pow.f64 b 2)) (pow.f64 a 2))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 b b) (.f64 a a))
(fma.f64 b b (*.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(fma.f64 b b (*.f64 a a))
(+.f64 (.f64 (.f64 a a) 1) (*.f64 b b))
(fma.f64 b b (*.f64 a a))
(-.f64 (.f64 a a) (.f64 b b))
(-.f64 (+.f64 1 (pow.f64 (hypot.f64 a b) 2)) 1)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(*.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(*.f64 1 (pow.f64 (hypot.f64 a b) 2))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(*.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(*.f64 (pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 2) (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(*.f64 (hypot.f64 a b) (hypot.f64 a b))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(/.f64 (+.f64 (pow.f64 (.f64 a a) 3) (pow.f64 (.f64 b b) 3)) (+.f64 (.f64 (.f64 a a) (.f64 a a)) (-.f64 (.f64 b (pow.f64 b 3)) (.f64 (.f64 a a) (*.f64 b b)))))
(/.f64 (+.f64 (pow.f64 (.f64 a a) 3) (pow.f64 (.f64 b b) 3)) (fma.f64 (.f64 a a) (.f64 a a) (-.f64 (.f64 b (pow.f64 b 3)) (.f64 (.f64 b b) (.f64 a a)))))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 b 6)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (.f64 b (.f64 b (*.f64 a a))))))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 b 6)) (fma.f64 b (.f64 b (-.f64 (.f64 b b) (*.f64 a a))) (pow.f64 a 4)))
(/.f64 (+.f64 (pow.f64 a 6) (pow.f64 b 6)) (fma.f64 (.f64 b b) (fma.f64 a (neg.f64 a) (.f64 b b)) (pow.f64 a 4)))
(/.f64 (-.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 b (pow.f64 b 3))) (pow.f64 (hypot.f64 a b) 2))
(/.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (pow.f64 (hypot.f64 a b) 2))
(pow.f64 (pow.f64 (hypot.f64 a b) 2) 1)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(pow.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 2)) 3)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(pow.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3) 1/3)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(pow.f64 (hypot.f64 a b) 2)
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(sqrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 2))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(log.f64 (exp.f64 (pow.f64 (hypot.f64 a b) 2)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(cbrt.f64 (pow.f64 (pow.f64 (hypot.f64 a b) 2) 3))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(expm1.f64 (log1p.f64 (pow.f64 (hypot.f64 a b) 2)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(exp.f64 (log.f64 (pow.f64 (hypot.f64 a b) 2)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)
(log1p.f64 (expm1.f64 (pow.f64 (hypot.f64 a b) 2)))
(+.f64 1 (-.f64 (pow.f64 (hypot.f64 a b) 2) 1))
(+.f64 (pow.f64 (hypot.f64 a b) 2) 0)
(pow.f64 (hypot.f64 a b) 2)

eval23.0ms (1.1%)

Compiler: Compiled 1560 to 562 computations (64% saved)

prune13.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	104	3	107

Accurracy

100.0%

Counts

107 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	92.6%	(-.f64 (.f64 a a) (.f64 b b))
▶	53.6%	(*.f64 b (neg.f64 b))
▶	53.9%	(*.f64 a a)

Compiler

Compiled 20 to 12 computations (40% saved)

localize15.0ms (0.7%)

Compiler: Compiled 7 to 4 computations (42.9% saved)

localize25.0ms (1.1%)

Compiler: Compiled 10 to 5 computations (50% saved)

eval0.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Accurracy

100.0%

Counts

3 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	92.6%	(-.f64 (.f64 a a) (.f64 b b))
✓	53.6%	(*.f64 b (neg.f64 b))
✓	53.9%	(*.f64 a a)

Compiler

Compiled 20 to 12 computations (40% saved)

regimes24.0ms (1.1%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 a a)
(*.f64 b (neg.f64 b))
(-.f64 (.f64 a a) (.f64 b b))
(fma.f64 a a (*.f64 b (neg.f64 b)))

Outputs
(fma.f64 a a (*.f64 b (neg.f64 b)))

Calls

5 calls:

11.0ms	b
4.0ms	a
3.0ms	(-.f64 (.f64 a a) (.f64 b b))
3.0ms	(*.f64 a a)
3.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
96.9%	1	`a`
96.9%	1	`b`
96.9%	1	`(-.f64 (.f64 a a) (.f64 b b))`
96.9%	1	`(*.f64 a a)`
96.9%	1	`(*.f64 b b)`

Compiler

Compiled 48 to 23 computations (52.1% saved)

regimes37.0ms (1.7%)

Counts

3 → 2

Calls

Call 1

Inputs
(*.f64 a a)
(*.f64 b (neg.f64 b))
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 b (neg.f64 b))

Calls

5 calls:

10.0ms	a
10.0ms	b
5.0ms	(-.f64 (.f64 a a) (.f64 b b))
5.0ms	(*.f64 b b)
5.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
95.7%	3	`a`
96.9%	3	`b`
96.9%	2	`(-.f64 (.f64 a a) (.f64 b b))`
95.7%	2	`(*.f64 a a)`
96.9%	2	`(*.f64 b b)`

Compiler

Compiled 41 to 22 computations (46.3% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.5667720770613775e+305	4.617144940164367e+305

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes48.0ms (2.2%)

Accuracy

Total -48.2b remaining (-451%)

Threshold costs -48.2b (-451%)

Counts

2 → 5

Calls

Call 1

Inputs
(*.f64 a a)
(*.f64 b (neg.f64 b))

Outputs
(*.f64 b (neg.f64 b))
(*.f64 a a)
(*.f64 b (neg.f64 b))
(*.f64 a a)
(*.f64 b (neg.f64 b))

Calls

3 calls:

17.0ms	b
17.0ms	a
13.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
80.8%	5	`a`
83.3%	5	`b`
81.6%	6	`(*.f64 a a)`

Compiler

Compiled 20 to 12 computations (40% saved)

bsearch60.0ms (2.7%)

Algorithm

4×	binary-search

Stop Event

1×	narrow-enough
1×	narrow-enough
1×	narrow-enough
1×	narrow-enough

Steps

Time	Left	Right
19.0ms	1332591.4541642922	7210028158448.267
14.0ms	-5.336201669709312e-89	-5.615476354401502e-95
14.0ms	-2.413131317783845e-19	-2.2093846267911508e-26
14.0ms	-1.45818398782691e+84	-9.087655051752552e+79

Results

38.0ms	389×	body	256	valid
16.0ms	171×	body	256	infinite

Compiler

Compiled 469 to 324 computations (30.9% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

8×	`not-or`
6×	`sub-neg`
6×	`+-commutative`
6×	`not-not`
6×	`if-if-or-not`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	150
1	44	150
2	52	146
3	61	142
4	66	142
5	70	142
6	71	142
7	72	142

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(fma.f64 a a (*.f64 b (neg.f64 b)))
(if (<=.f64 (.f64 b b) 399999999999999975701421002214584874401611488804692998127630862852928182520529356113732370297620309937474244722246486903148687749705441221209431953634675310999492057667280441642708410126497636233748792101942063963065587302032873306381964490784317992213841396746502896256304175233838394482996173925525749760) (-.f64 (.f64 a a) (.f64 b b)) (.f64 b (neg.f64 b)))
(if (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (.f64 b (neg.f64 b)) (if (<=.f64 b -6911985578081563/2658455991569831745807614120560689152) (.f64 a a) (if (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208) (.f64 b (neg.f64 b)) (if (<=.f64 b 2500000000000) (.f64 a a) (*.f64 b (neg.f64 b))))))
(*.f64 a a)

Outputs
(fma.f64 a a (*.f64 b (neg.f64 b)))
(if (<=.f64 (.f64 b b) 399999999999999975701421002214584874401611488804692998127630862852928182520529356113732370297620309937474244722246486903148687749705441221209431953634675310999492057667280441642708410126497636233748792101942063963065587302032873306381964490784317992213841396746502896256304175233838394482996173925525749760) (-.f64 (.f64 a a) (.f64 b b)) (.f64 b (neg.f64 b)))
(if (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (.f64 b (neg.f64 b)) (if (<=.f64 b -6911985578081563/2658455991569831745807614120560689152) (.f64 a a) (if (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208) (.f64 b (neg.f64 b)) (if (<=.f64 b 2500000000000) (.f64 a a) (*.f64 b (neg.f64 b))))))
(if (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (.f64 b (neg.f64 b)) (if (<=.f64 b -6911985578081563/2658455991569831745807614120560689152) (.f64 a a) (if (or (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208) (not (<=.f64 b 2500000000000))) (.f64 b (neg.f64 b)) (.f64 a a))))
(if (or (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (not (or (<=.f64 b -6911985578081563/2658455991569831745807614120560689152) (not (or (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208) (not (<=.f64 b 2500000000000))))))) (.f64 b (neg.f64 b)) (.f64 a a))
(if (or (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (not (or (<=.f64 b -6911985578081563/2658455991569831745807614120560689152) (and (not (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208)) (<=.f64 b 2500000000000))))) (.f64 b (neg.f64 b)) (.f64 a a))
(if (or (<=.f64 b -3799999999999999658746226936107099740187701272956725709319955091447999262309220352) (and (not (<=.f64 b -6911985578081563/2658455991569831745807614120560689152)) (or (<=.f64 b -949651770683389/17917957937422433684459538244547554224973163977877196279199912807710334969441287563047019946172856926208) (not (<=.f64 b 2500000000000))))) (.f64 b (neg.f64 b)) (.f64 a a))
(*.f64 a a)

Compiler

Compiled 60 to 37 computations (38.3% saved)

soundness414.0ms (18.7%)

Rules

2086×	`fma-def`
1818×	`fma-def`
1818×	`fma-def`
1386×	`distribute-lft-out`
998×	`distribute-lft-out--`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	19
1	18	19
2	30	19
3	59	19
4	134	19
5	384	19
6	843	19
7	1706	19
8	3850	19
9	5508	19
10	6382	19
11	6751	19
12	6981	19
13	7095	19
14	7095	19
0	128	2078
1	346	1964
2	1526	1810
0	128	2078
1	346	1964
2	1526	1810

Stop Event

1×	node limit
1×	node limit
1×	node limit

Compiler

Compiled 51 to 27 computations (47.1% saved)

end88.0ms (4%)

Compiler: Compiled 144 to 70 computations (51.4% saved)

Difference of squares

Details

analyze0.0ms (0%)

sample835.0ms (37.8%)

preprocess170.0ms (7.7%)

simplify160.0ms (7.3%)

eval0.0ms (0%)

prune1.0ms (0%)

localize22.0ms (1%)

series2.0ms (0.1%)

rewrite67.0ms (3%)

simplify53.0ms (2.4%)

localize27.0ms (1.2%)

series2.0ms (0.1%)

rewrite55.0ms (2.5%)

simplify56.0ms (2.5%)

eval23.0ms (1.1%)

prune13.0ms (0.6%)

localize15.0ms (0.7%)

localize25.0ms (1.1%)

eval0.0ms (0%)

prune2.0ms (0.1%)

regimes24.0ms (1.1%)

regimes37.0ms (1.7%)

bsearch0.0ms (0%)

regimes48.0ms (2.2%)

bsearch60.0ms (2.7%)

simplify12.0ms (0.5%)

soundness414.0ms (18.7%)

end88.0ms (4%)

Profiling