Details

analyze360.0ms (7.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 43 to 31 computations (27.9% saved)

sample1.4s (28.5%)

Results

1.2s	7956×	body	128	valid
148.0ms	1023×	body	128	invalid
82.0ms	300×	body	256	valid

Compiler

Compiled 86 to 62 computations (27.9% saved)

preprocess45.0ms (0.9%)

Algorithm

2×	egg-herbie

Rules

795×	`fma-def_binary64`
731×	`div-sub_binary64`
295×	`fma-neg_binary64`
212×	`associate-/l*_binary64`
209×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	104
1	92	88
2	213	88
3	440	88
4	758	88
5	1251	88
6	2221	88
7	4457	88
0	3	3

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 20 to 14 computations (30% saved)

simplify31.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1220×	`fma-neg_binary64`
367×	`fma-def_binary64`
351×	`times-frac_binary64`
266×	`associate-/l*_binary64`
254×	`div-sub_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	69	22
3	160	22
4	264	22
5	433	22
6	744	22
7	1341	22
8	2769	22
9	4702	22

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.1%)

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

Error

28.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
	28.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))

Compiler

Compiled 111 to 75 computations (32.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 a (.f64 c -3))
✓	0.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))
✓	0.4b	(/.f64 1/3 a)
✓	28.3b	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)

series96.0ms (1.9%)

Counts

4 → 64

Calls

27 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))	a	-inf
9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))	a	inf
9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))	c	inf
7.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (/.f64 1/3 a))	c	-inf
7.0ms	(-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b)	b	inf

rewrite69.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

737×	`prod-diff_binary64`
143×	`egg-rr`
140×	`add-sqr-sqrt_binary64`
133×	`log1p-expm1-u_binary64`
133×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	49
1	282	47
2	3646	47

Stop Event

1×	node limit

Counts

4 → 143

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

744×	`times-frac_binary64`
459×	`associate-/l*_binary64`
392×	`associate-/r*_binary64`
316×	`fma-def_binary64`
174×	`associate-*l/_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	118	1538
1	369	1520
2	1302	1491

Stop Event

1×	node limit

Counts

207 → 192

prune137.0ms (2.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	176	16	192
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	177	17	194

Error

0.8b

Counts

194 → 17

Alt Table

Status	Error	Program
	40.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (log.f64 (exp.f64 (/.f64 1/3 a))))
▶	4.6b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	4.8b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	4.9b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	29.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	6.7b	(.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) -9/8 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) -27/16))) (/.f64 1/3 a))
	30.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	28.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	10.5b	(fma.f64 -1/2 (/.f64 c b) (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a) -3/8))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))

Compiler

Compiled 5621 to 3619 computations (35.6% saved)

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 c c) (pow.f64 b 3))
✓	0.3b	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))
✓	0.4b	(/.f64 (pow.f64 c 4) (pow.f64 b 7))
✓	0.4b	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))

series227.0ms (4.5%)

Counts

4 → 96

Calls

30 calls:

14.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))	a	inf
13.0ms	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))	a	-inf
13.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))	c	0
12.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3))	a	-inf
12.0ms	(/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a))	c	-inf

rewrite38.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

205×	`add-sqr-sqrt_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`
197×	`add-cbrt-cube_binary64`
194×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	49
1	449	49

Stop Event

1×	node limit

Counts

4 → 107

simplify50.0ms (1%)

Algorithm

1×	egg-herbie

Rules

854×	`associate-/l*_binary64`
424×	`associate-l_binary64`
421×	`associate-/r*_binary64`
375×	`associate-r_binary64`
202×	`associate-/r/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	1284
1	59	1284
2	177	1284
3	811	1284
4	4913	1284

Stop Event

1×	node limit

Counts

203 → 111

prune215.0ms (4.3%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	16	16
Picked	0	1	1
Done	0	0	0
Total	110	18	128

Error

0.7b

Counts

128 → 18

Alt Table

Status	Error	Program
	40.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (log.f64 (exp.f64 (/.f64 1/3 a))))
✓	4.6b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
▶	4.8b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	4.9b	(.f64 (neg.f64 (+.f64 (.f64 3/2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 9/8 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 27/16 (/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (/.f64 1/3 a))
	29.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))
	6.7b	(.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) -9/8 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) -27/16))) (/.f64 1/3 a))
	30.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	28.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	24.2b	(-.f64 (.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 c 3)) (/.f64 a (pow.f64 b 5)))) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	10.5b	(fma.f64 -1/2 (/.f64 c b) (.f64 (.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a) -3/8))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))

Compiler

Compiled 6333 to 4252 computations (32.9% saved)

localize31.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (pow.f64 c 4) (pow.f64 b 7))
✓	0.4b	(.f64 (/.f64 -3/2 b) (.f64 c a))
	0.4b	(/.f64 1/3 a)
✓	0.4b	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))

series103.0ms (2%)

Counts

2 → 72

Calls

18 calls:

14.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))	c	inf
11.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))	c	0
11.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))	c	-inf
11.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))	a	0
11.0ms	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))	a	inf

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

279×	`expm1-udef_binary64`
279×	`log1p-udef_binary64`
158×	`add-sqr-sqrt_binary64`
154×	`log1p-expm1-u_binary64`
154×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	332	23
2	4123	23

Stop Event

1×	node limit

Counts

2 → 50

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

1164×	`associate-/l/_binary64`
445×	`unswap-sqr_binary64`
339×	`times-frac_binary64`
271×	`*-commutative_binary64`
251×	`associate-/l*_binary64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	15	936
1	34	936
2	92	936
3	311	936
4	2056	936
5	3019	828
6	3087	828
7	3225	828
8	3387	828
9	3539	828

Stop Event

1×	node limit

Counts

122 → 53

prune205.0ms (4.1%)

Pruning

21 alts after pruning (20 fresh and 1 done)

	Pruned	Kept	Total
New	94	7	101
Fresh	3	13	16
Picked	1	0	1
Done	0	1	1
Total	98	21	119

Error

0.7b

Counts

119 → 21

Alt Table

Status	Error	Program
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))
	22.4b	(.f64 (-.f64 (log.f64 (exp.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c))) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	40.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (log.f64 (exp.f64 (/.f64 1/3 a))))
✓	4.6b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
▶	4.8b	(.f64 (-.f64 (/.f64 (.f64 c a) (.f64 b -2/3)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	4.8b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (pow.f64 (*.f64 a 3) -1))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	24.8b	(.f64 (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c))) 1) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	4.9b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (cbrt.f64 (pow.f64 (/.f64 1/3 a) 3)))
	4.8b	(.f64 (-.f64 (.f64 c (.f64 -3/2 (/.f64 a b))) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	30.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	28.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	24.2b	(-.f64 (.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 c 3)) (/.f64 a (pow.f64 b 5)))) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	5.1b	(.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c) 3)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	29.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))

Compiler

Compiled 6992 to 4788 computations (31.5% saved)

localize33.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.4b	(/.f64 (pow.f64 c 4) (pow.f64 b 7))
	0.4b	(/.f64 1/3 a)
✓	0.4b	(/.f64 (.f64 c a) (.f64 b -2/3))
	0.4b	(*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4))

series13.0ms (0.3%)

Counts

1 → 36

Calls

9 calls:

2.0ms	(/.f64 (.f64 c a) (.f64 b -2/3))	c	0
2.0ms	(/.f64 (.f64 c a) (.f64 b -2/3))	c	inf
2.0ms	(/.f64 (.f64 c a) (.f64 b -2/3))	c	-inf
2.0ms	(/.f64 (.f64 c a) (.f64 b -2/3))	a	-inf
2.0ms	(/.f64 (.f64 c a) (.f64 b -2/3))	a	inf

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
230×	`pow2_binary64`
163×	`pow-unpow_binary64`
163×	`pow1/3_binary64`
158×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	171	10
2	2437	10

Stop Event

1×	node limit

Counts

1 → 60

simplify19.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

15×	`associate-/l*_binary64`
14×	`*-commutative_binary64`
11×	`associate-/r/_binary64`
10×	`associate-r_binary64`
8×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	360
1	14	360
2	29	360
3	55	360
4	85	360
5	96	360

Stop Event

1×

saturated

Counts

96 → 62

prune234.0ms (4.7%)

Pruning

22 alts after pruning (20 fresh and 2 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	1	18	19
Picked	0	1	1
Done	0	1	1
Total	135	22	157

Error

0.7b

Counts

157 → 22

Alt Table

Status	Error	Program
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (exp.f64 (log.f64 (/.f64 1/3 a))))
	22.4b	(.f64 (-.f64 (log.f64 (exp.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c))) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	40.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (log.f64 (exp.f64 (/.f64 1/3 a))))
✓	4.6b	(-.f64 (.f64 (.f64 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) a)) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (cbrt.f64 (/.f64 1/3 a)) 3))
	5.6b	(.f64 (-.f64 (.f64 (cbrt.f64 (.f64 a (.f64 c (/.f64 -3/2 b)))) (pow.f64 (cbrt.f64 (.f64 a (.f64 c (/.f64 -3/2 b)))) 2)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (*.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 (cbrt.f64 (/.f64 1/3 a)) (cbrt.f64 (/.f64 1/9 (*.f64 a a)))))
✓	4.8b	(.f64 (-.f64 (/.f64 (.f64 c a) (.f64 b -2/3)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) b) (.f64 1/3 (pow.f64 a -1)))
	4.8b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (pow.f64 (*.f64 a 3) -1))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (-.f64 (exp.f64 (log1p.f64 (/.f64 1/3 a))) 1))
	24.8b	(.f64 (-.f64 (-.f64 (exp.f64 (log1p.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c))) 1) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	29.6b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 -1 b b)) (/.f64 1/3 a))
	4.9b	(.f64 (-.f64 (.f64 (/.f64 -3/2 b) (.f64 c a)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (cbrt.f64 (pow.f64 (/.f64 1/3 a) 3)))
	30.3b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (cbrt.f64 b)) (pow.f64 (cbrt.f64 b) 2) b)) (/.f64 1/3 a))
	28.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	24.2b	(-.f64 (.f64 (.f64 (log.f64 (pow.f64 (exp.f64 (pow.f64 c 3)) (/.f64 a (pow.f64 b 5)))) a) -9/16) (fma.f64 1/2 (/.f64 c b) (fma.f64 135/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 3)) (.f64 3/8 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a)))))
	5.6b	(.f64 (-.f64 (.f64 (/.f64 (pow.f64 (cbrt.f64 (.f64 c a)) 2) 1) (/.f64 (cbrt.f64 (.f64 c a)) (.f64 b -2/3))) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	5.1b	(.f64 (-.f64 (cbrt.f64 (pow.f64 (.f64 (.f64 (/.f64 -3/2 b) a) c) 3)) (fma.f64 9/8 (.f64 (.f64 (/.f64 (.f64 c c) (pow.f64 b 3)) a) a) (fma.f64 27/16 (/.f64 (pow.f64 c 3) (/.f64 (pow.f64 b 5) (pow.f64 a 3))) (.f64 405/128 (.f64 (/.f64 (pow.f64 c 4) (pow.f64 b 7)) (pow.f64 a 4)))))) (/.f64 1/3 a))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (sqrt.f64 (/.f64 1/3 a)) 2))
	28.4b	(.f64 (-.f64 (sqrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3)))) b) (pow.f64 (pow.f64 (/.f64 1/3 a) 3) 1/3))
	29.5b	(.f64 (+.f64 (fma.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (fma.f64 b b (.f64 a (.f64 c -3)))) 2)) (sqrt.f64 (cbrt.f64 (fma.f64 b b (.f64 a (*.f64 c -3))))) (neg.f64 b)) (fma.f64 (neg.f64 (sqrt.f64 b)) (sqrt.f64 b) b)) (/.f64 1/3 a))

Compiler

Compiled 8326 to 5661 computations (32% saved)

regimes837.0ms (16.7%)

Accuracy

Total 4.7b remaining (85.3%)

Threshold costs 0b (0%)

Counts

95 → 2

Compiler

Compiled 21966 to 15856 computations (27.8% saved)

bsearch6.0ms (0.1%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 3 a) c)))) (*.f64 3 a))

Steps

Iters	Point		Range
-0.25532699160432076	∈ [	-0.25532699160432076	,	-0.24397713399526116	]

Compiler

Compiled 20 to 14 computations (30% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`*-commutative_binary64`
10×	`+-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	121
1	79	119
2	102	119
3	113	119
4	120	119
5	122	119

Stop Event

1×

saturated

end556.0ms (11.1%)

Stop Event

1×

fuel

Compiler

Compiled 1039 to 740 computations (28.8% saved)

Details

analyze360.0ms (7.2%)

sample1.4s (28.5%)

preprocess45.0ms (0.9%)

simplify31.0ms (0.6%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

series96.0ms (1.9%)

rewrite69.0ms (1.4%)

simplify39.0ms (0.8%)

prune137.0ms (2.7%)

localize33.0ms (0.7%)

series227.0ms (4.5%)

rewrite38.0ms (0.8%)

simplify50.0ms (1%)

prune215.0ms (4.3%)

localize31.0ms (0.6%)

series103.0ms (2%)

rewrite53.0ms (1.1%)

simplify84.0ms (1.7%)

prune205.0ms (4.1%)

localize33.0ms (0.7%)

series13.0ms (0.3%)

rewrite44.0ms (0.9%)

simplify19.0ms (0.4%)

prune234.0ms (4.7%)

regimes837.0ms (16.7%)

bsearch6.0ms (0.1%)

simplify5.0ms (0.1%)

end556.0ms (11.1%)

Profiling