Details

analyze1.2s (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
3%	46.9%	50%	13
3.1%	46.8%	50%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample3.8s (33.3%)

Results

2.3s	4058×	body	2048	valid
875.0ms	2056×	body	1024	valid
335.0ms	1031×	body	512	valid
134.0ms	538×	body	256	valid
73.0ms	572×	body	128	valid
1.0ms	1×	body	4096	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify73.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

686×	`div-sub_binary64`
546×	`sub-neg_binary64`
397×	`neg-mul-1_binary64`
344×	`neg-sub0_binary64`
311×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	31	19
2	72	17
3	203	17
4	532	17
5	1340	17
6	2710	17
7	3748	17
8	4643	17
9	4981	17

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.6b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 v (*.f64 v -5) 1)
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series7.0ms (0.1%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
2.0ms	(fma.f64 v (*.f64 v -5) 1)
2.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 49

Calls

3 calls:

2.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
0.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
0.0ms	(fma.f64 v (*.f64 v -5) 1)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

670×	`fma-def_binary64`
523×	`associate-/l*_binary64`
370×	`fma-neg_binary64`
263×	`associate-/l/_binary64`
248×	`distribute-rgt-in_binary64`

Counts

85 → 77

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	110	1613
1	221	1461
2	571	1457
3	1601	1455
4	4588	1455
5	5008	1455

prune71.0ms (0.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	73	4	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	4	78

Error

0.5b

Counts

78 → 4

Alt Table

Status	Error	Program
▶	0.6b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.8b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	2.1b	(.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 1615 to 1164 computations (27.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series496.0ms (4.3%)

Counts

2 → 24

Calls

2 calls:

494.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
2.0ms	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

rewrite4.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-prod_binary64`

Counts

2 → 31

Calls

2 calls:

2.0ms	(exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))
1.0ms	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

simplify186.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

620×	`unswap-sqr_binary64`
480×	`fma-neg_binary64`
451×	`fma-def_binary64`
352×	`associate-/l*_binary64`
293×	`associate-/r*_binary64`

Counts

55 → 43

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	1240
1	53	1120
2	73	1120
3	100	1112
4	157	1112
5	256	1112
6	481	1112
7	1150	1112
8	2469	1112
9	4309	1112
10	4996	1112
11	4779	1112

prune117.0ms (1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Error

0.5b

Counts

107 → 6

Alt Table

Status	Error	Program
	2.5b	(exp.f64 (+.f64 (log.f64 (.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (log.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))
	0.8b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	2.1b	(.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	0.6b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	3.2b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 2687 to 1994 computations (25.8% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
✓	0.0b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series1.9s (16.5%)

Counts

2 → 24

Calls

2 calls:

1.5s

(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

429.0ms

(exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`exp-prod_binary64`
12×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 47

Calls

2 calls:

3.0ms

(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

2.0ms

(exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

simplify218.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

430×	`exp-prod_binary64`
327×	`associate-l_binary64`
313×	`sqr-pow_binary64`
313×	`fma-def_binary64`
304×	`*-commutative_binary64`

Counts

71 → 56

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	68	2355
1	107	2262
2	236	2262
3	507	2262
4	1531	2262
5	3499	2262
6	4526	2262
7	4918	2262
8	4967	2262
9	4760	2262

prune157.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	114	2	116
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

0.5b

Counts

122 → 6

Alt Table

Status	Error	Program
	2.1b	(.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
▶	0.6b	(pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	0.8b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	3.2b	(pow.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	3.2b	(pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 5166 to 3845 computations (25.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	0.0b	(pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
✓	0.0b	(pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	0.5b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series2.2s (19.4%)

Counts

2 → 24

Calls

2 calls:

1.6s

(pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

624.0ms

(pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow-unpow_binary64`
13×	`unpow-prod-down_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

3.0ms

(pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

2.0ms

(pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))

simplify151.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-l_binary64`
444×	`exp-prod_binary64`
385×	`associate-r_binary64`
343×	`log-prod_binary64`
331×	`prod-exp_binary64`

Counts

78 → 75

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	81	2852
1	136	2705
2	298	2705
3	645	2705
4	2095	2705
5	3895	2705
6	4274	2705
7	5062	2705

prune173.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	135	6	141

Error

0.5b

Counts

141 → 6

Alt Table

Status	Error	Program
	0.6b	(expm1.f64 (log1p.f64 (pow.f64 (pow.f64 (E.f64) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))))
	0.8b	(acos.f64 (fma.f64 4 (+.f64 (pow.f64 v 4) (fma.f64 v v (pow.f64 v 6))) -1))
	3.2b	(pow.f64 (.f64 (.f64 (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (cbrt.f64 (exp.f64 (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))
	2.1b	(.f64 (.f64 (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (cbrt.f64 (exp.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))))
	3.4b	(pow.f64 (.f64 (pow.f64 (.f64 (cbrt.f64 (E.f64)) (cbrt.f64 (E.f64))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (pow.f64 (cbrt.f64 (E.f64)) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))))) (sqrt.f64 (log.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))))
	1.5b	(.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 6000 to 4364 computations (27.3% saved)

regimes327.0ms (2.8%)

Accuracy

Total 0.0b remaining (3.2%)

Threshold costs 0.0b (3.2%)

Counts

89 → 1

Compiler

Compiled 8581 to 6414 computations (25.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`e-exp-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	48
1	19	48
2	18	48

end203.0ms (1.8%)

Compiler: Compiled 309 to 229 computations (25.9% saved)

Details

analyze1.2s (10.6%)

sample3.8s (33.3%)

simplify73.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series7.0ms (0.1%)

rewrite5.0ms (0%)

simplify74.0ms (0.6%)

prune71.0ms (0.6%)

localize10.0ms (0.1%)

series496.0ms (4.3%)

rewrite4.0ms (0%)

simplify186.0ms (1.6%)

prune117.0ms (1%)

localize15.0ms (0.1%)

series1.9s (16.5%)

rewrite8.0ms (0.1%)

simplify218.0ms (1.9%)

prune157.0ms (1.4%)

localize14.0ms (0.1%)

series2.2s (19.4%)

rewrite8.0ms (0.1%)

simplify151.0ms (1.3%)

prune173.0ms (1.5%)

regimes327.0ms (2.8%)

simplify2.0ms (0%)

end203.0ms (1.8%)

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