Details

analyze1.1s (22.1%)

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)

sample88.0ms (1.7%)

Algorithm

1×

intervals

Results

44.0ms	129×	body	2048	valid
21.0ms	60×	body	1024	valid
10.0ms	40×	body	512	valid
2.0ms	15×	body	128	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 32 to 22 computations (31.3% saved)

simplify78.0ms (1.5%)

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 (0.1%)

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

0.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

Compiler

Compiled 53 to 36 computations (32.1% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
✓	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
8×	`add-exp-log_binary64`
8×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`

Counts

2 → 78

Calls

2 calls:

23.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
15.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

series13.0ms (0.3%)

Counts

2 → 24

Calls

2 calls:

8.0ms	(/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))
5.0ms	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))

simplify109.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

619×	`times-frac_binary64`
449×	`fma-neg_binary64`
261×	`associate-l_binary64`
261×	`associate-/l*_binary64`
208×	`associate-r_binary64`

Counts

102 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	119	1768
1	274	1649
2	811	1630
3	3653	1614
4	4837	1614
5	5001	1614

prune68.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	6	145

Error

0.7b

Counts

145 → 6

Alt Table

Status	Error	Program
	2.2b	(.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)))))
	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))) 3))
	1.7b	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)
	1.7b	(pow.f64 (cbrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 3)
▶	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))
	62.8b	(/.f64 (-.f64 (/.f64 (.f64 PI.f64 PI.f64) 4) (.f64 (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))) (asin.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))

Compiler

Compiled 2205 to 1583 computations (28.2% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.7b	(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`acos-asin_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 32

Calls

1 calls:

14.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series1.0ms (0%)

Counts

1 → 0

Calls

1 calls:

1.0ms

(acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

894×	`unswap-sqr_binary64`
611×	`fma-neg_binary64`
351×	`distribute-rgt-in_binary64`
347×	`*-commutative_binary64`
303×	`distribute-lft-in_binary64`

Counts

32 → 38

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	565
1	97	536
2	178	530
3	330	530
4	686	530
5	1839	530
6	3583	530
7	5570	530

prune39.0ms (0.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	32	6	38
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	37	7	44

Error

0.7b

Counts

44 → 7

Alt Table

Status	Error	Program
	2.3b	(.f64 (.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))
	1.7b	(cbrt.f64 (pow.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) 3))
	1.7b	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)
	1.7b	(pow.f64 (sqrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 2)
	1.7b	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)
▶	0.7b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	62.9b	(/.f64 (-.f64 (.f64 PI.f64 (/.f64 PI.f64 4)) (.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (+.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))

Compiler

Compiled 954 to 717 computations (24.8% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
✓	0.8b	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-cube-cbrt_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
8×	`pow1_binary64`
6×	`flip3--_binary64`

Counts

2 → 80

Calls

2 calls:

18.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
13.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

series10.0ms (0.2%)

Counts

2 → 12

Calls

2 calls:

8.0ms	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
1.0ms	(asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))

simplify115.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-neg_binary64`
420×	`times-frac_binary64`
289×	`fma-def_binary64`
287×	`distribute-rgt-neg-in_binary64`
274×	`associate-l_binary64`

Counts

92 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	2166
1	242	2114
2	707	2053
3	2273	2014
4	4223	2008
5	4861	2008

prune101.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	121	6	127

Error

0.7b

Counts

127 → 6

Alt Table

Status	Error	Program
▶	1.7b	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)
	1.7b	(pow.f64 (cbrt.f64 (acos.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3)
✓	0.7b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	2.3b	(-.f64 (/.f64 PI.f64 2) (pow.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 3))
	62.9b	(/.f64 (-.f64 (*.f64 (/.f64 PI.f64 4) PI.f64) (pow.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 6)) (+.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (/.f64 PI.f64 2)))
	2.7b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 PI.f64 2)) (cbrt.f64 (/.f64 PI.f64 2))) (cbrt.f64 (/.f64 PI.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))

Compiler

Compiled 3984 to 2997 computations (24.8% saved)

localize10.0ms (0.2%)

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))
	0.7b	(acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))
✓	1.0b	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))
✓	1.0b	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cube-cbrt_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`pow1_binary64`
6×	`add-cbrt-cube_binary64`
6×	`log1p-expm1-u_binary64`

Counts

2 → 75

Calls

2 calls:

15.0ms	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)
13.0ms	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

series33.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

25.0ms	(pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))) 2)
8.0ms	(sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1))))

simplify106.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1012×	`fma-def_binary64`
866×	`exp-sum_binary64`
582×	`distribute-rgt-in_binary64`
504×	`distribute-lft-in_binary64`
385×	`exp-prod_binary64`

Counts

99 → 158

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	68	1492
1	93	1441
2	195	1441
3	712	1392
4	1477	1390
5	4066	1390
6	5681	1390

prune109.0ms (2.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	300	2	302
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	303	5	308

Error

0.7b

Counts

308 → 5

Alt Table

Status	Error	Program
✓	0.7b	(-.f64 (/.f64 PI.f64 2) (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))
	3.7b	(pow.f64 (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (*.f64 v -5) 1) (fma.f64 v v -1)))))) 2)
	2.6b	(pow.f64 (pow.f64 (sqrt.f64 (acos.f64 (/.f64 (fma.f64 v (.f64 v -5) 1) (fma.f64 v v -1)))) (.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2))
	62.9b	(/.f64 (-.f64 (*.f64 (/.f64 PI.f64 4) PI.f64) (pow.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) 6)) (+.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)) (/.f64 PI.f64 2)))
	2.7b	(+.f64 (fma.f64 (.f64 (cbrt.f64 (/.f64 PI.f64 2)) (cbrt.f64 (/.f64 PI.f64 2))) (cbrt.f64 (/.f64 PI.f64 2)) (neg.f64 (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))))))) (fma.f64 (neg.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (.f64 (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1))) (cbrt.f64 (asin.f64 (fma.f64 4 (fma.f64 v v (pow.f64 v 4)) -1)))))))

Compiler

Compiled 4104 to 3084 computations (24.9% saved)

regimes137.0ms (2.7%)

Accuracy

Total 0.0b remaining (1.4%)

Threshold costs 0.0b (1.4%)

Compiler

Compiled 3690 to 2796 computations (24.2% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
3×	`distribute-lft-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	21
1	22	21
2	29	21
3	36	21
4	41	21
5	44	21
6	45	21
7	42	21

end0.0ms (0%)

Compiler: Compiled 15 to 10 computations (33.3% saved)

sample2.8s (53.6%)

Algorithm

1×

intervals

Results

1.4s	3983×	body	2048	valid
600.0ms	2047×	body	1024	valid
181.0ms	962×	body	512	valid
59.0ms	470×	body	256	valid
38.0ms	535×	body	128	valid
2.0ms	3×	body	4096	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 275 to 209 computations (24% saved)

Details

analyze1.1s (22.1%)

sample88.0ms (1.7%)

simplify78.0ms (1.5%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite48.0ms (0.9%)

series13.0ms (0.3%)

simplify109.0ms (2.1%)

prune68.0ms (1.3%)

localize6.0ms (0.1%)

rewrite16.0ms (0.3%)

series1.0ms (0%)

simplify69.0ms (1.3%)

prune39.0ms (0.8%)

localize8.0ms (0.2%)

rewrite37.0ms (0.7%)

series10.0ms (0.2%)

simplify115.0ms (2.2%)

prune101.0ms (2%)

localize10.0ms (0.2%)

rewrite31.0ms (0.6%)

series33.0ms (0.6%)

simplify106.0ms (2.1%)

prune109.0ms (2.1%)

regimes137.0ms (2.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.8s (53.6%)

Profiling