Details

analyze695.0ms (9.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
49.9%	49.9%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
53%	46.8%	0.2%	8
57.7%	42.1%	0.2%	9
61.6%	38.2%	0.2%	10
63.5%	30%	6.4%	11
63.5%	30%	6.4%	12
67.6%	25.9%	6.4%	13
68.9%	24.7%	6.4%	14

Compiler

Compiled 20 to 15 computations (25% saved)

sample116.0ms (1.5%)

Algorithm

1×

intervals

Results

28.0ms	54×	body	1024	valid
17.0ms	42×	body	1024	invalid
12.0ms	130×	body	128	valid
12.0ms	39×	body	512	valid
10.0ms	111×	body	128	invalid
8.0ms	32×	body	256	valid
7.0ms	24×	body	512	invalid
1.0ms	7×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

745×	`fma-def_binary64`
657×	`div-sub_binary64`
464×	`fma-neg_binary64`
424×	`times-frac_binary64`
411×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	29	22
2	53	22
3	105	22
4	233	22
5	540	22
6	1242	22
7	2242	22
8	3501	22
9	4490	22
10	4976	22

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

19.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 69 to 44 computations (36.2% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	0.2b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	5.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series59.0ms (0.8%)

Counts

3 → 80

Calls

3 calls:

39.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
17.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
27×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 92

Calls

3 calls:

8.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))
0.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

simplify197.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

374×	`times-frac_binary64`
336×	`cancel-sign-sub-inv_binary64`
309×	`fma-neg_binary64`
281×	`associate-r_binary64`
279×	`associate-l_binary64`

Counts

172 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	3960
1	572	3266
2	2075	3044
3	4373	3044
4	4843	3044
5	4992	3044
6	4994	3044
7	4848	3044

prune164.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	165	4	169
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	165	5	170

Error

0.3b

Counts

170 → 5

Alt Table

Status	Error	Program
✓	19.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
▶	1.1b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
	1.2b	(fma.f64 2 (.f64 l (.f64 J (cos.f64 (*.f64 1/2 K)))) U)
	20.1b	(fma.f64 (/.f64 (*.f64 J (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2))) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	19.8b	(fma.f64 (.f64 J (.f64 (+.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))) (-.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 4627 to 1752 computations (62.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
✓	0.0b	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
✓	0.1b	(*.f64 1/3 (pow.f64 l 3))

series142.0ms (1.9%)

Counts

4 → 108

Calls

4 calls:

64.0ms	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
51.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
20.0ms	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))
5.0ms	(*.f64 1/3 (pow.f64 l 3))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64`

Counts

4 → 99

Calls

4 calls:

5.0ms	(.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))
5.0ms	(*.f64 1/3 (pow.f64 l 3))
5.0ms	(.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3)))))
3.0ms	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))

simplify137.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

602×	`cancel-sign-sub-inv_binary64`
535×	`fma-neg_binary64`
484×	`distribute-rgt-in_binary64`
312×	`associate-r_binary64`
264×	`associate-l_binary64`

Counts

207 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	4721
1	562	4169
2	2138	4110
3	4470	4110
4	4986	4110

prune234.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	175	7	182

Error

0.3b

Counts

182 → 7

Alt Table

Status	Error	Program
	42.9b	(.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (.f64 1/2 K)))) (.f64 2 (.f64 l (cos.f64 (*.f64 1/2 K))))) J)
✓	1.1b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
✓	19.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
▶	1.1b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	20.1b	(fma.f64 (/.f64 (*.f64 J (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2))) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	19.8b	(fma.f64 (.f64 J (.f64 (+.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))) (-.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))))) (cos.f64 (/.f64 K 2)) U)
	14.9b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (cbrt.f64 (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) J) 3))))

Compiler

Compiled 4901 to 3486 computations (28.9% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
✓	0.1b	(.f64 J (cos.f64 (.f64 K 1/2)))
	0.1b	(*.f64 1/3 (pow.f64 l 3))

series67.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

58.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
9.0ms	(.f64 J (cos.f64 (.f64 K 1/2)))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`
4×	`add-exp-log_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 J (cos.f64 (.f64 K 1/2)))
0.0ms	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)

simplify103.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
366×	`cancel-sign-sub-inv_binary64`
355×	`*-commutative_binary64`
352×	`sub-neg_binary64`
334×	`distribute-rgt-neg-in_binary64`

Counts

102 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2419
1	338	1909
2	1231	1872
3	3816	1872
4	4879	1872
5	4980	1872

prune166.0ms (2.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	121	9	130

Error

0.2b

Counts

130 → 9

Alt Table

Status	Error	Program
	42.9b	(.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (.f64 1/2 K)))) (.f64 2 (.f64 l (cos.f64 (*.f64 1/2 K))))) J)
✓	1.1b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
▶	1.4b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (*.f64 K 1/2)))) U)
	20.1b	(fma.f64 (/.f64 (*.f64 J (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2))) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	19.8b	(fma.f64 (.f64 J (.f64 (+.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))) (-.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))))) (cos.f64 (/.f64 K 2)) U)
	26.0b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) 3)) U)
✓	19.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	1.1b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	14.9b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (cbrt.f64 (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) J) 3))))

Compiler

Compiled 3230 to 2265 computations (29.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2))))
✓	0.5b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series263.0ms (3.5%)

Counts

4 → 72

Calls

4 calls:

168.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2)))
37.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
35.0ms	(cbrt.f64 J)
24.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2))))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`
20×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64`

Counts

4 → 103

Calls

4 calls:

7.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2))))
5.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
4.0ms	(.f64 (cbrt.f64 J) (cos.f64 (.f64 K 1/2)))
1.0ms	(cbrt.f64 J)

simplify152.0ms (2%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-neg_binary64`
455×	`*-commutative_binary64`
421×	`cancel-sign-sub-inv_binary64`
385×	`unswap-sqr_binary64`
323×	`sub-neg_binary64`

Counts

175 → 163

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	143	1945
1	302	1727
2	1132	1668
3	2242	1652
4	4280	1554
5	4570	1554
6	4885	1554
7	4873	1554

prune256.0ms (3.4%)

Pruning

9 alts after pruning (5 fresh and 4 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	5	5
Picked	0	1	1
Done	0	3	3
Total	199	9	208

Error

0.2b

Counts

208 → 9

Alt Table

Status	Error	Program
	42.9b	(.f64 (+.f64 (.f64 1/3 (.f64 (pow.f64 l 3) (cos.f64 (.f64 1/2 K)))) (.f64 2 (.f64 l (cos.f64 (*.f64 1/2 K))))) J)
✓	1.1b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (.f64 J (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))))))
✓	1.4b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.f64 J) (cos.f64 (*.f64 K 1/2)))) U)
	20.1b	(fma.f64 (/.f64 (*.f64 J (-.f64 (pow.f64 (exp.f64 l) 2) (pow.f64 (exp.f64 l) -2))) (+.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	19.8b	(fma.f64 (.f64 J (.f64 (+.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))) (-.f64 (sqrt.f64 (exp.f64 l)) (sqrt.f64 (exp.f64 (neg.f64 l)))))) (cos.f64 (/.f64 K 2)) U)
	26.0b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (cbrt.f64 (pow.f64 (.f64 (cos.f64 (*.f64 1/2 K)) J) 3)) U)
✓	19.8b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	1.1b	(fma.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) (.f64 J (cos.f64 (*.f64 K 1/2))) U)
	14.9b	(+.f64 U (.f64 (cos.f64 (.f64 1/2 K)) (cbrt.f64 (pow.f64 (.f64 (fma.f64 2 l (.f64 1/3 (pow.f64 l 3))) J) 3))))

Compiler

Compiled 5716 to 3228 computations (43.5% saved)

regimes531.0ms (7.1%)

Accuracy

Total 0.1b remaining (63.7%)

Threshold costs 0.1b (63.7%)

Counts

49 → 1

Compiler

Compiled 11628 to 8413 computations (27.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	18
1	14	18
2	14	18

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample4.0s (53.7%)

Algorithm

1×

intervals

Results

913.0ms	1664×	body	1024	valid
811.0ms	1966×	body	1024	invalid
397.0ms	4434×	body	128	valid
320.0ms	1135×	body	512	valid
295.0ms	3453×	body	128	invalid
247.0ms	981×	body	512	invalid
134.0ms	697×	body	256	valid
86.0ms	494×	body	256	invalid
59.0ms	70×	body	2048	valid

Compiler

Compiled 255 to 186 computations (27.1% saved)

Details

analyze695.0ms (9.3%)

sample116.0ms (1.5%)

simplify70.0ms (0.9%)

prune3.0ms (0%)

localize11.0ms (0.1%)

series59.0ms (0.8%)

rewrite19.0ms (0.3%)

simplify197.0ms (2.6%)

prune164.0ms (2.2%)

localize12.0ms (0.2%)

series142.0ms (1.9%)

rewrite23.0ms (0.3%)

simplify137.0ms (1.8%)

prune234.0ms (3.1%)

localize11.0ms (0.2%)

series67.0ms (0.9%)

rewrite5.0ms (0.1%)

simplify103.0ms (1.4%)

prune166.0ms (2.2%)

localize15.0ms (0.2%)

series263.0ms (3.5%)

rewrite22.0ms (0.3%)

simplify152.0ms (2%)

prune256.0ms (3.4%)

regimes531.0ms (7.1%)

simplify2.0ms (0%)

end1.0ms (0%)

sample4.0s (53.7%)

Profiling