Details

analyze671.0ms (7.5%)

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)

sample118.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	56×	body	1024	valid
23.0ms	59×	body	1024	invalid
11.0ms	132×	body	128	valid
11.0ms	39×	body	512	valid
10.0ms	96×	body	128	invalid
8.0ms	29×	body	512	invalid
4.0ms	26×	body	256	valid
3.0ms	18×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify74.0ms (0.8%)

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

prune4.0ms (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

19.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	19.4b	(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)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	0.0b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
✓	6.1b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite20.0ms (0.2%)

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))))
5.0ms	(-.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)

series119.0ms (1.3%)

Counts

3 → 80

Calls

3 calls:

94.0ms	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
22.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
3.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify222.0ms (2.5%)

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 → 306

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

prune157.0ms (1.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	304	2	306
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	305	2	307

Error

0.0b

Counts

307 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
	0.1b	(+.f64 (.f64 (.f64 J (cos.f64 (.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))) U)

Status

Error

Program

▶

0.0b

(fma.f64 (*.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)

0.1b

(+.f64 (*.f64 (*.f64 J (cos.f64 (*.f64 1/2 K))) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))) U)

Compiler

Compiled 4458 to 1650 computations (63% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))
✓	0.0b	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64`
10×	`associate-r_binary64`
9×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64`

Counts

4 → 69

Calls

4 calls:

4.0ms	(*.f64 1/60 (pow.f64 l 5))
3.0ms	(.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))
0.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
0.0ms	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)

series480.0ms (5.4%)

Counts

4 → 84

Calls

4 calls:

275.0ms	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
115.0ms	(.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))
69.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
19.0ms	(*.f64 1/60 (pow.f64 l 5))

simplify120.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

666×	`distribute-rgt-in_binary64`
326×	`fma-def_binary64`
297×	`associate-r_binary64`
250×	`cancel-sign-sub-inv_binary64`
248×	`associate-l_binary64`

Counts

153 → 268

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	277	5530
1	696	4638
2	2589	4162
3	5053	4162

prune208.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	265	3	268
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.0b	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
▶	0.0b	(+.f64 (.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) U)
	32.7b	(fma.f64 (.f64 (.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 5386 to 3986 computations (26% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/60 (pow.f64 l 5))
✓	0.1b	(.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))))
✓	0.1b	(.f64 (cos.f64 (.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))
	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

2 → 46

Calls

2 calls:

4.0ms

(*.f64 J (*.f64 (cos.f64 (*.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

3.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))

series330.0ms (3.7%)

Counts

2 → 60

Calls

2 calls:

238.0ms

(*.f64 J (*.f64 (cos.f64 (*.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

91.0ms

(*.f64 (cos.f64 (*.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))

simplify151.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

432×	`cancel-sign-sub-inv_binary64`
378×	`fma-def_binary64`
362×	`associate-r_binary64`
341×	`fma-neg_binary64`
322×	`associate-l_binary64`

Counts

106 → 206

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	267	5514
1	750	4264
2	3041	4146
3	4620	4146
4	5068	4146

prune259.0ms (2.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	278	4	282

Error

Counts

282 → 4

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.0b	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(+.f64 (.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) U)
▶	32.7b	(fma.f64 (.f64 (.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 6745 to 5079 computations (24.7% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
	0.1b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
✓	0.1b	(.f64 (.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))))
✓	0.1b	(.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-r_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 47

Calls

2 calls:

6.0ms

(*.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

5.0ms

(*.f64 (*.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

series257.0ms (2.9%)

Counts

2 → 36

Calls

2 calls:

142.0ms

(*.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

115.0ms

(*.f64 (*.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))))))

simplify145.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

686×	`distribute-rgt-in_binary64`
672×	`distribute-lft-in_binary64`
400×	`fma-def_binary64`
383×	`sqr-pow_binary64`
215×	`exp-prod_binary64`

Counts

83 → 157

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	101	2832
1	241	2591
2	759	2574
3	3095	2574
4	4023	2574
5	4403	2574
6	5131	2574

prune200.0ms (2.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	349	0	349
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	349	4	353

Error

Counts

353 → 4

Alt Table

Status	Error	Program
	35.9b	(cbrt.f64 (pow.f64 (fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U) 3))
✓	0.0b	(fma.f64 (.f64 J (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5)))))) (cos.f64 (/.f64 K 2)) U)
✓	0.0b	(+.f64 (.f64 J (.f64 (cos.f64 (.f64 1/2 K)) (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 l 2 (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) U)
✓	32.7b	(fma.f64 (.f64 (.f64 J (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (sqrt.f64 (fma.f64 1/2520 (pow.f64 l 7) (fma.f64 2 l (fma.f64 1/3 (pow.f64 l 3) (.f64 1/60 (pow.f64 l 5))))))) (cos.f64 (/.f64 K 2)) U)

Compiler

Compiled 6292 to 4849 computations (22.9% saved)

regimes1.4s (16.1%)

Accuracy

Total 0.0b remaining (10.8%)

Threshold costs 0.0b (10.8%)

Compiler

Compiled 31508 to 23664 computations (24.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	37
1	25	37
2	25	37

end1.0ms (0%)

Compiler: Compiled 30 to 23 computations (23.3% saved)

sample3.9s (43.2%)

Algorithm

1×

intervals

Results

873.0ms	1639×	body	1024	valid
755.0ms	1899×	body	1024	invalid
370.0ms	4372×	body	128	valid
362.0ms	1208×	body	512	valid
282.0ms	3309×	body	128	invalid
241.0ms	985×	body	512	invalid
128.0ms	721×	body	256	valid
90.0ms	491×	body	256	invalid
52.0ms	60×	body	2048	valid

Compiler

Compiled 199 to 155 computations (22.1% saved)

Details

analyze671.0ms (7.5%)

sample118.0ms (1.3%)

simplify74.0ms (0.8%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite20.0ms (0.2%)

series119.0ms (1.3%)

simplify222.0ms (2.5%)

prune157.0ms (1.8%)

localize17.0ms (0.2%)

rewrite11.0ms (0.1%)

series480.0ms (5.4%)

simplify120.0ms (1.3%)

prune208.0ms (2.3%)

localize18.0ms (0.2%)

rewrite11.0ms (0.1%)

series330.0ms (3.7%)

simplify151.0ms (1.7%)

prune259.0ms (2.9%)

localize20.0ms (0.2%)

rewrite15.0ms (0.2%)

series257.0ms (2.9%)

simplify145.0ms (1.6%)

prune200.0ms (2.2%)

regimes1.4s (16.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample3.9s (43.2%)

Profiling