Details

analyze650.0ms (7.3%)

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)

sample211.0ms (2.4%)

Algorithm

1×

intervals

Results

33.0ms	52×	body	1024	valid
31.0ms	78×	body	1024	invalid
18.0ms	42×	body	512	valid
16.0ms	135×	body	128	valid
9.0ms	112×	body	128	invalid
7.0ms	28×	body	512	invalid
5.0ms	24×	body	256	valid
3.0ms	17×	body	256	invalid
2.0ms	3×	body	2048	valid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify68.0ms (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

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

17.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	17.5b	(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)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
✓	6.7b	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

series14.0ms (0.2%)

Counts

2 → 32

Calls

2 calls:

12.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
2.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
27×	`prod-diff_binary64`
26×	`add-cube-cbrt_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 82

Calls

2 calls:

7.0ms	(*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l))))
4.0ms	(-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))

simplify118.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

453×	`fma-def_binary64`
405×	`fma-neg_binary64`
321×	`associate-/r*_binary64`
267×	`exp-prod_binary64`
250×	`neg-mul-1_binary64`

Counts

114 → 124

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	163	2026
1	303	1740
2	954	1535
3	2479	1535
4	4342	1532
5	4908	1532
6	4751	1532

prune109.0ms (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	123	2	125

Error

0.1b

Counts

125 → 2

Alt Table

Status	Error	Program
▶	0.3b	(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)
✓	17.5b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)

Status

Error

Program

▶

0.3b

(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)

✓

17.5b

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

Compiler

Compiled 3392 to 1169 computations (65.5% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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	(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 1/60 (pow.f64 l 5))
✓	0.2b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

series204.0ms (2.3%)

Counts

4 → 72

Calls

4 calls:

189.0ms	(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)
7.0ms	(*.f64 1/60 (pow.f64 l 5))
4.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))
4.0ms	(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)))))

rewrite9.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`add-exp-log_binary64`
7×	`associate-r_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-cube-cbrt_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 1/60 (pow.f64 l 5))
0.0ms	(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 (.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)
0.0ms	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

simplify109.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-neg_binary64`
406×	`associate--l+_binary64`
286×	`fma-def_binary64`
250×	`cancel-sign-sub-inv_binary64`
241×	`distribute-rgt-in_binary64`

Counts

129 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	4640
1	623	3836
2	2212	3375
3	4861	3375
4	5380	3375

prune176.0ms (2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	121	4	125

Error

0.0b

Counts

125 → 4

Alt Table

Status	Error	Program
▶	0.3b	(+.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)
✓	0.3b	(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)
✓	17.5b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	29.3b	(.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))

Compiler

Compiled 4579 to 3394 computations (25.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.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)))))))
✓	0.2b	(.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))))))
	0.2b	(fma.f64 1/3 (pow.f64 l 3) (*.f64 1/60 (pow.f64 l 5)))

series196.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

137.0ms

(*.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)))))))

58.0ms

(*.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))))))

rewrite12.0ms (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))))))

simplify123.0ms (1.4%)

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 → 121

Iterations

Useful iterations: 2 (0.0ms)

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

prune287.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	166	5	171

Error

0.0b

Counts

171 → 5

Alt Table

Status	Error	Program
✓	0.3b	(+.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)
✓	0.3b	(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)
✓	17.5b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
▶	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.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)
	29.3b	(.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))

Compiler

Compiled 6833 to 5137 computations (24.8% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.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)))))))
✓	0.3b	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.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))))))))
✓	0.6b	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
✓	0.6b	(cbrt.f64 J)

series567.0ms (6.3%)

Counts

4 → 96

Calls

4 calls:

323.0ms	(.f64 (cbrt.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)))))))
169.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.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))))))))
38.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
36.0ms	(cbrt.f64 J)

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`pow1_binary64`
32×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
20×	`pow-prod-down_binary64`

Counts

4 → 120

Calls

4 calls:

13.0ms	(.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.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))))))))
5.0ms	(.f64 (cbrt.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)))))))
5.0ms	(*.f64 (cbrt.f64 J) (cbrt.f64 J))
1.0ms	(cbrt.f64 J)

simplify157.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

852×	`associate-r_binary64`
742×	`associate-l_binary64`
421×	`fma-def_binary64`
273×	`*-commutative_binary64`
218×	`associate-+r+_binary64`

Counts

216 → 210

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	374	7718
1	1021	6546
2	4703	6546
3	4996	6546

prune392.0ms (4.4%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	243	6	249

Error

Counts

249 → 6

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (.f64 (.f64 (cbrt.f64 J) (cbrt.f64 J)) (.f64 (cbrt.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)
	31.8b	(+.f64 (.f64 (.f64 (cbrt.f64 J) (.f64 (cbrt.f64 (sqrt.f64 J)) (cbrt.f64 (sqrt.f64 J)))) (.f64 (cbrt.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)
✓	0.3b	(+.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)
✓	0.3b	(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)
✓	17.5b	(fma.f64 (*.f64 J (-.f64 (exp.f64 l) (exp.f64 (neg.f64 l)))) (cos.f64 (/.f64 K 2)) U)
	29.3b	(.f64 (sqrt.f64 (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)) (sqrt.f64 (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)))

Compiler

Compiled 11155 to 7240 computations (35.1% saved)

regimes1.2s (13.5%)

Accuracy

Total 0.1b remaining (56.7%)

Threshold costs 0.1b (56.7%)

Counts

97 → 1

Compiler

Compiled 31436 to 23271 computations (26% saved)

simplify3.0ms (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)

sample4.2s (47.2%)

Algorithm

1×

intervals

Results

973.0ms	1630×	body	1024	valid
839.0ms	1898×	body	1024	invalid
398.0ms	4434×	body	128	valid
360.0ms	1188×	body	512	valid
314.0ms	3453×	body	128	invalid
270.0ms	985×	body	512	invalid
125.0ms	694×	body	256	valid
83.0ms	473×	body	256	invalid
44.0ms	54×	body	2048	valid

Compiler

Compiled 259 to 193 computations (25.5% saved)

Details

analyze650.0ms (7.3%)

sample211.0ms (2.4%)

simplify68.0ms (0.8%)

prune3.0ms (0%)

localize10.0ms (0.1%)

series14.0ms (0.2%)

rewrite16.0ms (0.2%)

simplify118.0ms (1.3%)

prune109.0ms (1.2%)

localize19.0ms (0.2%)

series204.0ms (2.3%)

rewrite9.0ms (0.1%)

simplify109.0ms (1.2%)

prune176.0ms (2%)

localize17.0ms (0.2%)

series196.0ms (2.2%)

rewrite12.0ms (0.1%)

simplify123.0ms (1.4%)

prune287.0ms (3.2%)

localize22.0ms (0.2%)

series567.0ms (6.3%)

rewrite33.0ms (0.4%)

simplify157.0ms (1.7%)

prune392.0ms (4.4%)

regimes1.2s (13.5%)

simplify3.0ms (0%)

end1.0ms (0%)

sample4.2s (47.2%)

Profiling