Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample161.0ms (0.9%)

Algorithm

1×

intervals

Results

67.0ms	73×	body	2048	valid
62.0ms	119×	body	1024	valid
12.0ms	38×	body	512	valid
4.0ms	18×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify178.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune4.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

40.6b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.3b	(cos.f64 (+.f64 x eps))
1.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
1.6b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
2.3b	(cos.f64 (+.f64 x eps))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070`
4×	`add-log-exp_binary64_1109`
3×	`cancel-sign-sub-inv_binary64_1036` `add-cube-cbrt_binary64_1105`
2×	`cos-sum_binary64_1204` `add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `pow1_binary64_1131`
1×	`flip--_binary64_1045` `flip3--_binary64_1074` `distribute-lft-out--_binary64_1022` `diff-cos_binary64_1221` `difference-of-squares_binary64_1039` `associate--l-_binary64_1008` `sub-neg_binary64_1063` `diff-log_binary64_1162`

Counts

2 → 26

Calls

4 calls:

13.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
8.0ms	(cos.f64 (+.f64 x eps))
0.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
0.0ms	(cos.f64 (+.f64 x eps))

series206.0ms (1.2%)

Counts

2 → 24

Calls

2 calls:

129.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
77.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 379 to 301 computations (20.6% saved)

simplify111.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5016	764

prune122.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	42	8	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	8	51

Error

0.3b

Counts

51 → 8

Compiler

Compiled 763 to 277 computations (63.7% saved)

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite82.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_1070`
11×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `pow1_binary64_1131`
9×	`add-sqr-sqrt_binary64_1092` `add-log-exp_binary64_1109`
7×	`add-cube-cbrt_binary64_1105`
6×	`associate-l_binary64_1011`
4×	`associate-r_binary64_1010` `cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `pow-prod-down_binary64_1141`
3×	`distribute-lft-out_binary64_1021` `sum-log_binary64_1161`
2×	`sin-mult_binary64_1225` `*-commutative_binary64_1001`
1×	`flip-+_binary64_1044` `associate-*r/_binary64_1012` `+-commutative_binary64_1000` `unswap-sqr_binary64_1038` `flip3-+_binary64_1073` `associate-+r+_binary64_1002`

Counts

4 → 60

Calls

8 calls:

24.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
23.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
14.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
11.0ms	(+.f64 x (+.f64 x eps))
0.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))

series738.0ms (4.2%)

Counts

4 → 48

Calls

4 calls:

275.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
239.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
113.0ms	(+.f64 x (+.f64 x eps))
110.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 1176 to 1059 computations (9.9% saved)

simplify167.0ms (1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4932	2050
1	4932	2050

prune262.0ms (1.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	8	108
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	102	14	116

Error

0.2b

Counts

116 → 14

Compiler

Compiled 2346 to 1564 computations (33.3% saved)

localize35.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
4×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-log-exp_binary64_1109` `pow1_binary64_1131`
3×	`cbrt-prod_binary64_1101`
1×	`pow1/3_binary64_1152`

Counts

4 → 32

Calls

8 calls:

15.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
14.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
14.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
13.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0ms	(.f64 -2 (.f64 (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) (sin.f64 (/.f64 eps 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))

series975.0ms (5.6%)

Counts

4 → 46

Calls

4 calls:

589.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
130.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
129.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
126.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 2794 to 2106 computations (24.6% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5177	1478

prune316.0ms (1.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	77	15	92

Error

0.2b

Counts

92 → 15

Compiler

Compiled 3589 to 2176 computations (39.4% saved)

localize38.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))))
0.6b	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.3b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite68.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
4×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-log-exp_binary64_1109` `pow1_binary64_1131`
3×	`cbrt-prod_binary64_1101`
1×	`pow1/3_binary64_1152`

Counts

4 → 32

Calls

8 calls:

16.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
15.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
15.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
13.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (.f64 (.f64 (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))) (cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))))

series959.0ms (5.5%)

Counts

4 → 46

Calls

4 calls:

605.0ms	(cbrt.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
125.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
117.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
111.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

Compiler

Compiled 2794 to 2106 computations (24.6% saved)

simplify91.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5177	1478

prune268.0ms (1.5%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	78	15	93

Error

0.2b

Counts

93 → 15

Compiler

Compiled 3227 to 1926 computations (40.3% saved)

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	375	1499
1	375	1499

regimes702.0ms (4%)

Accuracy

Total 0.5b remaining (65.9%)

Threshold costs 0.5b (65.9%)

Compiler

Compiled 1888 to 1386 computations (26.6% saved)

bsearch105.0ms (0.6%)

Steps

Iters	Range		Point
9	0.0008458657080035314	58.40097343030177	0.0013137094133468092
6	-0.134927473509972	-0.027796361353954066	-0.028077178329225884

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	77	81
1	77	81

end0.0ms (0%)

sample11.5s (66.3%)

Algorithm

1×

intervals

Results

2.3s	2081×	body	2048	valid
1.8s	3803×	body	1024	valid
405.0ms	1317×	body	512	valid
108.0ms	534×	body	256	valid
37.0ms	261×	body	128	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 2936 to 2130 computations (27.5% saved)

Pareto

0.00901237435240908

Details

analyze4.0ms (0%)

sample161.0ms (0.9%)

simplify178.0ms (1%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite25.0ms (0.1%)

series206.0ms (1.2%)

simplify111.0ms (0.6%)

prune122.0ms (0.7%)

localize23.0ms (0.1%)

rewrite82.0ms (0.5%)

series738.0ms (4.2%)

simplify167.0ms (1%)

prune262.0ms (1.5%)

localize35.0ms (0.2%)

rewrite65.0ms (0.4%)

series975.0ms (5.6%)

simplify91.0ms (0.5%)

prune316.0ms (1.8%)

localize38.0ms (0.2%)

rewrite68.0ms (0.4%)

series959.0ms (5.5%)

simplify91.0ms (0.5%)

prune268.0ms (1.5%)

simplify41.0ms (0.2%)

regimes702.0ms (4%)

bsearch105.0ms (0.6%)

simplify6.0ms (0%)

end0.0ms (0%)

sample11.5s (66.3%)

Profiling