Details

analyze887.0ms (15.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	22
1	50	22
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
37.5%	62.5%	0%	4
43.7%	56.2%	0%	5
46.9%	53.1%	0%	6
48.4%	51.5%	0%	7
49.2%	50.8%	0%	8
49.6%	50.4%	0%	9
49.8%	50.2%	0%	10
49.9%	50.1%	0%	11
49.9%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 17 to 15 computations (11.8% saved)

sample63.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	65×	body	1024	valid
13.0ms	138×	body	128	valid
8.0ms	27×	body	256	valid
7.0ms	24×	body	512	valid
2.0ms	2×	body	2048	valid

Compiler

Compiled 33 to 30 computations (9.1% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	50	22
1	50	22

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

13.3b

Counts

2 → 1

Compiler

Compiled 28 to 24 computations (14.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
0.3b	(.f64 8/3 (sin.f64 (.f64 x 1/2)))
13.2b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
10×	`add-sqr-sqrt_binary64_20219` `pow1_binary64_20258`
8×	`*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
7×	`cbrt-unprod_binary64_20230` `prod-exp_binary64_20246`
6×	`associate-l_binary64_20138`
4×	`pow-prod-down_binary64_20268` `associate-r_binary64_20137`
3×	`add-log-exp_binary64_20236` `times-frac_binary64_20203` `associate-/r*_binary64_20141` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231`
2×	`*-commutative_binary64_20128`
1×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `unswap-sqr_binary64_20165` `div-inv_binary64_20194` `associate-/l*_binary64_20142`

Counts

3 → 59

Calls

3 calls:

8.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
7.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
5.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

series118.0ms (2%)

Counts

3 → 9

Calls

3 calls:

63.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2)))) (sin.f64 x))
36.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (.f64 8/3 (sin.f64 (.f64 x 1/2))))
18.0ms	(.f64 8/3 (sin.f64 (.f64 x 1/2)))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4934	1066
1	4934	1066

prune99.0ms (1.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	55	13	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	13	69

Error

0.0b

Counts

69 → 13

Compiler

Compiled 1365 to 1047 computations (23.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.3b	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
14×	`add-sqr-sqrt_binary64_20219`
10×	`-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232` `associate-r*_binary64_20137`
7×	`pow1_binary64_20258`
6×	`cbrt-unprod_binary64_20230` `times-frac_binary64_20203` `prod-exp_binary64_20246` `associate-l_binary64_20138`
4×	`div-exp_binary64_20248` `cbrt-undiv_binary64_20231`
3×	`add-log-exp_binary64_20236` `associate-/r*_binary64_20141`
2×	`unswap-sqr_binary64_20165` `div-inv_binary64_20194` `*-commutative_binary64_20128` `pow-prod-down_binary64_20268`
1×	`frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/l_binary64_20142` `associate-r/_binary64_20139`

Counts

3 → 66

Calls

3 calls:

8.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
5.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

series120.0ms (2%)

Counts

3 → 9

Calls

3 calls:

60.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x)))
43.0ms	(/.f64 (.f64 (sin.f64 (.f64 x 1/2)) 8/3) (sin.f64 x))
16.0ms	(.f64 (sin.f64 (.f64 x 1/2)) 8/3)

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4958	1245
1	4958	1245

prune100.0ms (1.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	70	5	75
Fresh	5	7	12
Picked	0	1	1
Done	0	0	0
Total	75	13	88

Error

0.0b

Counts

88 → 13

Compiler

Compiled 1567 to 1182 computations (24.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.7b	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`add-sqr-sqrt_binary64_20219`
38×	`times-frac_binary64_20203`
37×	`*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
36×	`associate-r_binary64_20137`
28×	`unpow-prod-down_binary64_20276` `cube-prod_binary64_20225`
17×	`add-exp-log_binary64_20235`
10×	`add-cbrt-cube_binary64_20233`
7×	`unswap-sqr_binary64_20165` `pow1_binary64_20258`
6×	`associate-l_binary64_20138`
5×	`prod-exp_binary64_20246`
4×	`cube-div_binary64_20226` `add-log-exp_binary64_20236` `div-inv_binary64_20194` `associate-*r/_binary64_20139` `pow-exp_binary64_20265`
3×	`pow-unpow_binary64_20274` `sqr-pow_binary64_20169`
2×	`cbrt-prod_binary64_20228` `rem-cube-cbrt_binary64_20220` `cbrt-unprod_binary64_20230` `unpow3_binary64_20263` `div-exp_binary64_20248` `*-commutative_binary64_20128` `pow-to-exp_binary64_20266` `cube-mult_binary64_20227` `cbrt-div_binary64_20229`
1×	`pow1/3_binary64_20279` `pow-pow_binary64_20269` `pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231`

Counts

4 → 131

Calls

4 calls:

13.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
6.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))
5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
5.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)

series310.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))
76.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3))))
63.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
62.0ms	(cbrt.f64 (.f64 512/27 (pow.f64 (/.f64 (sin.f64 (.f64 x 1/2)) (sin.f64 x)) 3)))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5124	2969

prune227.0ms (3.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	4	7	11
Picked	0	1	1
Done	1	0	1
Total	144	12	156

Error

Counts

156 → 12

Compiler

Compiled 3638 to 2780 computations (23.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.4b	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
0.8b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0b	(cbrt.f64 512/27)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_20219`
39×	`cbrt-prod_binary64_20228`
38×	`*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
36×	`times-frac_binary64_20203`
26×	`unpow-prod-down_binary64_20276` `cube-prod_binary64_20225`
9×	`add-exp-log_binary64_20235`
8×	`add-cbrt-cube_binary64_20233`
7×	`pow1_binary64_20258`
6×	`associate-r_binary64_20137`
4×	`add-log-exp_binary64_20236` `div-inv_binary64_20194`
3×	`pow-unpow_binary64_20274` `associate-l_binary64_20138`
2×	`rem-cube-cbrt_binary64_20220` `pow1/3_binary64_20279` `cube-div_binary64_20226` `unswap-sqr_binary64_20165` `unpow3_binary64_20263` `sqr-pow_binary64_20169` `pow-exp_binary64_20265` `cube-mult_binary64_20227`
1×	`cbrt-unprod_binary64_20230` `pow-pow_binary64_20269` `div-exp_binary64_20248` `rem-cbrt-cube_binary64_20221` `prod-exp_binary64_20246` `*-commutative_binary64_20128` `pow-to-exp_binary64_20266` `pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231` `cbrt-div_binary64_20229`

Counts

4 → 121

Calls

4 calls:

5.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
5.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
5.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
1.0ms	(cbrt.f64 512/27)

series132.0ms (2.2%)

Counts

4 → 10

Calls

4 calls:

73.0ms	(pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3)
31.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 (*.f64 x 1/2)) (sin.f64 x)) 3))
27.0ms	(.f64 (sin.f64 (.f64 x 1/2)) (cbrt.f64 512/27))
0.0ms	(cbrt.f64 512/27)

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5536	2404

prune187.0ms (3.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	131	12	143

Error

Counts

143 → 12

Compiler

Compiled 3082 to 2352 computations (23.7% saved)

regimes212.0ms (3.6%)

Accuracy

Total 0.4b remaining (99.8%)

Threshold costs 0.4b (99.8%)

Compiler

Compiled 2020 to 1726 computations (14.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	29
1	16	29

end0.0ms (0%)

sample3.0s (50.5%)

Algorithm

1×

intervals

Results

799.0ms	1934×	body	1024	valid
446.0ms	4498×	body	128	valid
304.0ms	1030×	body	512	valid
105.0ms	531×	body	256	valid
5.0ms	7×	body	2048	valid

Compiler

Compiled 1044 to 894 computations (14.4% saved)

Details

analyze887.0ms (15.1%)

sample63.0ms (1.1%)

simplify8.0ms (0.1%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

rewrite24.0ms (0.4%)

series118.0ms (2%)

simplify85.0ms (1.4%)

prune99.0ms (1.7%)

localize9.0ms (0.1%)

rewrite23.0ms (0.4%)

series120.0ms (2%)

simplify70.0ms (1.2%)

prune100.0ms (1.7%)

localize11.0ms (0.2%)

rewrite43.0ms (0.7%)

series310.0ms (5.3%)

simplify57.0ms (1%)

prune227.0ms (3.9%)

localize12.0ms (0.2%)

rewrite29.0ms (0.5%)

series132.0ms (2.2%)

simplify77.0ms (1.3%)

prune187.0ms (3.2%)

regimes212.0ms (3.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (50.5%)

Profiling