Details

analyze1.5s (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample147.0ms (0.4%)

Algorithm

1×

intervals

Results

56.0ms	43×	body	2048	valid
54.0ms	113×	body	1024	valid
14.0ms	46×	body	512	valid
3.0ms	37×	body	128	valid
3.0ms	17×	body	256	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify169.0ms (0.4%)

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

36.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize14.0ms (0%)

Local error

Found 4 expressions with local error:

3.5b	(tan.f64 (+.f64 x eps))
1.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
1.8b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
3.5b	(tan.f64 (+.f64 x eps))

rewrite26.0ms (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` `tan-quot_binary64_1229`
3×	`cancel-sign-sub-inv_binary64_1036` `add-cube-cbrt_binary64_1105`
2×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `frac-sub_binary64_1079` `tan-sum_binary64_1205` `pow1_binary64_1131`
1×	`flip--_binary64_1045` `flip3--_binary64_1074` `distribute-lft-out--_binary64_1022` `difference-of-squares_binary64_1039` `sub-neg_binary64_1063` `diff-log_binary64_1162`

Counts

2 → 27

Calls

4 calls:

14.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	(tan.f64 (+.f64 x eps))
0.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
0.0ms	(tan.f64 (+.f64 x eps))

series815.0ms (2.1%)

Counts

2 → 21

Calls

2 calls:

512.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
303.0ms	(tan.f64 (+.f64 x eps))

Compiler

Compiled 904 to 607 computations (32.9% saved)

simplify125.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4976	1156
1	4976	1156

prune190.0ms (0.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	6	49

Error

0.2b

Counts

49 → 6

Compiler

Compiled 1073 to 386 computations (64% saved)

localize23.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite77.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_1070`
23×	`add-sqr-sqrt_binary64_1092`
16×	`add-cube-cbrt_binary64_1105`
13×	`times-frac_binary64_1076`
9×	`tan-quot_binary64_1229`
8×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-log-exp_binary64_1109`
6×	`pow1_binary64_1131`
5×	`distribute-lft-out_binary64_1021`
4×	`associate-/l*_binary64_1015`
3×	`cancel-sign-sub-inv_binary64_1036` `associate-r_binary64_1010` `associate-l_binary64_1011` `associate-/l/_binary64_1017` `associate-/r*_binary64_1014`
2×	`flip--_binary64_1045` `associate-/r/_binary64_1016` `flip-+_binary64_1044` `flip3--_binary64_1074` `frac-add_binary64_1078` `difference-of-squares_binary64_1039` `flip3-+_binary64_1073`
1×	`frac-2neg_binary64_1081` `frac-sub_binary64_1079` `cbrt-undiv_binary64_1104` `cbrt-unprod_binary64_1103` `-commutative_binary64_1001` `associate-l/_binary64_1013` `frac-times_binary64_1080` `prod-exp_binary64_1119` `associate-*r/_binary64_1012` `clear-num_binary64_1069` `+-commutative_binary64_1000` `distribute-lft-out--_binary64_1022` `unswap-sqr_binary64_1038` `div-exp_binary64_1121` `pow-prod-down_binary64_1141` `sub-neg_binary64_1063` `diff-log_binary64_1162` `sum-log_binary64_1161` `div-inv_binary64_1067`

Counts

4 → 88

Calls

8 calls:

25.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
17.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
9.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))

series3.5s (9%)

Counts

4 → 40

Calls

4 calls:

1.8s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))
982.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
394.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
323.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 1962 to 1251 computations (36.2% saved)

simplify133.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5129	3629

prune374.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	122	12	134

Error

0.1b

Counts

134 → 12

Compiler

Compiled 3768 to 1279 computations (66.1% saved)

localize35.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
0.1b	(*.f64 (cos.f64 x) (cos.f64 eps))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
3.7b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite106.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`*-un-lft-identity_binary64_1070`
41×	`add-sqr-sqrt_binary64_1092`
26×	`times-frac_binary64_1076`
20×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108`
19×	`add-cube-cbrt_binary64_1105`
12×	`difference-of-squares_binary64_1039`
7×	`distribute-lft-out_binary64_1021` `associate-/r*_binary64_1014`
6×	`distribute-lft-out--_binary64_1022` `add-log-exp_binary64_1109` `pow1_binary64_1131`
5×	`cbrt-undiv_binary64_1104` `cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `div-exp_binary64_1121` `associate-/l*_binary64_1015`
4×	`associate-/l/_binary64_1017`
3×	`cancel-sign-sub-inv_binary64_1036` `associate-r_binary64_1010` `associate-/r/_binary64_1016` `associate-l_binary64_1011` `tan-quot_binary64_1229`
2×	`sin-mult_binary64_1225` `frac-2neg_binary64_1081` `flip--_binary64_1045` `flip3--_binary64_1074` `clear-num_binary64_1069` `div-inv_binary64_1067`
1×	`frac-sub_binary64_1079` `*-commutative_binary64_1001` `flip-+_binary64_1044` `cos-mult_binary64_1224` `unswap-sqr_binary64_1038` `frac-add_binary64_1078` `pow-prod-down_binary64_1141` `flip3-+_binary64_1073` `sub-neg_binary64_1063` `diff-log_binary64_1162`

Counts

4 → 111

Calls

8 calls:

35.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
22.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
13.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
12.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
0.0ms	(-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))

series3.3s (8.5%)

Counts

4 → 40

Calls

4 calls:

1.7s	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))
1.0s	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
418.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
191.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))

Compiler

Compiled 2044 to 1301 computations (36.4% saved)

simplify218.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4972	5328
1	4972	5328

prune350.0ms (0.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	149	2	151
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	150	13	163

Error

0.1b

Counts

163 → 13

Compiler

Compiled 5347 to 1531 computations (71.4% saved)

localize42.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)))
0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.0b	(-.f64 1 (pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3))
0.0b	(+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
0.3b	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
3.7b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))

rewrite128.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`pow1_binary64_1131`
45×	`tan-quot_binary64_1229`
21×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `frac-times_binary64_1080`
19×	`pow-prod-down_binary64_1141`
15×	`associate-*r/_binary64_1012`
14×	`associate-*l/_binary64_1013`
10×	`cbrt-unprod_binary64_1103` `prod-exp_binary64_1119` `add-sqr-sqrt_binary64_1092`
8×	`*-un-lft-identity_binary64_1070` `add-cube-cbrt_binary64_1105`
6×	`add-log-exp_binary64_1109`
5×	`frac-sub_binary64_1079`
4×	`associate-r_binary64_1010` `associate-l_binary64_1011` `pow-sqr_binary64_1043` `pow-prod-up_binary64_1140`
3×	`cancel-sign-sub-inv_binary64_1036` `cube-div_binary64_1099` `pow-unpow_binary64_1147`
2×	`pow-plus_binary64_1133` `*-commutative_binary64_1001` `flip-+_binary64_1044` `pow-pow_binary64_1142` `rem-cube-cbrt_binary64_1093` `pow-exp_binary64_1138` `flip3-+_binary64_1073` `associate--l+_binary64_1007`
1×	`flip--_binary64_1045` `swap-sqr_binary64_1037` `cube-prod_binary64_1098` `flip3--_binary64_1074` `pow2_binary64_1151` `sqr-pow_binary64_1042` `unswap-sqr_binary64_1038` `unpow3_binary64_1136` `unpow-prod-down_binary64_1149` `pow-to-exp_binary64_1139` `cube-mult_binary64_1100` `distribute-rgt-in_binary64_1020` `sub-neg_binary64_1063` `diff-log_binary64_1162` `distribute-lft-in_binary64_1019`

Counts

4 → 116

Calls

8 calls:

44.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
21.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
11.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
10.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
0.0ms	(+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))

series12.0s (31.1%)

Counts

4 → 39

Calls

4 calls:

10.1s	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (pow.f64 (.f64 (tan.f64 x) (tan.f64 eps)) 3))) (+.f64 (.f64 1 1) (+.f64 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))) (.f64 1 (.f64 (tan.f64 x) (tan.f64 eps)))))) (tan.f64 x))
784.0ms	(pow.f64 (*.f64 (tan.f64 x) (tan.f64 eps)) 3)
673.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
401.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))

Compiler

Compiled 4626 to 2909 computations (37.1% saved)

simplify163.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4983	5341
1	4983	5341

prune602.0ms (1.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	152	3	155
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	155	13	168

Error

0.1b

Counts

168 → 13

Compiler

Compiled 8122 to 3248 computations (60% saved)

simplify409.0ms (1.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (337.0ms)

Iter	Nodes	Cost
0	3544	2790
1	3544	2790

regimes930.0ms (2.4%)

Accuracy

Total 0.2b remaining (65.4%)

Threshold costs 0.2b (65.4%)

Compiler

Compiled 3436 to 1904 computations (44.6% saved)

bsearch178.0ms (0.5%)

Steps

Iters	Range		Point
10	6.987784473726812e-17	0.0003068032426017399	4.7921130663532265e-05
9	-0.006861731457339584	-2.421970164132134e-09	-4.1505143183695406e-05

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	117	242
1	117	242

end0.0ms (0%)

sample13.0s (33.7%)

Algorithm

1×

intervals

Results

1.7s	3488×	body	1024	valid
1.1s	1275×	body	2048	valid
384.0ms	1360×	body	512	valid
112.0ms	1297×	body	128	valid
106.0ms	576×	body	256	valid
7.0ms	4×	body	4096	valid

Compiler

Compiled 5468 to 3005 computations (45% saved)

Pareto

0.12690450725380445

Details

analyze1.5s (3.9%)

sample147.0ms (0.4%)

simplify169.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0%)

rewrite26.0ms (0.1%)

series815.0ms (2.1%)

simplify125.0ms (0.3%)

prune190.0ms (0.5%)

localize23.0ms (0.1%)

rewrite77.0ms (0.2%)

series3.5s (9%)

simplify133.0ms (0.3%)

prune374.0ms (1%)

localize35.0ms (0.1%)

rewrite106.0ms (0.3%)

series3.3s (8.5%)

simplify218.0ms (0.6%)

prune350.0ms (0.9%)

localize42.0ms (0.1%)

rewrite128.0ms (0.3%)

series12.0s (31.1%)

simplify163.0ms (0.4%)

prune602.0ms (1.6%)

simplify409.0ms (1.1%)

regimes930.0ms (2.4%)

bsearch178.0ms (0.5%)

simplify8.0ms (0%)

end0.0ms (0%)

sample13.0s (33.7%)

Profiling