Details

analyze306.0ms (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample26.0ms (0.9%)

Algorithm

1×

intervals

Results

12.0ms	87×	body	1024	valid
4.0ms	48×	body	512	valid
2.0ms	85×	body	128	valid
1.0ms	10×	body	2048	valid
1.0ms	26×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify90.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune2.0ms (0.1%)

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

Merged error: 44.7b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
4.2b	(-.f64 (exp.f64 x) 1)

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1123`
30×	`*-un-lft-identity_binary64_1101`
21×	`times-frac_binary64_1107`
15×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070`
7×	`associate-/r*_binary64_1045`
5×	`difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`add-exp-log_binary64_1139` `associate-/l*_binary64_1046` `cancel-sign-sub-inv_binary64_1067`
2×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 63

Calls

2 calls:

12.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series43.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

34.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
9.0ms	(-.f64 (exp.f64 x) 1)

simplify74.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4915	1129
1	4915	1129

prune70.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

Compiler

Compiled 957 to 474 computations (50.5% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
0.0b	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite31.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_1123`
17×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
15×	`add-cbrt-cube_binary64_1137`
14×	`add-exp-log_binary64_1139`
13×	`pow1_binary64_1162`
9×	`times-frac_binary64_1107` `associate-l_binary64_1042`
7×	`associate-r_binary64_1041`
6×	`associate-*r/_binary64_1043`
5×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `distribute-lft-in_binary64_1050` `pow-prod-down_binary64_1172` `distribute-rgt-in_binary64_1051`
4×	`add-log-exp_binary64_1140`
3×	`-commutative_binary64_1032` `flip3-+_binary64_1104` `associate-/l_binary64_1046` `flip-+_binary64_1075` `associate-/r*_binary64_1045`
2×	`associate-/r/_binary64_1047` `unswap-sqr_binary64_1069`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

4 → 93

Calls

4 calls:

7.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
6.0ms	(*.f64 x 1/6)
6.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
6.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))

series112.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))
34.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
26.0ms	(/.f64 (exp.f64 x) (+.f64 x (.f64 x (.f64 x (+.f64 1/2 (*.f64 x 1/6))))))
12.0ms	(*.f64 x 1/6)

simplify94.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4908	1844
1	4908	1844

prune101.0ms (3.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	105	3	108

Merged error: 0.0b

Counts

108 → 3

Compiler

Compiled 2160 to 1340 computations (38% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_1140`
6×	`add-sqr-sqrt_binary64_1123`
4×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
3×	`sum-log_binary64_1192` `associate-r_binary64_1041` `associate-l_binary64_1042`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-+r+_binary64_1033` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

2 → 31

Calls

2 calls:

9.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series19.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

11.0ms	(*.f64 x 1/12)
9.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify82.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4872	417
1	4872	417

prune35.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	37	3	40

Merged error: 0.0b

Counts

40 → 3

Compiler

Compiled 533 to 428 computations (19.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

rewrite60.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1132`
23×	`add-sqr-sqrt_binary64_1123`
18×	`cbrt-div_binary64_1133`
15×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
11×	`pow1_binary64_1162`
9×	`pow1/3_binary64_1183` `flip3-+_binary64_1104` `flip-+_binary64_1075`
6×	`add-exp-log_binary64_1139` `swap-sqr_binary64_1068` `associate-r_binary64_1041` `associate-l_binary64_1042`
4×	`frac-times_binary64_1111` `add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137` `unswap-sqr_binary64_1069`
2×	`pow-prod-up_binary64_1171` `associate-r/_binary64_1043` `pow-sqr_binary64_1074` `pow-prod-down_binary64_1172` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `pow2_binary64_1182`

Counts

4 → 87

Calls

4 calls:

22.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
9.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
9.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
9.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

series170.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
41.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
40.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
39.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

simplify101.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4865	2822
1	4865	2822

prune234.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	99	3	102

Merged error: 0.0b

Counts

102 → 3

Compiler

Compiled 3987 to 3261 computations (18.2% saved)

regimes132.0ms (4.3%)

Compiler: Compiled 1516 to 1144 computations (24.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample1.2s (39.4%)

Algorithm

1×

intervals

Results

368.0ms	2601×	body	1024	valid
103.0ms	1310×	body	512	valid
73.0ms	3120×	body	128	valid
44.0ms	286×	body	2048	valid
35.0ms	683×	body	256	valid

Compiler

Compiled 451 to 349 computations (22.6% saved)

Details

analyze306.0ms (10%)

sample26.0ms (0.9%)

simplify90.0ms (3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite22.0ms (0.7%)

series43.0ms (1.4%)

simplify74.0ms (2.4%)

prune70.0ms (2.3%)

localize9.0ms (0.3%)

rewrite31.0ms (1%)

series112.0ms (3.7%)

simplify94.0ms (3.1%)

prune101.0ms (3.3%)

localize6.0ms (0.2%)

rewrite14.0ms (0.5%)

series19.0ms (0.6%)

simplify82.0ms (2.7%)

prune35.0ms (1.2%)

localize11.0ms (0.3%)

rewrite60.0ms (2%)

series170.0ms (5.6%)

simplify101.0ms (3.3%)

prune234.0ms (7.7%)

regimes132.0ms (4.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (39.4%)

Profiling