Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample31.0ms (1%)

Algorithm

1×

intervals

Results

13.0ms	256×	pre	128	true
10.0ms	256×	body	128	valid

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify202.0ms (6.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	498	10
1	498	10

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

Error

8.4b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.5b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite27.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_1123`
28×	`*-un-lft-identity_binary64_1101`
19×	`times-frac_binary64_1107`
14×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070`
6×	`associate-/r*_binary64_1045`
5×	`distribute-lft-out--_binary64_1053`
4×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`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 → 58

Calls

2 calls:

13.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series86.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

55.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
31.0ms	(/.f64 x0 (-.f64 1 x1))

simplify69.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5131	940

prune61.0ms (1.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	2	65

Error

6.7b

Counts

65 → 2

Compiler

Compiled 896 to 538 computations (40% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.0b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite69.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_1101`
52×	`add-sqr-sqrt_binary64_1123`
22×	`add-cube-cbrt_binary64_1136`
19×	`times-frac_binary64_1107`
18×	`difference-of-squares_binary64_1070`
11×	`pow1_binary64_1162` `distribute-lft-out--_binary64_1053`
9×	`cancel-sign-sub-inv_binary64_1067`
8×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `flip--_binary64_1076` `flip3--_binary64_1105` `add-cbrt-cube_binary64_1137` `swap-sqr_binary64_1068`
6×	`associate-r_binary64_1041` `associate-l_binary64_1042` `associate-/r*_binary64_1045`
4×	`frac-times_binary64_1111` `distribute-lft-in_binary64_1050` `distribute-rgt-in_binary64_1051`
3×	`sub-neg_binary64_1094` `associate-/l*_binary64_1046`
2×	`associate-r/_binary64_1043` `associate-/r/_binary64_1047` `associate-l/_binary64_1044`
1×	`pow-plus_binary64_1164` `diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `pow-prod-up_binary64_1171` `prod-exp_binary64_1150` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `pow-sqr_binary64_1074` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `pow2_binary64_1182`

Counts

4 → 122

Calls

4 calls:

21.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
15.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
11.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
11.0ms	(/.f64 x0 (-.f64 1 x1))

series146.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
34.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
31.0ms	(/.f64 x0 (-.f64 1 x1))
15.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify121.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5011	1914

prune171.0ms (5.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	134	2	136

Error

5.3b

Counts

136 → 2

Compiler

Compiled 3610 to 2261 computations (37.4% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 x1 (+.f64 x1 -2))
0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
6.0b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite43.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_1123`
36×	`*-un-lft-identity_binary64_1101`
19×	`times-frac_binary64_1107`
18×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070`
8×	`add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`pow1_binary64_1162` `associate-/r*_binary64_1045`
5×	`distribute-lft-out--_binary64_1053`
4×	`associate-r_binary64_1041`
3×	`associate-/l_binary64_1046` `associate-l*_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
2×	`distribute-lft-out_binary64_1052` `flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-*r/_binary64_1043` `associate-/r/_binary64_1047` `flip-+_binary64_1075`
1×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `div-inv_binary64_1098` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `distribute-rgt-in_binary64_1051`

Counts

4 → 93

Calls

4 calls:

10.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
6.0ms	(*.f64 x1 (+.f64 x1 -2))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series149.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

68.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
30.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
26.0ms	(*.f64 x1 (+.f64 x1 -2))
25.0ms	(/.f64 x0 (-.f64 1 x1))

simplify81.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4931	1557
1	4931	1557

prune123.0ms (3.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Error

4.3b

Counts

107 → 2

Compiler

Compiled 2920 to 1812 computations (37.9% saved)

localize17.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.9b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
6.0b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite49.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_1123`
37×	`*-un-lft-identity_binary64_1101`
20×	`times-frac_binary64_1107`
19×	`add-cube-cbrt_binary64_1136`
12×	`difference-of-squares_binary64_1070`
8×	`add-log-exp_binary64_1140`
7×	`log-prod_binary64_1187` `log-pow_binary64_1190`
6×	`add-exp-log_binary64_1139` `distribute-lft-out--_binary64_1053` `exp-prod_binary64_1153` `add-cbrt-cube_binary64_1137` `cancel-sign-sub-inv_binary64_1067` `associate-/r*_binary64_1045`
5×	`pow1_binary64_1162`
4×	`exp-sum_binary64_1147`
3×	`associate-/l*_binary64_1046`
2×	`sub-neg_binary64_1094` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `distribute-lft-out_binary64_1052` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `rem-log-exp_binary64_1142` `exp-diff_binary64_1149` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `+-commutative_binary64_1031` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `log-div_binary64_1188`

Counts

4 → 93

Calls

4 calls:

13.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
11.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series292.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
70.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
28.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
27.0ms	(/.f64 x0 (-.f64 1 x1))

simplify77.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5624	1841

prune146.0ms (4.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	2	107

Error

3.3b

Counts

107 → 2

Compiler

Compiled 3107 to 1988 computations (36% saved)

regimes157.0ms (5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Compiler

Compiled 2252 to 1662 computations (26.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	111
1	58	111

end0.0ms (0%)

sample997.0ms (31.6%)

Algorithm

1×

intervals

Results

230.0ms	8000×	pre	128	true
185.0ms	8000×	body	128	valid

Compiler

Compiled 590 to 434 computations (26.4% saved)

Details

analyze6.0ms (0.2%)

sample31.0ms (1%)

simplify202.0ms (6.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite27.0ms (0.9%)

series86.0ms (2.7%)

simplify69.0ms (2.2%)

prune61.0ms (1.9%)

localize10.0ms (0.3%)

rewrite69.0ms (2.2%)

series146.0ms (4.6%)

simplify121.0ms (3.8%)

prune171.0ms (5.4%)

localize12.0ms (0.4%)

rewrite43.0ms (1.4%)

series149.0ms (4.7%)

simplify81.0ms (2.6%)

prune123.0ms (3.9%)

localize17.0ms (0.5%)

rewrite49.0ms (1.6%)

series292.0ms (9.3%)

simplify77.0ms (2.4%)

prune146.0ms (4.6%)

regimes157.0ms (5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample997.0ms (31.6%)

Profiling