Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

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

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample18.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	256×	pre	128	true
6.0ms	256×	body	128	valid

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify142.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

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

Merged error: 8.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

1.0b	(/.f64 x0 (-.f64 1 x1))
7.4b	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_3169`
28×	`*-un-lft-identity_binary64_3147`
19×	`times-frac_binary64_3153`
14×	`add-cube-cbrt_binary64_3182`
10×	`difference-of-squares_binary64_3116`
6×	`associate-/r*_binary64_3091`
5×	`distribute-lft-out--_binary64_3099`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
3×	`cancel-sign-sub-inv_binary64_3113` `associate-/l*_binary64_3092`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `pow1_binary64_3208` `associate-/r/_binary64_3093`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `div-inv_binary64_3144`

Counts

2 → 58

Calls

2 calls:

14.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
6.0ms	(/.f64 x0 (-.f64 1 x1))

series61.0ms (2.1%)

Counts

2 → 6

Calls

2 calls:

34.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
27.0ms	(/.f64 x0 (-.f64 1 x1))

simplify63.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5131	940

prune49.0ms (1.7%)

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

Merged error: 6.6b

Counts

65 → 2

Compiler

Compiled 896 to 538 computations (40% saved)

localize13.0ms (0.5%)

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))
5.9b	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)

rewrite57.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_3147`
52×	`add-sqr-sqrt_binary64_3169`
22×	`add-cube-cbrt_binary64_3182`
19×	`times-frac_binary64_3153`
18×	`difference-of-squares_binary64_3116`
11×	`distribute-lft-out--_binary64_3099` `pow1_binary64_3208`
9×	`cancel-sign-sub-inv_binary64_3113`
8×	`flip--_binary64_3122` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `swap-sqr_binary64_3114` `flip3--_binary64_3151` `add-log-exp_binary64_3186`
6×	`associate-r_binary64_3087` `associate-/r_binary64_3091` `associate-l*_binary64_3088`
4×	`frac-times_binary64_3157` `distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097`
3×	`sub-neg_binary64_3140` `associate-/l*_binary64_3092`
2×	`associate-l/_binary64_3090` `associate-/r/_binary64_3093` `associate-r/_binary64_3089`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `clear-num_binary64_3146` `flip-+_binary64_3121` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `pow-plus_binary64_3210` `cbrt-undiv_binary64_3181` `pow2_binary64_3228` `pow-prod-up_binary64_3217` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `diff-log_binary64_3239` `pow-sqr_binary64_3120` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 122

Calls

4 calls:

17.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
12.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))
11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series133.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
29.0ms	(/.f64 x0 (-.f64 1 x1))
28.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
9.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5011	1914

prune158.0ms (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

Merged error: 5.2b

Counts

136 → 2

Compiler

Compiled 3610 to 2261 computations (37.4% saved)

localize14.0ms (0.5%)

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))
5.9b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite45.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_3169`
36×	`*-un-lft-identity_binary64_3147`
19×	`times-frac_binary64_3153`
18×	`add-cube-cbrt_binary64_3182`
10×	`difference-of-squares_binary64_3116`
8×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
6×	`associate-/r*_binary64_3091` `pow1_binary64_3208`
5×	`distribute-lft-out--_binary64_3099`
4×	`associate-r_binary64_3087`
3×	`cancel-sign-sub-inv_binary64_3113` `associate-/l_binary64_3092` `associate-l*_binary64_3088`
2×	`flip--_binary64_3122` `flip-+_binary64_3121` `flip3--_binary64_3151` `flip3-+_binary64_3150` `distribute-lft-out_binary64_3098` `associate-/r/_binary64_3093` `associate-*r/_binary64_3089`
1×	`*-commutative_binary64_3078` `unswap-sqr_binary64_3115` `clear-num_binary64_3146` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `sub-neg_binary64_3140` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `distribute-lft-in_binary64_3096` `cbrt-undiv_binary64_3181` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `diff-log_binary64_3239` `distribute-rgt-in_binary64_3097` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 93

Calls

4 calls:

14.0ms	(+.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))

series154.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
29.0ms	(*.f64 x1 (+.f64 x1 -2))
27.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
27.0ms	(/.f64 x0 (-.f64 1 x1))

simplify76.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4931	1557
1	4931	1557

prune119.0ms (4.1%)

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

Merged error: 4.1b

Counts

107 → 2

Compiler

Compiled 2920 to 1812 computations (37.9% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
1.0b	(/.f64 x0 (-.f64 1 x1))
4.7b	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
5.9b	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)

rewrite48.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_3169`
37×	`*-un-lft-identity_binary64_3147`
20×	`times-frac_binary64_3153`
19×	`add-cube-cbrt_binary64_3182`
12×	`difference-of-squares_binary64_3116`
8×	`add-log-exp_binary64_3186`
7×	`log-prod_binary64_3233` `log-pow_binary64_3236`
6×	`add-exp-log_binary64_3185` `cancel-sign-sub-inv_binary64_3113` `add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091` `distribute-lft-out--_binary64_3099` `exp-prod_binary64_3199`
5×	`pow1_binary64_3208`
4×	`exp-sum_binary64_3193`
3×	`associate-/l*_binary64_3092`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `sub-neg_binary64_3140` `associate-/r/_binary64_3093`
1×	`rem-log-exp_binary64_3188` `clear-num_binary64_3146` `flip-+_binary64_3121` `frac-2neg_binary64_3158` `flip3-+_binary64_3150` `distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `exp-diff_binary64_3195` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239` `log-div_binary64_3234` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 93

Calls

4 calls:

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

series293.0ms (10%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
71.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
27.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
27.0ms	(/.f64 x0 (-.f64 1 x1))

simplify76.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5624	1841

prune133.0ms (4.5%)

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

Merged error: 3.1b

Counts

107 → 2

Compiler

Compiled 3107 to 1988 computations (36% saved)

regimes157.0ms (5.3%)

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%)

sample1.0s (34.3%)

Algorithm

1×

intervals

Results

249.0ms	8000×	pre	128	true
179.0ms	8000×	body	128	valid

Compiler

Compiled 590 to 434 computations (26.4% saved)

Details

analyze3.0ms (0.1%)

sample18.0ms (0.6%)

simplify142.0ms (4.8%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite23.0ms (0.8%)

series61.0ms (2.1%)

simplify63.0ms (2.1%)

prune49.0ms (1.7%)

localize13.0ms (0.5%)

rewrite57.0ms (1.9%)

series133.0ms (4.5%)

simplify68.0ms (2.3%)

prune158.0ms (5.4%)

localize14.0ms (0.5%)

rewrite45.0ms (1.5%)

series154.0ms (5.2%)

simplify76.0ms (2.6%)

prune119.0ms (4.1%)

localize16.0ms (0.6%)

rewrite48.0ms (1.6%)

series293.0ms (10%)

simplify76.0ms (2.6%)

prune133.0ms (4.5%)

regimes157.0ms (5.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (34.3%)

Profiling