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)

sample23.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
8.0ms	256×	pre	128	true

Compiler

Compiled 29 to 25 computations (13.8% saved)

simplify141.0ms (4.7%)

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: 8.3b

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

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_4533`
28×	`*-un-lft-identity_binary64_4511`
19×	`times-frac_binary64_4517`
14×	`add-cube-cbrt_binary64_4546`
10×	`difference-of-squares_binary64_4480`
6×	`associate-/r*_binary64_4455`
5×	`distribute-lft-out--_binary64_4463`
4×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549` `add-log-exp_binary64_4550`
3×	`associate-/l*_binary64_4456` `cancel-sign-sub-inv_binary64_4477`
2×	`flip--_binary64_4486` `pow1_binary64_4572` `flip3--_binary64_4515` `associate-/r/_binary64_4457`
1×	`div-exp_binary64_4562` `diff-log_binary64_4603` `frac-2neg_binary64_4522` `sub-neg_binary64_4504` `clear-num_binary64_4510` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`

Counts

2 → 58

Calls

2 calls:

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

series65.0ms (2.2%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(-.f64 (/.f64 x0 (-.f64 1 x1)) x0)
27.0ms	(/.f64 x0 (-.f64 1 x1))

simplify60.0ms (2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5131	940

prune50.0ms (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: 6.7b

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)

rewrite61.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64_4511`
52×	`add-sqr-sqrt_binary64_4533`
22×	`add-cube-cbrt_binary64_4546`
19×	`times-frac_binary64_4517`
18×	`difference-of-squares_binary64_4480`
11×	`distribute-lft-out--_binary64_4463` `pow1_binary64_4572`
9×	`cancel-sign-sub-inv_binary64_4477`
8×	`flip--_binary64_4486` `add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549` `flip3--_binary64_4515` `add-log-exp_binary64_4550` `swap-sqr_binary64_4478`
6×	`associate-l_binary64_4452` `associate-r_binary64_4451` `associate-/r*_binary64_4455`
4×	`distribute-lft-in_binary64_4460` `distribute-rgt-in_binary64_4461` `frac-times_binary64_4521`
3×	`associate-/l*_binary64_4456` `sub-neg_binary64_4504`
2×	`associate-r/_binary64_4453` `associate-/r/_binary64_4457` `associate-l/_binary64_4454`
1×	`pow-prod-up_binary64_4581` `pow-plus_binary64_4574` `flip-+_binary64_4485` `distribute-lft-out_binary64_4462` `flip3-+_binary64_4514` `unswap-sqr_binary64_4479` `pow2_binary64_4592` `+-commutative_binary64_4441` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `div-exp_binary64_4562` `pow-sqr_binary64_4484` `diff-log_binary64_4603` `sum-log_binary64_4602` `frac-2neg_binary64_4522` `pow-prod-down_binary64_4582` `*-commutative_binary64_4442` `clear-num_binary64_4510` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`

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))

series132.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (/.f64 x0 (*.f64 (-.f64 1 x1) (-.f64 1 x1))) x0)
29.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
28.0ms	(/.f64 x0 (-.f64 1 x1))
9.0ms	(*.f64 (-.f64 1 x1) (-.f64 1 x1))

simplify73.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5011	1914

prune163.0ms (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: 5.3b

Counts

136 → 2

Compiler

Compiled 3610 to 2261 computations (37.4% saved)

localize15.0ms (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))
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_4533`
36×	`*-un-lft-identity_binary64_4511`
19×	`times-frac_binary64_4517`
18×	`add-cube-cbrt_binary64_4546`
10×	`difference-of-squares_binary64_4480`
8×	`add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549` `add-log-exp_binary64_4550`
6×	`pow1_binary64_4572` `associate-/r*_binary64_4455`
5×	`distribute-lft-out--_binary64_4463`
4×	`associate-r_binary64_4451`
3×	`associate-/l_binary64_4456` `associate-l*_binary64_4452` `cancel-sign-sub-inv_binary64_4477`
2×	`flip--_binary64_4486` `flip-+_binary64_4485` `distribute-lft-out_binary64_4462` `flip3-+_binary64_4514` `flip3--_binary64_4515` `associate-*r/_binary64_4453` `associate-/r/_binary64_4457`
1×	`unswap-sqr_binary64_4479` `distribute-lft-in_binary64_4460` `+-commutative_binary64_4441` `prod-exp_binary64_4560` `cbrt-unprod_binary64_4544` `div-exp_binary64_4562` `diff-log_binary64_4603` `sum-log_binary64_4602` `distribute-rgt-in_binary64_4461` `frac-2neg_binary64_4522` `pow-prod-down_binary64_4582` `sub-neg_binary64_4504` `*-commutative_binary64_4442` `clear-num_binary64_4510` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`

Counts

4 → 93

Calls

4 calls:

11.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
10.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
7.0ms	(*.f64 x1 (+.f64 x1 -2))
6.0ms	(/.f64 x0 (-.f64 1 x1))

series156.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
29.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
26.0ms	(/.f64 x0 (-.f64 1 x1))
24.0ms	(*.f64 x1 (+.f64 x1 -2))

simplify78.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4931	1557
1	4931	1557

prune123.0ms (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: 4.3b

Counts

107 → 2

Compiler

Compiled 2920 to 1812 computations (37.9% saved)

localize16.0ms (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)

rewrite48.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64_4533`
37×	`*-un-lft-identity_binary64_4511`
20×	`times-frac_binary64_4517`
19×	`add-cube-cbrt_binary64_4546`
12×	`difference-of-squares_binary64_4480`
8×	`add-log-exp_binary64_4550`
7×	`log-pow_binary64_4600` `log-prod_binary64_4597`
6×	`distribute-lft-out--_binary64_4463` `add-cbrt-cube_binary64_4547` `add-exp-log_binary64_4549` `exp-prod_binary64_4563` `cancel-sign-sub-inv_binary64_4477` `associate-/r*_binary64_4455`
5×	`pow1_binary64_4572`
4×	`exp-sum_binary64_4557`
3×	`associate-/l*_binary64_4456`
2×	`flip--_binary64_4486` `flip3--_binary64_4515` `associate-/r/_binary64_4457` `sub-neg_binary64_4504`
1×	`flip-+_binary64_4485` `distribute-lft-out_binary64_4462` `flip3-+_binary64_4514` `exp-diff_binary64_4559` `+-commutative_binary64_4441` `div-exp_binary64_4562` `rem-log-exp_binary64_4552` `diff-log_binary64_4603` `sum-log_binary64_4602` `frac-2neg_binary64_4522` `log-div_binary64_4598` `clear-num_binary64_4510` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`

Counts

4 → 93

Calls

4 calls:

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

series308.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(log.f64 (exp.f64 (-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)))
79.0ms	(-.f64 (/.f64 x0 (+.f64 1 (*.f64 x1 (+.f64 x1 -2)))) x0)
32.0ms	(+.f64 x0 (/.f64 x0 (-.f64 1 x1)))
29.0ms	(/.f64 x0 (-.f64 1 x1))

simplify85.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5624	1841

prune136.0ms (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: 3.3b

Counts

107 → 2

Compiler

Compiled 3107 to 1988 computations (36% saved)

regimes170.0ms (5.7%)

Compiler: Compiled 2252 to 1662 computations (26.2% saved)

bsearch1.0ms (0%)

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

simplify4.0ms (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 (33.6%)

Algorithm

1×

intervals

Results

247.0ms	8000×	pre	128	true
178.0ms	8000×	body	128	valid

Compiler

Compiled 590 to 434 computations (26.4% saved)

Details

analyze3.0ms (0.1%)

sample23.0ms (0.8%)

simplify141.0ms (4.7%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite25.0ms (0.8%)

series65.0ms (2.2%)

simplify60.0ms (2%)

prune50.0ms (1.7%)

localize10.0ms (0.3%)

rewrite61.0ms (2%)

series132.0ms (4.4%)

simplify73.0ms (2.4%)

prune163.0ms (5.4%)

localize15.0ms (0.5%)

rewrite43.0ms (1.4%)

series156.0ms (5.2%)

simplify78.0ms (2.6%)

prune123.0ms (4.1%)

localize16.0ms (0.5%)

rewrite48.0ms (1.6%)

series308.0ms (10.2%)

simplify85.0ms (2.8%)

prune136.0ms (4.5%)

regimes170.0ms (5.7%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.0s (33.6%)

Profiling