Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify99.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 1 (-.f64 x 1))

rewrite54.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_4511`
41×	`times-frac_binary64_4517`
40×	`add-sqr-sqrt_binary64_4533`
24×	`add-cube-cbrt_binary64_4546`
12×	`distribute-lft-out_binary64_4462`
11×	`associate-/r*_binary64_4455`
9×	`add-exp-log_binary64_4549`
8×	`difference-of-squares_binary64_4480`
7×	`add-cbrt-cube_binary64_4547`
6×	`distribute-lft-out--_binary64_4463` `associate-/l*_binary64_4456`
5×	`add-log-exp_binary64_4550`
4×	`pow1_binary64_4572` `difference-of-sqr-1_binary64_4481` `associate-/r/_binary64_4457`
3×	`div-exp_binary64_4562` `div-inv_binary64_4508`
2×	`flip-+_binary64_4485` `flip3-+_binary64_4514` `frac-2neg_binary64_4522` `clear-num_binary64_4510` `cbrt-undiv_binary64_4545`
1×	`flip--_binary64_4486` `1-exp_binary64_4555` `frac-add_binary64_4519` `flip3--_binary64_4515` `+-commutative_binary64_4441` `inv-pow_binary64_4596` `sum-log_binary64_4602` `pow-flip_binary64_4585` `rec-exp_binary64_4561`

Counts

3 → 100

Calls

3 calls:

35.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
7.0ms	(/.f64 1 (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series120.0ms (5.4%)

Counts

3 → 33

Calls

3 calls:

66.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
28.0ms	(/.f64 1 (-.f64 x 1))
26.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 508 to 442 computations (13% saved)

simplify105.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4922	1807
1	4922	1807

prune122.0ms (5.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	131	2	133
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	2	134

Error

Counts

134 → 2

Compiler

Compiled 2140 to 1560 computations (27.1% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 1 x))
0.0b	(/.f64 1 (+.f64 -1 x))
0.0b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
0.0b	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)

rewrite79.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`*-un-lft-identity_binary64_4511`
56×	`times-frac_binary64_4517`
48×	`distribute-lft-out_binary64_4462`
28×	`add-sqr-sqrt_binary64_4533` `add-cube-cbrt_binary64_4546`
24×	`cbrt-prod_binary64_4542`
18×	`cube-prod_binary64_4539` `unpow-prod-down_binary64_4590`
11×	`add-exp-log_binary64_4549`
9×	`add-cbrt-cube_binary64_4547`
8×	`associate-/r*_binary64_4455`
6×	`pow1_binary64_4572` `associate-/l*_binary64_4456` `cube-div_binary64_4540` `div-inv_binary64_4508`
4×	`flip-+_binary64_4485` `flip3-+_binary64_4514` `add-log-exp_binary64_4550` `associate-/r/_binary64_4457`
3×	`div-exp_binary64_4562` `cbrt-div_binary64_4543` `pow-unpow_binary64_4588`
2×	`frac-add_binary64_4519` `unpow3_binary64_4577` `sqr-pow_binary64_4483` `frac-2neg_binary64_4522` `cube-mult_binary64_4541` `clear-num_binary64_4510` `cbrt-undiv_binary64_4545`
1×	`1-exp_binary64_4555` `rem-cbrt-cube_binary64_4535` `pow1/3_binary64_4593` `pow-exp_binary64_4579` `rem-cube-cbrt_binary64_4534` `pow-to-exp_binary64_4580` `inv-pow_binary64_4596` `pow-flip_binary64_4585` `rec-exp_binary64_4561` `pow-pow_binary64_4583`

Counts

4 → 144

Calls

4 calls:

26.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
26.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
9.0ms	(/.f64 1 (+.f64 -1 x))
5.0ms	(/.f64 x (+.f64 1 x))

series222.0ms (10%)

Counts

4 → 44

Calls

4 calls:

80.0ms	(cbrt.f64 (pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3))
78.0ms	(pow.f64 (+.f64 (/.f64 1 (+.f64 -1 x)) (/.f64 x (+.f64 1 x))) 3)
34.0ms	(/.f64 x (+.f64 1 x))
30.0ms	(/.f64 1 (+.f64 -1 x))

Compiler

Compiled 754 to 682 computations (9.5% saved)

simplify94.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4939	3186
1	4939	3186

prune197.0ms (8.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	188	0	188
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	188	2	190

Error

Counts

190 → 2

Compiler

Compiled 3457 to 2676 computations (22.6% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
0.0b	(/.f64 x (+.f64 x 1))
0.1b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
14.5b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite51.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64_4511`
36×	`add-sqr-sqrt_binary64_4533`
32×	`times-frac_binary64_4517`
29×	`add-cube-cbrt_binary64_4546`
19×	`add-exp-log_binary64_4549`
15×	`associate-l_binary64_4452`
13×	`add-cbrt-cube_binary64_4547`
8×	`flip-+_binary64_4485` `flip3-+_binary64_4514`
7×	`pow1_binary64_4572` `associate-/r*_binary64_4455`
6×	`associate-/l*_binary64_4456` `add-log-exp_binary64_4550` `associate-/r/_binary64_4457`
5×	`frac-add_binary64_4519` `distribute-lft-out_binary64_4462` `div-exp_binary64_4562`
4×	`associate-r/_binary64_4453` `prod-exp_binary64_4560` `associate-r*_binary64_4451` `frac-times_binary64_4521`
3×	`unswap-sqr_binary64_4479` `div-inv_binary64_4508` `cbrt-undiv_binary64_4545`
2×	`1-exp_binary64_4555` `distribute-lft-in_binary64_4460` `cbrt-unprod_binary64_4544` `associate-+l+_binary64_4444` `distribute-rgt-in_binary64_4461` `frac-2neg_binary64_4522` `associate-*l/_binary64_4454` `rec-exp_binary64_4561` `clear-num_binary64_4510`
1×	`+-commutative_binary64_4441` `inv-pow_binary64_4596` `sum-log_binary64_4602` `pow-prod-down_binary64_4582` `pow-flip_binary64_4585` `*-commutative_binary64_4442`

Counts

4 → 128

Calls

4 calls:

16.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
12.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
7.0ms	(/.f64 x (+.f64 x 1))
5.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series204.0ms (9.1%)

Counts

4 → 44

Calls

4 calls:

84.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 x (+.f64 x 1)))
53.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
35.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
32.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 843 to 703 computations (16.6% saved)

simplify100.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4969	2597
1	4969	2597

prune184.0ms (8.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	172	2	174

Error

Counts

174 → 2

Compiler

Compiled 3593 to 2409 computations (33% saved)

regimes44.0ms (2%)

Accuracy

Total 0.0b remaining (98.9%)

Threshold costs 0.0b (98.9%)

Compiler

Compiled 297 to 245 computations (17.5% 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%)

sample511.0ms (22.9%)

Algorithm

1×

intervals

Results

231.0ms

8000×

body

128

valid

Compiler

Compiled 145 to 120 computations (17.2% saved)

Details

analyze4.0ms (0.2%)

sample12.0ms (0.5%)

simplify99.0ms (4.4%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

rewrite54.0ms (2.4%)

series120.0ms (5.4%)

simplify105.0ms (4.7%)

prune122.0ms (5.5%)

localize9.0ms (0.4%)

rewrite79.0ms (3.5%)

series222.0ms (10%)

simplify94.0ms (4.2%)

prune197.0ms (8.8%)

localize8.0ms (0.4%)

rewrite51.0ms (2.3%)

series204.0ms (9.1%)

simplify100.0ms (4.5%)

prune184.0ms (8.2%)

regimes44.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample511.0ms (22.9%)

Profiling