Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample27.0ms (0.1%)

Algorithm

1×

intervals

Results

10.0ms	65×	body	1024	valid
6.0ms	140×	body	128	valid
5.0ms	43×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify114.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune5.0ms (0%)

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

Merged error: 20.7b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize20.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite71.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_4192`
118×	`times-frac_binary64_4176`
113×	`*-un-lft-identity_binary64_4170`
72×	`sqrt-prod_binary64_4186`
54×	`add-cube-cbrt_binary64_4205`
27×	`cancel-sign-sub-inv_binary64_4136`
25×	`difference-of-squares_binary64_4139`
13×	`distribute-lft-out--_binary64_4122` `associate-/r*_binary64_4114`
11×	`add-exp-log_binary64_4208`
10×	`distribute-lft-out_binary64_4121`
7×	`pow1_binary64_4231` `add-cbrt-cube_binary64_4206` `div-inv_binary64_4167`
6×	`pow-flip_binary64_4244` `associate-/l*_binary64_4115`
5×	`add-log-exp_binary64_4209`
4×	`sqrt-div_binary64_4187` `associate-/r/_binary64_4116` `div-exp_binary64_4221`
2×	`1-exp_binary64_4214` `flip-+_binary64_4144` `frac-2neg_binary64_4181` `inv-pow_binary64_4255` `rec-exp_binary64_4220` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169`
1×	`frac-sub_binary64_4179` `flip3--_binary64_4174` `diff-log_binary64_4262` `flip--_binary64_4145` `sub-neg_binary64_4163`

Counts

3 → 173

Calls

3 calls:

44.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series97.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(/.f64 1 (sqrt.f64 x))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify104.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4920	3438
1	4920	3438

prune547.0ms (1.6%)

Pruning

54 alts after pruning (53 fresh and 1 done)

	Pruned	Kept	Total
New	129	53	182
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	129	54	183

Merged error: 20.2b

Counts

183 → 54

Compiler

Compiled 2734 to 2128 computations (22.2% saved)

localize26.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
2.7b	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))

rewrite229.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

254×	`add-sqr-sqrt_binary64_4192`
240×	`times-frac_binary64_4176`
198×	`*-un-lft-identity_binary64_4170`
140×	`cbrt-prod_binary64_4201`
139×	`sqrt-prod_binary64_4186`
100×	`add-cube-cbrt_binary64_4205`
49×	`difference-of-squares_binary64_4139`
48×	`cancel-sign-sub-inv_binary64_4136`
20×	`distribute-lft-out--_binary64_4122`
19×	`distribute-lft-out_binary64_4121`
13×	`associate-/r*_binary64_4114`
12×	`associate-/l*_binary64_4115`
7×	`add-exp-log_binary64_4208`
5×	`add-cbrt-cube_binary64_4206` `div-inv_binary64_4167` `add-log-exp_binary64_4209`
4×	`sqrt-div_binary64_4187` `associate-/r/_binary64_4116`
3×	`pow1_binary64_4231`
2×	`flip-+_binary64_4144` `frac-2neg_binary64_4181` `flip3-+_binary64_4173` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169` `div-exp_binary64_4221`
1×	`frac-sub_binary64_4179` `flip3--_binary64_4174` `diff-log_binary64_4262` `flip--_binary64_4145` `sub-neg_binary64_4163`

Counts

3 → 258

Calls

3 calls:

145.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
9.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))

series94.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

36.0ms	(-.f64 (/.f64 (cbrt.f64 1) (sqrt.f64 x)) (/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x))))
31.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 x))
27.0ms	(/.f64 (cbrt.f64 1) (sqrt.f64 (+.f64 1 x)))

simplify113.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

267 → 267

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5057	7305

prune1.8s (5.4%)

Pruning

128 alts after pruning (126 fresh and 2 done)

	Pruned	Kept	Total
New	190	77	267
Fresh	3	49	52
Picked	0	1	1
Done	0	1	1
Total	193	128	321

Merged error: 20.2b

Counts

321 → 128

Compiler

Compiled 7898 to 6816 computations (13.7% saved)

localize9.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))

rewrite86.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_4192`
118×	`times-frac_binary64_4176`
113×	`*-un-lft-identity_binary64_4170`
72×	`sqrt-prod_binary64_4186`
54×	`add-cube-cbrt_binary64_4205`
27×	`cancel-sign-sub-inv_binary64_4136`
25×	`difference-of-squares_binary64_4139`
13×	`distribute-lft-out--_binary64_4122` `associate-/r*_binary64_4114`
11×	`add-exp-log_binary64_4208`
10×	`distribute-lft-out_binary64_4121`
7×	`pow1_binary64_4231` `add-cbrt-cube_binary64_4206` `div-inv_binary64_4167`
6×	`pow-flip_binary64_4244` `associate-/l*_binary64_4115`
5×	`add-log-exp_binary64_4209`
4×	`sqrt-div_binary64_4187` `associate-/r/_binary64_4116` `div-exp_binary64_4221`
2×	`1-exp_binary64_4214` `flip-+_binary64_4144` `frac-2neg_binary64_4181` `inv-pow_binary64_4255` `rec-exp_binary64_4220` `pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `flip3-+_binary64_4173` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169`
1×	`frac-sub_binary64_4179` `flip3--_binary64_4174` `diff-log_binary64_4262` `flip--_binary64_4145` `sub-neg_binary64_4163`

Counts

3 → 173

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

series104.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

53.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 1 x))))
32.0ms	(/.f64 1 (sqrt.f64 x))
18.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))

simplify122.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4944	3438
1	4944	3438

prune1.3s (3.9%)

Pruning

165 alts after pruning (162 fresh and 3 done)

	Pruned	Kept	Total
New	136	46	182
Fresh	9	116	125
Picked	0	1	1
Done	0	2	2
Total	145	165	310

Merged error: 20.2b

Counts

310 → 165

Compiler

Compiled 6488 to 5519 computations (14.9% saved)

localize30.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x)))

0.3b

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x))

2.7b

(-.f64 (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x))))

rewrite348.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

432×	`cbrt-prod_binary64_4201`
416×	`add-sqr-sqrt_binary64_4192`
378×	`times-frac_binary64_4176`
285×	`*-un-lft-identity_binary64_4170`
214×	`sqrt-prod_binary64_4186`
146×	`add-cube-cbrt_binary64_4205`
81×	`difference-of-squares_binary64_4139`
69×	`cancel-sign-sub-inv_binary64_4136`
29×	`distribute-lft-out--_binary64_4122`
28×	`distribute-lft-out_binary64_4121`
18×	`associate-/l*_binary64_4115`
13×	`associate-/r*_binary64_4114`
7×	`add-exp-log_binary64_4208`
5×	`add-cbrt-cube_binary64_4206` `div-inv_binary64_4167` `add-log-exp_binary64_4209`
4×	`sqrt-div_binary64_4187` `associate-/r/_binary64_4116`
3×	`pow1_binary64_4231`
2×	`flip-+_binary64_4144` `frac-2neg_binary64_4181` `flip3-+_binary64_4173` `cbrt-undiv_binary64_4204` `clear-num_binary64_4169` `div-exp_binary64_4221`
1×	`frac-sub_binary64_4179` `flip3--_binary64_4174` `diff-log_binary64_4262` `flip--_binary64_4145` `sub-neg_binary64_4163`

Counts

3 → 365

Calls

3 calls:

248.0ms

(-.f64 (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x))))

8.0ms

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x)))

6.0ms

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x))

series109.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

48.0ms

(-.f64 (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x)) (/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x))))

42.0ms

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 x))

19.0ms

(/.f64 (cbrt.f64 (cbrt.f64 1)) (sqrt.f64 (+.f64 1 x)))

simplify228.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

374 → 374

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4940	12630
1	4940	12630

prune4.6s (13.6%)

Pruning

249 alts after pruning (245 fresh and 4 done)

	Pruned	Kept	Total
New	280	94	374
Fresh	10	151	161
Picked	0	1	1
Done	0	3	3
Total	290	249	539

Merged error: 20.2b

Counts

539 → 249

Compiler

Compiled 8343 to 7385 computations (11.5% saved)

regimes3.3s (9.7%)

Compiler: Compiled 30831 to 28308 computations (8.2% saved)

bsearch1.9s (5.8%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	52
1	40	52

end0.0ms (0%)

sample18.2s (54.1%)

Algorithm

1×

intervals

Results

431.0ms	2262×	body	1024	valid
212.0ms	4260×	body	128	valid
137.0ms	974×	body	512	valid
47.0ms	504×	body	256	valid

Compiler

Compiled 15619 to 14338 computations (8.2% saved)

Pareto

1.0

Details

analyze2.0ms (0%)

sample27.0ms (0.1%)

simplify114.0ms (0.3%)

prune5.0ms (0%)

localize20.0ms (0.1%)

rewrite71.0ms (0.2%)

series97.0ms (0.3%)

simplify104.0ms (0.3%)

prune547.0ms (1.6%)

localize26.0ms (0.1%)

rewrite229.0ms (0.7%)

series94.0ms (0.3%)

simplify113.0ms (0.3%)

prune1.8s (5.4%)

localize9.0ms (0%)

rewrite86.0ms (0.3%)

series104.0ms (0.3%)

simplify122.0ms (0.4%)

prune1.3s (3.9%)

localize30.0ms (0.1%)

rewrite348.0ms (1%)

series109.0ms (0.3%)

simplify228.0ms (0.7%)

prune4.6s (13.6%)

regimes3.3s (9.7%)

bsearch1.9s (5.8%)

simplify8.0ms (0%)

end0.0ms (0%)

sample18.2s (54.1%)

Profiling