Details

analyze524.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify213.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	5230	22

prune2.0ms (0%)

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

30.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

30.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
30.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite17.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_4400` `add-cube-cbrt_binary64_4435` `add-sqr-sqrt_binary64_4422`
9×	`times-frac_binary64_4406`
4×	`add-cbrt-cube_binary64_4436` `add-exp-log_binary64_4438` `add-log-exp_binary64_4439`
3×	`associate-/l_binary64_4345` `associate-/r_binary64_4344`
2×	`flip3--_binary64_4404` `pow1_binary64_4461` `associate-/r/_binary64_4346` `associate-/l/_binary64_4347` `flip--_binary64_4375`
1×	`div-inv_binary64_4397` `flip3-+_binary64_4403` `flip-+_binary64_4374` `cancel-sign-sub-inv_binary64_4366` `cbrt-undiv_binary64_4434` `sub-neg_binary64_4393` `frac-2neg_binary64_4411` `clear-num_binary64_4399` `div-sub_binary64_4405` `div-exp_binary64_4451` `diff-log_binary64_4492`

Counts

2 → 44

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series462.0ms (5.3%)

Counts

2 → 48

Calls

2 calls:

315.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
147.0ms	(-.f64 (.f64 b c) (.f64 a d))

Compiler

Compiled 1068 to 882 computations (17.4% saved)

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4930	1785
1	4930	1785

prune134.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Error

7.3b

Counts

93 → 7

Compiler

Compiled 1841 to 240 computations (87% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

34.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
17.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
0.0b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
17.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
34.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
34.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_4422`
21×	`*-un-lft-identity_binary64_4400` `add-cube-cbrt_binary64_4435`
18×	`times-frac_binary64_4406` `sqrt-prod_binary64_4416`
6×	`sqrt-div_binary64_4417` `add-cbrt-cube_binary64_4436` `add-exp-log_binary64_4438` `pow1_binary64_4461` `add-log-exp_binary64_4439` `associate-/r*_binary64_4344`
3×	`flip3-+_binary64_4403` `flip-+_binary64_4374` `associate-/l*_binary64_4345`
2×	`flip3--_binary64_4404` `pow1/2_binary64_4480` `associate-/r/_binary64_4346` `associate-/l/_binary64_4347` `flip--_binary64_4375` `rem-sqrt-square_binary64_4413` `sqrt-pow1_binary64_4418`
1×	`div-inv_binary64_4397` `cancel-sign-sub-inv_binary64_4366` `cbrt-undiv_binary64_4434` `sub-neg_binary64_4393` `frac-2neg_binary64_4411` `clear-num_binary64_4399` `div-sub_binary64_4405` `div-exp_binary64_4451` `diff-log_binary64_4492`

Counts

4 → 86

Calls

8 calls:

10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

series833.0ms (9.5%)

Counts

4 → 89

Calls

4 calls:

419.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
157.0ms	(-.f64 (.f64 b c) (.f64 a d))
129.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
127.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3518 to 2484 computations (29.4% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4964	3536
1	4964	3536

prune157.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	172	3	175
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	172	10	182

Error

7.3b

Counts

182 → 10

Compiler

Compiled 5296 to 776 computations (85.3% saved)

localize14.0ms (0.2%)

Local error

Found 6 expressions with local error:

29.6b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
0.9b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
0.9b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
29.6b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_4422`
20×	`*-un-lft-identity_binary64_4400` `times-frac_binary64_4406`
19×	`add-cube-cbrt_binary64_4435`
16×	`add-exp-log_binary64_4438`
15×	`associate-r_binary64_4340`
10×	`add-cbrt-cube_binary64_4436`
6×	`pow1_binary64_4461`
5×	`add-log-exp_binary64_4439`
4×	`prod-exp_binary64_4449` `associate-/r/_binary64_4346` `div-exp_binary64_4451`
3×	`unswap-sqr_binary64_4368` `flip3--_binary64_4404` `flip--_binary64_4375` `associate-l_binary64_4341` `associate-/l_binary64_4345` `associate-/r_binary64_4344`
2×	`div-inv_binary64_4397` `associate-*l/_binary64_4343` `frac-times_binary64_4410` `flip3-+_binary64_4403` `flip-+_binary64_4374` `rec-exp_binary64_4450` `1-exp_binary64_4444` `cbrt-undiv_binary64_4434` `cbrt-unprod_binary64_4433`
1×	`pow-prod-down_binary64_4471` `-commutative_binary64_4331` `associate-r/_binary64_4342` `pow-flip_binary64_4474` `un-div-inv_binary64_4398` `cancel-sign-sub-inv_binary64_4366` `sub-neg_binary64_4393` `frac-2neg_binary64_4411` `clear-num_binary64_4399` `inv-pow_binary64_4485` `diff-log_binary64_4492`

Counts

3 → 87

Calls

6 calls:

14.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
6.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

series502.0ms (5.7%)

Counts

3 → 54

Calls

3 calls:

313.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
149.0ms	(-.f64 (.f64 b c) (.f64 a d))
39.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 1344 to 1134 computations (15.6% saved)

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5476	2543

prune109.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	139	2	141
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	142	9	151

Error

7.3b

Counts

151 → 9

Compiler

Compiled 3015 to 624 computations (79.3% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

29.6b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
0.1b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.5b	(-.f64 (.f64 b c) (.f64 a d))
29.6b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
34.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
34.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite107.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

270×	`times-frac_binary64_4406`
173×	`add-sqr-sqrt_binary64_4422`
150×	`associate-r_binary64_4340`
141×	`sqrt-prod_binary64_4416`
138×	`*-un-lft-identity_binary64_4400`
134×	`add-cube-cbrt_binary64_4435`
19×	`add-exp-log_binary64_4438`
18×	`sqrt-div_binary64_4417`
14×	`associate-/r/_binary64_4346`
13×	`add-cbrt-cube_binary64_4436`
12×	`unswap-sqr_binary64_4368`
9×	`flip3-+_binary64_4403` `flip-+_binary64_4374`
8×	`div-inv_binary64_4397` `pow1_binary64_4461`
6×	`add-log-exp_binary64_4439` `div-exp_binary64_4451`
5×	`prod-exp_binary64_4449`
3×	`flip3--_binary64_4404` `cbrt-undiv_binary64_4434` `cbrt-unprod_binary64_4433` `flip--_binary64_4375` `associate-l_binary64_4341`
2×	`associate-*l/_binary64_4343` `frac-times_binary64_4410` `pow1/2_binary64_4480` `rem-sqrt-square_binary64_4413` `sqrt-pow1_binary64_4418`
1×	`pow-prod-down_binary64_4471` `-commutative_binary64_4331` `rec-exp_binary64_4450` `associate-r/_binary64_4342` `1-exp_binary64_4444` `cancel-sign-sub-inv_binary64_4366` `sub-neg_binary64_4393` `diff-log_binary64_4492`

Counts

4 → 229

Calls

8 calls:

53.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
8.0ms	(-.f64 (.f64 b c) (.f64 a d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

series917.0ms (10.5%)

Counts

4 → 84

Calls

4 calls:

318.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
317.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
149.0ms	(-.f64 (.f64 b c) (.f64 a d))
133.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3120 to 2262 computations (27.5% saved)

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5174	8676

prune301.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	311	2	313
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	314	8	322

Error

6.4b

Counts

322 → 8

Compiler

Compiled 11293 to 1956 computations (82.7% saved)

simplify18.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	271	1368
1	271	1368

regimes867.0ms (9.9%)

Accuracy

Total 10.2b remaining (68.7%)

Threshold costs 0b (0%)

Compiler

Compiled 4727 to 2743 computations (42% saved)

bsearch90.0ms (1%)

Steps

Iters	Range		Point
7	4.5166016465378746e+97	2.0183781465867607e+99	2.405852373616342e+98
6	7.488680352529629e-129	5.514159515309266e-128	1.0231125141194154e-128
9	-1.8169334314121202e-277	-2.2835808633478233e-282	-1.3434382879141502e-278
7	-6.241293348906059e-139	-1.8282328041217717e-140	-7.2230969502839745e-140
5	-1.1698921252641593e+93	-3.950917608142549e+92	-1.1437132202364462e+93

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	148
1	85	148

end0.0ms (0%)

sample3.0s (34.7%)

Algorithm

1×

intervals

Results

344.0ms	8000×	body	128	valid
20.0ms	482×	body	128	invalid

Compiler

Compiled 2975 to 1673 computations (43.8% saved)

Pareto

0.14327194478833447

Details

analyze524.0ms (6%)

sample22.0ms (0.3%)

simplify213.0ms (2.4%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite17.0ms (0.2%)

series462.0ms (5.3%)

simplify85.0ms (1%)

prune134.0ms (1.5%)

localize12.0ms (0.1%)

rewrite31.0ms (0.3%)

series833.0ms (9.5%)

simplify60.0ms (0.7%)

prune157.0ms (1.8%)

localize14.0ms (0.2%)

rewrite31.0ms (0.4%)

series502.0ms (5.7%)

simplify76.0ms (0.9%)

prune109.0ms (1.2%)

localize14.0ms (0.2%)

rewrite107.0ms (1.2%)

series917.0ms (10.5%)

simplify104.0ms (1.2%)

prune301.0ms (3.4%)

simplify18.0ms (0.2%)

regimes867.0ms (9.9%)

bsearch90.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (34.7%)

Profiling