Details

analyze709.0ms (7.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4983	154
1	4983	154
0	4	4
1	4	4

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

Symmetry

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify128.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

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

25.8b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.7b	(-.f64 (.f64 b c) (.f64 a d))
25.3b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

25.6b

Rules

11×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `*-un-lft-identity_binary64_3147`
9×	`times-frac_binary64_3153`
7×	`add-log-exp_binary64_3186`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
3×	`pow1_binary64_3208` `associate-/l_binary64_3092` `associate-/r_binary64_3091`
2×	`flip3--_binary64_3151` `associate-/l/_binary64_3094` `flip--_binary64_3122` `flip3-+_binary64_3150` `associate-/r/_binary64_3093` `flip-+_binary64_3121`
1×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `div-sub_binary64_3152` `clear-num_binary64_3146` `div-inv_binary64_3144` `diff-log_binary64_3239` `sub-neg_binary64_3140` `cancel-sign-sub-inv_binary64_3113` `sum-log_binary64_3238` `+-commutative_binary64_3077`

Counts

3 → 55

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

Compiler

Compiled 1509 to 201 computations (86.7% saved)

series623.0ms (6.8%)

Error

4.2b

Counts

3 → 69

Calls

3 calls:

338.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
149.0ms	(-.f64 (.f64 b c) (.f64 a d))
86.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 2499 to 1600 computations (36% saved)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5011	2358

prune102.0ms (1.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	112	12	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Error

4.1b

Counts

125 → 12

Compiler

Compiled 2545 to 433 computations (83% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 c b) (.f64 d a))
15.7b	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
26.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite117.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

23×	`add-sqr-sqrt_binary64_3169`
21×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
18×	`sqrt-prod_binary64_3163` `times-frac_binary64_3153`
6×	`pow1_binary64_3208` `add-log-exp_binary64_3186` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164` `associate-/r*_binary64_3091`
3×	`flip3-+_binary64_3150` `flip-+_binary64_3121` `associate-/l*_binary64_3092`
2×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `flip3--_binary64_3151` `associate-/l/_binary64_3094` `flip--_binary64_3122` `associate-/r/_binary64_3093`
1×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `div-sub_binary64_3152` `clear-num_binary64_3146` `div-inv_binary64_3144` `diff-log_binary64_3239` `sub-neg_binary64_3140` `cancel-sign-sub-inv_binary64_3113`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
6.0ms	(-.f64 (.f64 c b) (.f64 d a))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3272 to 353 computations (89.2% saved)

series933.0ms (10.1%)

Error

4.1b

Counts

4 → 96

Calls

4 calls:

427.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
161.0ms	(-.f64 (.f64 c b) (.f64 d a))
131.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
130.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 6048 to 3256 computations (46.2% saved)

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5220	3816

prune167.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	178	4	182
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	183	11	194

Error

4.1b

Counts

194 → 11

Compiler

Compiled 5604 to 874 computations (84.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (.f64 c b) (.f64 d a))
15.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
26.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite113.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

23×	`add-sqr-sqrt_binary64_3169`
21×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
18×	`sqrt-prod_binary64_3163` `times-frac_binary64_3153`
6×	`pow1_binary64_3208` `add-log-exp_binary64_3186` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164` `associate-/l*_binary64_3092`
3×	`flip3-+_binary64_3150` `flip-+_binary64_3121` `associate-/r*_binary64_3091`
2×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `rem-sqrt-square_binary64_3160` `associate-/l/_binary64_3094` `flip3--_binary64_3151` `associate-/r/_binary64_3093` `flip--_binary64_3122`
1×	`div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144` `diff-log_binary64_3239` `sub-neg_binary64_3140` `cancel-sign-sub-inv_binary64_3113`

Counts

4 → 85

Calls

4 calls:

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

Compiler

Compiled 3408 to 523 computations (84.7% saved)

series866.0ms (9.4%)

Error

4.1b

Counts

4 → 92

Calls

4 calls:

357.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
159.0ms	(-.f64 (.f64 c b) (.f64 d a))
134.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
120.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 7206 to 4325 computations (40% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4999	3848
1	4999	3848

prune175.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	177	11	188

Error

4.1b

Counts

188 → 11

Compiler

Compiled 5910 to 1262 computations (78.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.5b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
0.7b	(-.f64 (.f64 c b) (.f64 d a))
24.9b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))

rewrite182.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

90×	`times-frac_binary64_3153`
56×	`add-cube-cbrt_binary64_3182` `add-sqr-sqrt_binary64_3169` `*-un-lft-identity_binary64_3147`
18×	`associate-/r*_binary64_3091`
17×	`add-exp-log_binary64_3185`
11×	`add-cbrt-cube_binary64_3183` `associate-/r/_binary64_3093`
8×	`div-exp_binary64_3198` `add-log-exp_binary64_3186`
6×	`div-inv_binary64_3144` `flip3--_binary64_3151` `flip--_binary64_3122` `associate-/l*_binary64_3092`
5×	`pow1_binary64_3208`
4×	`cbrt-undiv_binary64_3181`
2×	`frac-2neg_binary64_3158` `clear-num_binary64_3146` `flip3-+_binary64_3150` `associate-/l/_binary64_3094` `flip-+_binary64_3121` `1-exp_binary64_3191` `rec-exp_binary64_3197`
1×	`diff-log_binary64_3239` `sub-neg_binary64_3140` `cancel-sign-sub-inv_binary64_3113` `inv-pow_binary64_3232` `pow-flip_binary64_3221` `sum-log_binary64_3238` `+-commutative_binary64_3077`

Counts

4 → 138

Calls

4 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
9.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
4.0ms	(-.f64 (.f64 c b) (.f64 d a))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 4578 to 875 computations (80.9% saved)

series982.0ms (10.7%)

Error

4.1b

Counts

4 → 102

Calls

4 calls:

357.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
293.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
156.0ms	(-.f64 (.f64 c b) (.f64 d a))
90.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 4914 to 3396 computations (30.9% saved)

simplify86.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4997	6724
1	4997	6724

prune174.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	238	2	240
Fresh	1	7	8
Picked	1	0	1
Done	1	1	2
Total	241	10	251

Error

1.2b

Counts

251 → 10

Compiler

Compiled 5852 to 1028 computations (82.4% saved)

regimes1.6s (17%)

Accuracy

Total 13.3b remaining (92.1%)

Threshold costs 0b (0%)

Compiler

Compiled 9269 to 5378 computations (42% saved)

bsearch89.0ms (1%)

Steps

Iters	Range		Point
7	3.290682121393716e+152	2.422979362772352e+154	1.4163261492702185e+153
9	1.1684044936491682e-157	2.605506511486811e-150	5.980746905707731e-154
10	-4.998751043810138e-102	-1.1251155016854812e-112	-1.2031460365109471e-102
7	-2.846347883263074e+54	-4.362918788324185e+52	-2.6657023148269232e+54

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	81	122
1	81	122

Removed

()

end0.0ms (0%)

sample1.8s (19.7%)

Algorithm

1×

intervals

Results

342.0ms	8000×	body	128	valid
18.0ms	453×	body	128	invalid

Compiler

Compiled 1946 to 1120 computations (42.4% saved)

Details

analyze709.0ms (7.7%)

sample22.0ms (0.2%)

simplify128.0ms (1.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite81.0ms (0.9%)

series623.0ms (6.8%)

simplify66.0ms (0.7%)

prune102.0ms (1.1%)

localize12.0ms (0.1%)

rewrite117.0ms (1.3%)

series933.0ms (10.1%)

simplify81.0ms (0.9%)

prune167.0ms (1.8%)

localize16.0ms (0.2%)

rewrite113.0ms (1.2%)

series866.0ms (9.4%)

simplify76.0ms (0.8%)

prune175.0ms (1.9%)

localize14.0ms (0.2%)

rewrite182.0ms (2%)

series982.0ms (10.7%)

simplify86.0ms (0.9%)

prune174.0ms (1.9%)

regimes1.6s (17%)

bsearch89.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.8s (19.7%)

Profiling