Details

analyze525.0ms (5.7%)

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 (0.2%)

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)

simplify221.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (125.0ms)

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)

localize10.0ms (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)))

rewrite88.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

25.6b

Rules

11×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
9×	`times-frac_binary64_1448`
7×	`add-log-exp_binary64_1481`
5×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
3×	`pow1_binary64_1503` `associate-/l_binary64_1387` `associate-/r_binary64_1386`
2×	`flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `flip3-+_binary64_1445` `associate-/r/_binary64_1388` `flip-+_binary64_1416`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

3 → 55

Calls

3 calls:

13.0ms	(/.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)

series632.0ms (6.9%)

Error

4.2b

Counts

3 → 69

Calls

3 calls:

340.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
146.0ms	(-.f64 (.f64 b c) (.f64 a d))
94.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 2499 to 1600 computations (36% saved)

simplify61.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5011	2358

prune104.0ms (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)))

rewrite113.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

23×	`add-sqr-sqrt_binary64_1464`
21×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
18×	`sqrt-prod_binary64_1458` `times-frac_binary64_1448`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `associate-/r*_binary64_1386`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/l*_binary64_1387`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `flip3--_binary64_1446` `associate-/l/_binary64_1389` `flip--_binary64_1417` `associate-/r/_binary64_1388`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `div-sub_binary64_1447` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

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))))
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 3272 to 353 computations (89.2% saved)

series968.0ms (10.6%)

Error

4.1b

Counts

4 → 96

Calls

4 calls:

449.0ms	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
162.0ms	(-.f64 (.f64 c b) (.f64 d a))
137.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
127.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 6048 to 3256 computations (46.2% saved)

simplify82.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5220	3816

prune165.0ms (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)

localize14.0ms (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)))

rewrite122.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

23×	`add-sqr-sqrt_binary64_1464`
21×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
18×	`sqrt-prod_binary64_1458` `times-frac_binary64_1448`
6×	`pow1_binary64_1503` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-div_binary64_1459` `associate-/l*_binary64_1387`
3×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `associate-/r*_binary64_1386`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `rem-sqrt-square_binary64_1455` `associate-/l/_binary64_1389` `flip3--_binary64_1446` `associate-/r/_binary64_1388` `flip--_binary64_1417`
1×	`div-exp_binary64_1493` `cbrt-undiv_binary64_1476` `frac-2neg_binary64_1453` `clear-num_binary64_1441` `div-inv_binary64_1439` `diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408`

Counts

4 → 85

Calls

4 calls:

13.0ms	(/.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)

series873.0ms (9.5%)

Error

4.1b

Counts

4 → 92

Calls

4 calls:

356.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
158.0ms	(-.f64 (.f64 c b) (.f64 d a))
134.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
133.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 7206 to 4325 computations (40% saved)

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4999	3848
1	4999	3848

prune164.0ms (1.8%)

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)

localize12.0ms (0.1%)

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)))

rewrite166.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

90×	`times-frac_binary64_1448`
56×	`add-cube-cbrt_binary64_1477` `add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
18×	`associate-/r*_binary64_1386`
17×	`add-exp-log_binary64_1480`
11×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`div-exp_binary64_1493` `add-log-exp_binary64_1481`
6×	`div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417` `associate-/l*_binary64_1387`
5×	`pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476`
2×	`frac-2neg_binary64_1453` `clear-num_binary64_1441` `flip3-+_binary64_1445` `associate-/l/_binary64_1389` `flip-+_binary64_1416` `1-exp_binary64_1486` `rec-exp_binary64_1492`
1×	`diff-log_binary64_1534` `sub-neg_binary64_1435` `cancel-sign-sub-inv_binary64_1408` `inv-pow_binary64_1527` `pow-flip_binary64_1516` `sum-log_binary64_1533` `+-commutative_binary64_1372`

Counts

4 → 138

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
10.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 c b) (.f64 d a))

Compiler

Compiled 4578 to 875 computations (80.9% saved)

series958.0ms (10.4%)

Error

4.1b

Counts

4 → 102

Calls

4 calls:

347.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a))))
289.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 c b) (.f64 d a)))
153.0ms	(-.f64 (.f64 c b) (.f64 d a))
82.0ms	(+.f64 (.f64 c c) (.f64 d d))

Compiler

Compiled 4914 to 3396 computations (30.9% saved)

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

240 → 240

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4997	6724
1	4997	6724

prune183.0ms (2%)

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 (17.2%)

Accuracy

Total 13.3b remaining (92.1%)

Threshold costs 0b (0%)

Compiler

Compiled 9269 to 5378 computations (42% saved)

bsearch84.0ms (0.9%)

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

end0.0ms (0%)

sample1.9s (20.2%)

Algorithm

1×

intervals

Results

330.0ms	8000×	body	128	valid
17.0ms	453×	body	128	invalid

Compiler

Compiled 1946 to 1120 computations (42.4% saved)

Details

analyze525.0ms (5.7%)

sample22.0ms (0.2%)

simplify221.0ms (2.4%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite88.0ms (1%)

series632.0ms (6.9%)

simplify61.0ms (0.7%)

prune104.0ms (1.1%)

localize12.0ms (0.1%)

rewrite113.0ms (1.2%)

series968.0ms (10.6%)

simplify82.0ms (0.9%)

prune165.0ms (1.8%)

localize14.0ms (0.2%)

rewrite122.0ms (1.3%)

series873.0ms (9.5%)

simplify78.0ms (0.8%)

prune164.0ms (1.8%)

localize12.0ms (0.1%)

rewrite166.0ms (1.8%)

series958.0ms (10.4%)

simplify84.0ms (0.9%)

prune183.0ms (2%)

regimes1.6s (17.2%)

bsearch84.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.9s (20.2%)

Profiling