Details

analyze546.0ms (10.8%)

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)

sample20.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify220.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

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

Merged error: 28.6b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 b c) (.f64 a d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
28.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_3510` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
9×	`times-frac_binary64_3494`
7×	`add-log-exp_binary64_3527`
5×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
3×	`associate-/r_binary64_3432` `associate-/l_binary64_3433` `pow1_binary64_3549`
2×	`flip3--_binary64_3492` `associate-/l/_binary64_3435` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `flip--_binary64_3463`
1×	`clear-num_binary64_3487` `diff-log_binary64_3580` `cancel-sign-sub-inv_binary64_3454` `+-commutative_binary64_3418` `frac-2neg_binary64_3499` `div-exp_binary64_3539` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522` `div-sub_binary64_3493` `div-inv_binary64_3485` `sub-neg_binary64_3481`

Counts

3 → 55

Calls

3 calls:

9.0ms	(/.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))

series163.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
39.0ms	(-.f64 (.f64 b c) (.f64 a d))
22.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4935	1462
1	4935	1462

prune83.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	54	10	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	10	65

Merged error: 27.7b

Counts

65 → 10

Compiler

Compiled 1687 to 330 computations (80.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.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))))
16.6b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite84.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_3494`
164×	`add-sqr-sqrt_binary64_3510`
162×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
156×	`sqrt-prod_binary64_3504`
27×	`associate-/l*_binary64_3433`
22×	`sqrt-div_binary64_3505`
18×	`associate-/r/_binary64_3434`
12×	`associate-/r*_binary64_3432`
11×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `flip-+_binary64_3462` `flip3-+_binary64_3491`
9×	`div-inv_binary64_3485`
6×	`pow1_binary64_3549`
4×	`add-log-exp_binary64_3527` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
3×	`associate-/l/_binary64_3435` `div-sub_binary64_3493`
2×	`clear-num_binary64_3487` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`
1×	`flip3--_binary64_3492` `flip--_binary64_3463`

Counts

4 → 266

Calls

4 calls:

20.0ms	(/.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))))
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)))

series268.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
99.0ms	(/.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))))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
23.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify158.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4981	13644
1	4981	13644

prune278.0ms (5.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	272	6	278
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	277	11	288

Merged error: 25.4b

Counts

288 → 11

Compiler

Compiled 11235 to 1164 computations (89.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
16.7b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite59.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_3510`
28×	`add-exp-log_binary64_3526` `times-frac_binary64_3494`
26×	`*-un-lft-identity_binary64_3488`
24×	`associate-r_binary64_3428` `add-cube-cbrt_binary64_3523`
23×	`sqrt-prod_binary64_3504`
18×	`add-cbrt-cube_binary64_3524`
9×	`div-exp_binary64_3539`
8×	`sqrt-div_binary64_3505` `pow1_binary64_3549` `prod-exp_binary64_3537`
6×	`associate-/r*_binary64_3432` `associate-/l/_binary64_3435`
5×	`unswap-sqr_binary64_3456` `cbrt-undiv_binary64_3522`
4×	`associate-*l/_binary64_3431` `flip3--_binary64_3492` `flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `add-log-exp_binary64_3527` `flip--_binary64_3463`
3×	`associate-l_binary64_3429`
2×	`1-exp_binary64_3532` `rec-exp_binary64_3538` `associate-*r/_binary64_3430` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `un-div-inv_binary64_3486` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`
1×	`clear-num_binary64_3487` `associate-/l_binary64_3433` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `-commutative_binary64_3419`

Counts

4 → 122

Calls

4 calls:

20.0ms	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
17.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (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)))

series275.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

124.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
100.0ms	(/.f64 (.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d))))
26.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
25.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5220	3285

prune126.0ms (2.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	134	11	145

Merged error: 25.4b

Counts

145 → 11

Compiler

Compiled 4419 to 788 computations (82.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
16.7b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
33.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite58.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_3494`
100×	`add-sqr-sqrt_binary64_3510`
98×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
54×	`sqrt-prod_binary64_3504`
27×	`associate-/r*_binary64_3432`
17×	`add-exp-log_binary64_3526`
11×	`add-cbrt-cube_binary64_3524` `associate-/r/_binary64_3434`
9×	`associate-/l*_binary64_3433`
8×	`div-exp_binary64_3539`
7×	`pow1_binary64_3549`
6×	`sqrt-div_binary64_3505` `div-inv_binary64_3485`
5×	`flip3--_binary64_3492` `flip--_binary64_3463`
4×	`add-log-exp_binary64_3527` `cbrt-undiv_binary64_3522`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
2×	`1-exp_binary64_3532` `clear-num_binary64_3487` `associate-/l/_binary64_3435` `rec-exp_binary64_3538` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `rem-sqrt-square_binary64_3501`
1×	`pow-flip_binary64_3562` `inv-pow_binary64_3573`

Counts

4 → 193

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series241.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
92.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
23.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
22.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5368	7468

prune190.0ms (3.8%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	205	11	216

Merged error: 25.4b

Counts

216 → 11

Compiler

Compiled 8099 to 1043 computations (87.1% saved)

regimes442.0ms (8.8%)

Compiler: Compiled 6147 to 3121 computations (49.2% saved)

bsearch188.0ms (3.7%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	56	82
1	56	82

end0.0ms (0%)

sample1.3s (25.5%)

Algorithm

1×

intervals

Results

336.0ms	8000×	body	128	valid
21.0ms	426×	body	128	invalid

Compiler

Compiled 1296 to 651 computations (49.8% saved)

Details

analyze546.0ms (10.8%)

sample20.0ms (0.4%)

simplify220.0ms (4.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite21.0ms (0.4%)

series163.0ms (3.2%)

simplify83.0ms (1.6%)

prune83.0ms (1.6%)

localize13.0ms (0.3%)

rewrite84.0ms (1.7%)

series268.0ms (5.3%)

simplify158.0ms (3.1%)

prune278.0ms (5.5%)

localize13.0ms (0.3%)

rewrite59.0ms (1.2%)

series275.0ms (5.5%)

simplify75.0ms (1.5%)

prune126.0ms (2.5%)

localize13.0ms (0.3%)

rewrite58.0ms (1.2%)

series241.0ms (4.8%)

simplify121.0ms (2.4%)

prune190.0ms (3.8%)

regimes442.0ms (8.8%)

bsearch188.0ms (3.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (25.5%)

Profiling