Details

analyze552.0ms (10%)

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 (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	14×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify205.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	514	22
1	514	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: 23.9b

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 c c) (.f64 d d))
0.0b	(-.f64 (.f64 b c) (.f64 a d))
23.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210` `add-sqr-sqrt_binary64_3197`
9×	`times-frac_binary64_3181`
7×	`add-log-exp_binary64_3214`
5×	`add-cbrt-cube_binary64_3211` `add-exp-log_binary64_3213`
3×	`associate-/l_binary64_3120` `associate-/r_binary64_3119` `pow1_binary64_3236`
2×	`flip--_binary64_3150` `flip3--_binary64_3179` `flip-+_binary64_3149` `flip3-+_binary64_3178` `associate-/l/_binary64_3122` `associate-/r/_binary64_3121`
1×	`div-sub_binary64_3180` `diff-log_binary64_3267` `clear-num_binary64_3174` `div-inv_binary64_3172` `frac-2neg_binary64_3186` `sub-neg_binary64_3168` `+-commutative_binary64_3105` `cbrt-undiv_binary64_3209` `cancel-sign-sub-inv_binary64_3141` `div-exp_binary64_3226` `sum-log_binary64_3266`

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))

series319.0ms (5.8%)

Counts

3 → 9

Calls

3 calls:

200.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
78.0ms	(-.f64 (.f64 b c) (.f64 a d))
40.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6309	1462

prune294.0ms (5.3%)

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: 23.1b

Counts

65 → 10

Compiler

Compiled 7546 to 2981 computations (60.5% saved)

localize13.0ms (0.2%)

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))))
14.8b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite88.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64_3181`
164×	`add-sqr-sqrt_binary64_3197`
162×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210`
156×	`sqrt-prod_binary64_3191`
27×	`associate-/l*_binary64_3120`
22×	`sqrt-div_binary64_3192`
18×	`associate-/r/_binary64_3121`
12×	`associate-/r*_binary64_3119`
11×	`flip-+_binary64_3149` `add-cbrt-cube_binary64_3211` `flip3-+_binary64_3178` `add-exp-log_binary64_3213`
9×	`div-inv_binary64_3172`
6×	`pow1_binary64_3236`
4×	`cbrt-undiv_binary64_3209` `div-exp_binary64_3226` `add-log-exp_binary64_3214`
3×	`div-sub_binary64_3180` `associate-/l/_binary64_3122`
2×	`clear-num_binary64_3174` `sqrt-pow1_binary64_3193` `frac-2neg_binary64_3186` `rem-sqrt-square_binary64_3188` `pow1/2_binary64_3255`
1×	`flip--_binary64_3150` `flip3--_binary64_3179`

Counts

4 → 266

Calls

4 calls:

22.0ms	(/.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))))
13.0ms	(/.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)))

series554.0ms (10%)

Counts

4 → 12

Calls

4 calls:

252.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
200.0ms	(/.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))))
55.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify156.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4981	13644
1	4981	13644

prune513.0ms (9.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	271	7	278
Fresh	6	3	9
Picked	0	1	1
Done	0	0	0
Total	277	11	288

Merged error: 20.8b

Counts

288 → 11

Compiler

Compiled 16971 to 4016 computations (76.3% saved)

localize14.0ms (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))))
14.9b	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite64.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

162×	`times-frac_binary64_3181`
100×	`add-sqr-sqrt_binary64_3197`
98×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210`
54×	`sqrt-prod_binary64_3191`
27×	`associate-/r*_binary64_3119`
17×	`add-exp-log_binary64_3213`
11×	`add-cbrt-cube_binary64_3211` `associate-/r/_binary64_3121`
9×	`associate-/l*_binary64_3120`
8×	`div-exp_binary64_3226`
7×	`pow1_binary64_3236`
6×	`div-inv_binary64_3172` `sqrt-div_binary64_3192`
5×	`flip--_binary64_3150` `flip3--_binary64_3179`
4×	`cbrt-undiv_binary64_3209` `add-log-exp_binary64_3214`
3×	`flip-+_binary64_3149` `flip3-+_binary64_3178`
2×	`clear-num_binary64_3174` `sqrt-pow1_binary64_3193` `frac-2neg_binary64_3186` `1-exp_binary64_3219` `rem-sqrt-square_binary64_3188` `pow1/2_binary64_3255` `associate-/l/_binary64_3122` `rec-exp_binary64_3225`
1×	`pow-flip_binary64_3249` `inv-pow_binary64_3260`

Counts

4 → 193

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
10.0ms	(/.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)))

series488.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a))))
170.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (-.f64 (.f64 c b) (.f64 d a)))
51.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify121.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5306	7468

prune227.0ms (4.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	204	1	205
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	204	12	216

Merged error: 20.8b

Counts

216 → 12

Compiler

Compiled 8581 to 1323 computations (84.6% saved)

localize14.0ms (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))))
14.9b	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
26.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite63.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64_3197`
28×	`times-frac_binary64_3181` `add-exp-log_binary64_3213`
26×	`*-un-lft-identity_binary64_3175`
24×	`add-cube-cbrt_binary64_3210` `associate-r_binary64_3115`
23×	`sqrt-prod_binary64_3191`
18×	`add-cbrt-cube_binary64_3211`
9×	`div-exp_binary64_3226`
8×	`prod-exp_binary64_3224` `pow1_binary64_3236` `sqrt-div_binary64_3192`
6×	`associate-/r*_binary64_3119` `associate-/l/_binary64_3122`
5×	`cbrt-undiv_binary64_3209` `unswap-sqr_binary64_3143`
4×	`flip--_binary64_3150` `frac-times_binary64_3185` `flip3--_binary64_3179` `flip-+_binary64_3149` `cbrt-unprod_binary64_3208` `flip3-+_binary64_3178` `associate-*l/_binary64_3118` `associate-/r/_binary64_3121` `add-log-exp_binary64_3214`
3×	`associate-l_binary64_3116`
2×	`associate-*r/_binary64_3117` `sqrt-pow1_binary64_3193` `div-inv_binary64_3172` `1-exp_binary64_3219` `rem-sqrt-square_binary64_3188` `pow1/2_binary64_3255` `un-div-inv_binary64_3173` `rec-exp_binary64_3225`
1×	`-commutative_binary64_3106` `pow-prod-down_binary64_3246` `clear-num_binary64_3174` `associate-/l_binary64_3120` `frac-2neg_binary64_3186`

Counts

4 → 122

Calls

4 calls:

20.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
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))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series549.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(.f64 (-.f64 (.f64 b c) (.f64 a d)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
201.0ms	(/.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))))
48.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5220	3285

prune118.0ms (2.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	134	12	146

Merged error: 20.8b

Counts

146 → 12

Compiler

Compiled 4227 to 663 computations (84.3% saved)

regimes134.0ms (2.4%)

Compiler: Compiled 1422 to 865 computations (39.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms (0%)

sample848.0ms (15.3%)

Algorithm

1×

intervals

Results

350.0ms	8000×	body	128	valid
21.0ms	491×	body	128	invalid

Compiler

Compiled 345 to 204 computations (40.9% saved)

Details

analyze552.0ms (10%)

sample22.0ms (0.4%)

simplify205.0ms (3.7%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite22.0ms (0.4%)

series319.0ms (5.8%)

simplify72.0ms (1.3%)

prune294.0ms (5.3%)

localize13.0ms (0.2%)

rewrite88.0ms (1.6%)

series554.0ms (10%)

simplify156.0ms (2.8%)

prune513.0ms (9.3%)

localize14.0ms (0.3%)

rewrite64.0ms (1.2%)

series488.0ms (8.8%)

simplify121.0ms (2.2%)

prune227.0ms (4.1%)

localize14.0ms (0.3%)

rewrite63.0ms (1.1%)

series549.0ms (9.9%)

simplify74.0ms (1.3%)

prune118.0ms (2.1%)

regimes134.0ms (2.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample848.0ms (15.3%)

Profiling