Details

analyze253.0ms (5.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample64.0ms (1.4%)

Algorithm

1×

intervals

Results

29.0ms	87×	body	1024	valid
14.0ms	43×	body	2048	valid
7.0ms	36×	body	512	valid
3.0ms	70×	body	128	valid
2.0ms	19×	body	256	valid
0.0ms	1×	body	4096	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune2.0ms (0.1%)

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

55.0b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
15.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_3488`
6×	`add-sqr-sqrt_binary64_3510`
5×	`add-cube-cbrt_binary64_3523` `add-log-exp_binary64_3527` `pow1_binary64_3549`
4×	`add-exp-log_binary64_3526` `log-prod_binary64_3574`
3×	`add-cbrt-cube_binary64_3524` `flip-+_binary64_3462` `flip3-+_binary64_3491` `sqrt-prod_binary64_3504`
2×	`distribute-lft-out_binary64_3439` `sqrt-div_binary64_3505` `log-div_binary64_3575`
1×	`rem-log-exp_binary64_3529` `log-pow_binary64_3577` `+-commutative_binary64_3418` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `sum-log_binary64_3579` `rem-sqrt-square_binary64_3501`

Counts

3 → 42

Calls

3 calls:

7.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
7.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series97.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

48.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
30.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
19.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify63.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5224	862

prune65.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	47	4	51
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	4	52

Error

0.0b

Counts

52 → 4

Compiler

Compiled 812 to 538 computations (33.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
20.2b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_3510`
15×	`associate-l_binary64_3429`
13×	`add-exp-log_binary64_3526`
10×	`associate-r_binary64_3428` `add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
8×	`unpow-prod-down_binary64_3567` `add-log-exp_binary64_3527`
7×	`unswap-sqr_binary64_3456` `add-cbrt-cube_binary64_3524`
6×	`prod-exp_binary64_3537`
4×	`cube-prod_binary64_3516` `sqr-pow_binary64_3460`
3×	`pow1_binary64_3549`
2×	`pow-exp_binary64_3556` `diff-log_binary64_3580` `cbrt-unprod_binary64_3521` `pow-to-exp_binary64_3557` `*-commutative_binary64_3419`
1×	`unpow3_binary64_3554` `flip3--_binary64_3492` `cancel-sign-sub-inv_binary64_3454` `flip--_binary64_3463` `cube-mult_binary64_3518` `associate--l+_binary64_3425` `sum-log_binary64_3579` `sub-neg_binary64_3481`

Counts

3 → 70

Calls

3 calls:

7.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
6.0ms	(*.f64 (pow.f64 x 3) 1/6)
6.0ms	(*.f64 3/40 (pow.f64 x 5))

series94.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

33.0ms	(*.f64 3/40 (pow.f64 x 5))
32.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
30.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5018	1015

prune87.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Error

0.0b

Counts

83 → 4

Compiler

Compiled 1456 to 1129 computations (22.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
11.4b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite110.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64_3488`
73×	`add-sqr-sqrt_binary64_3510` `times-frac_binary64_3494`
47×	`add-cube-cbrt_binary64_3523`
26×	`unpow-prod-down_binary64_3567`
19×	`associate-/r*_binary64_3432`
15×	`add-exp-log_binary64_3526`
14×	`cube-prod_binary64_3516`
11×	`log-prod_binary64_3574`
10×	`difference-of-squares_binary64_3457` `sqr-pow_binary64_3460`
9×	`add-log-exp_binary64_3527`
8×	`add-cbrt-cube_binary64_3524`
6×	`distribute-lft-out_binary64_3439` `distribute-lft-out--_binary64_3440` `associate-/l*_binary64_3433` `frac-sub_binary64_3497` `div-exp_binary64_3539`
5×	`cancel-sign-sub-inv_binary64_3454` `log-div_binary64_3575` `pow1_binary64_3549`
4×	`unpow3_binary64_3554` `cube-mult_binary64_3518`
2×	`pow-exp_binary64_3556` `clear-num_binary64_3487` `frac-add_binary64_3496` `flip3--_binary64_3492` `flip-+_binary64_3462` `diff-log_binary64_3580` `flip3-+_binary64_3491` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `flip--_binary64_3463` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
1×	`rem-log-exp_binary64_3529` `log-pow_binary64_3577` `associate--r+_binary64_3424` `sum-log_binary64_3579` `sub-neg_binary64_3481`

Counts

4 → 164

Calls

4 calls:

43.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
42.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
5.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series134.0ms (3%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
36.0ms	(/.f64 1/16 (pow.f64 x 5))
28.0ms	(/.f64 1/8 (pow.f64 x 3))
28.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5284	3670

prune271.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	176	4	180

Error

0.0b

Counts

180 → 4

Compiler

Compiled 4173 to 3320 computations (20.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.0b	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
0.3b	(/.f64 1/8 (pow.f64 x 3))
9.2b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite104.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64_3494`
97×	`*-un-lft-identity_binary64_3488`
87×	`add-sqr-sqrt_binary64_3510`
80×	`cancel-sign-sub-inv_binary64_3454`
74×	`add-cube-cbrt_binary64_3523`
42×	`associate-+r+_binary64_3420`
31×	`unpow-prod-down_binary64_3567` `cube-prod_binary64_3516`
18×	`add-log-exp_binary64_3527`
12×	`associate-/r*_binary64_3432`
11×	`sqr-pow_binary64_3460`
10×	`unpow3_binary64_3554` `add-exp-log_binary64_3526` `cube-mult_binary64_3518`
9×	`distribute-lft-out_binary64_3439`
6×	`distribute-lft-out--_binary64_3440` `add-cbrt-cube_binary64_3524` `log-prod_binary64_3574`
5×	`difference-of-squares_binary64_3457` `sum-log_binary64_3579` `pow1_binary64_3549`
4×	`diff-log_binary64_3580`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433` `div-exp_binary64_3539` `div-inv_binary64_3485`
2×	`log-div_binary64_3575` `frac-sub_binary64_3497` `associate--l+_binary64_3425` `sub-neg_binary64_3481`
1×	`pow-exp_binary64_3556` `rem-log-exp_binary64_3529` `clear-num_binary64_3487` `log-pow_binary64_3577` `flip3--_binary64_3492` `+-commutative_binary64_3418` `pow-to-exp_binary64_3557` `frac-2neg_binary64_3499` `flip--_binary64_3463` `associate-+r-_binary64_3422` `cbrt-undiv_binary64_3522`

Counts

4 → 203

Calls

4 calls:

28.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
27.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
23.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series118.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
30.0ms	(+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3))))
28.0ms	(/.f64 1/8 (pow.f64 x 3))
19.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify85.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4897	3393
1	4897	3393

prune257.0ms (5.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	215	4	219

Error

0.0b

Counts

219 → 4

Compiler

Compiled 4392 to 3145 computations (28.4% saved)

regimes120.0ms (2.7%)

Accuracy

Total 0.2b remaining (92.5%)

Threshold costs 0.2b (92.5%)

Compiler

Compiled 775 to 596 computations (23.1% saved)

bsearch42.0ms (0.9%)

Steps

Iters	Range		Point
9	0.030554996636246903	100746.03170612353	0.9541805591384409
10	-354571085860.00684	-0.0014570036075567533	-1.0842361546612322

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	76
1	117	76

end0.0ms (0%)

sample2.2s (49.2%)

Algorithm

1×

intervals

Results

874.0ms	2447×	body	1024	valid
396.0ms	1222×	body	2048	valid
244.0ms	1206×	body	512	valid
119.0ms	2472×	body	128	valid
69.0ms	607×	body	256	valid
20.0ms	46×	body	4096	valid

Compiler

Compiled 316 to 244 computations (22.8% saved)

Details

analyze253.0ms (5.6%)

sample64.0ms (1.4%)

simplify98.0ms (2.2%)

prune2.0ms (0.1%)

localize6.0ms (0.1%)

rewrite20.0ms (0.5%)

series97.0ms (2.1%)

simplify63.0ms (1.4%)

prune65.0ms (1.4%)

localize8.0ms (0.2%)

rewrite23.0ms (0.5%)

series94.0ms (2.1%)

simplify70.0ms (1.6%)

prune87.0ms (1.9%)

localize11.0ms (0.2%)

rewrite110.0ms (2.4%)

series134.0ms (3%)

simplify87.0ms (1.9%)

prune271.0ms (6%)

localize9.0ms (0.2%)

rewrite104.0ms (2.3%)

series118.0ms (2.6%)

simplify85.0ms (1.9%)

prune257.0ms (5.7%)

regimes120.0ms (2.7%)

bsearch42.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (49.2%)

Profiling