Details

analyze364.0ms (8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14
0	1	1
1	1	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)

sample63.0ms (1.4%)

Algorithm

1×

intervals

Results

32.0ms	89×	body	1024	valid
9.0ms	43×	body	512	valid
9.0ms	29×	body	2048	valid
3.0ms	70×	body	128	valid
3.0ms	25×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify7.0ms (0.2%)

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

Merged error: 53.4b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

1.0b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
2.9b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
12.2b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite20.0ms (0.4%)

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:

6.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
6.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series88.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
24.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
18.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify59.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5224	862

prune66.0ms (1.5%)

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

Merged error: 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))
0.2b	(*.f64 (pow.f64 x 3) 1/6)
17.1b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite24.0ms (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:

6.0ms	(-.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))

series82.0ms (1.8%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(*.f64 3/40 (pow.f64 x 5))
28.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
25.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (53.0ms)

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

Merged error: 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:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
13.4b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.3b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite116.0ms (2.6%)

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:

45.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
39.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
6.0ms	(/.f64 1/8 (pow.f64 x 3))
5.0ms	(/.f64 1/16 (pow.f64 x 5))

series117.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
30.0ms	(/.f64 1/16 (pow.f64 x 5))
25.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
22.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5284	3670

prune278.0ms (6.1%)

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

Merged error: 0b

Counts

180 → 4

Compiler

Compiled 4173 to 3320 computations (20.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
0.2b	(/.f64 1/8 (pow.f64 x 3))
12.2b	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))

rewrite76.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 144

Calls

3 calls:

30.0ms	(log.f64 (+.f64 x (-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))))
26.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))
6.0ms	(/.f64 1/8 (pow.f64 x 3))

series88.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

38.0ms	(log.f64 (+.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))
22.0ms	(-.f64 (+.f64 x (/.f64 1/2 x)) (/.f64 1/8 (pow.f64 x 3)))

simplify93.0ms (2%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4907	2410
1	4907	2410

prune167.0ms (3.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	153	4	157

Merged error: 0b

Counts

157 → 4

Compiler

Compiled 2915 to 2123 computations (27.2% saved)

regimes152.0ms (3.4%)

Compiler: Compiled 1070 to 814 computations (23.9% saved)

bsearch42.0ms (0.9%)

Steps

Iters	Range		Point
9	0.3634205432438087	1264679.9391604443	0.9597103890461449
10	-8731.982202357365	-2.2693245879818854e-14	-1.0759722586128024

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%)

sample2.3s (51.7%)

Algorithm

1×

intervals

Results

926.0ms	2567×	body	1024	valid
387.0ms	1234×	body	2048	valid
249.0ms	1227×	body	512	valid
108.0ms	2298×	body	128	valid
70.0ms	625×	body	256	valid
21.0ms	49×	body	4096	valid

Compiler

Compiled 391 to 300 computations (23.3% saved)

Details

analyze364.0ms (8%)

sample63.0ms (1.4%)

simplify7.0ms (0.2%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite20.0ms (0.4%)

series88.0ms (1.9%)

simplify59.0ms (1.3%)

prune66.0ms (1.5%)

localize8.0ms (0.2%)

rewrite24.0ms (0.5%)

series82.0ms (1.8%)

simplify70.0ms (1.5%)

prune87.0ms (1.9%)

localize11.0ms (0.2%)

rewrite116.0ms (2.6%)

series117.0ms (2.6%)

simplify89.0ms (2%)

prune278.0ms (6.1%)

localize9.0ms (0.2%)

rewrite76.0ms (1.7%)

series88.0ms (1.9%)

simplify93.0ms (2%)

prune167.0ms (3.7%)

regimes152.0ms (3.4%)

bsearch42.0ms (0.9%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.3s (51.7%)

Profiling