Details

analyze6.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample51.0ms (1.6%)

Algorithm

1×

intervals

Results

29.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify214.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	5050	41

prune10.0ms (0.3%)

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

0.0b

Counts

2 → 2

Compiler

Compiled 119 to 75 computations (37% saved)

localize23.0ms (0.7%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (fabs.f64 x) (/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64)))
0.0b	(/.f64 (+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4))))) (sqrt.f64 PI.f64))
0.0b	(+.f64 (.f64 1/21 (pow.f64 x 6)) (+.f64 2 (+.f64 (.f64 2/3 (.f64 x x)) (.f64 1/5 (pow.f64 x 4)))))
0.0b	(+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4)))
0.1b	(*.f64 1/21 (pow.f64 x 6))
0.1b	(*.f64 1/5 (pow.f64 x 4))
0.2b	(.f64 2/3 (.f64 x x))
1.0b	(sqrt.f64 PI.f64)

rewrite28.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2757`
19×	`add-exp-log_binary64_2773`
15×	`associate-r_binary64_2675`
13×	`add-cbrt-cube_binary64_2771`
12×	`*-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770`
10×	`pow1_binary64_2796`
9×	`associate-l_binary64_2676` `prod-exp_binary64_2784`
8×	`unpow-prod-down_binary64_2814`
7×	`unswap-sqr_binary64_2703`
5×	`cbrt-unprod_binary64_2768`
4×	`sqr-pow_binary64_2707` `add-log-exp_binary64_2774`
3×	`sqrt-prod_binary64_2751` `pow-prod-down_binary64_2806` `*-commutative_binary64_2666`
2×	`pow-to-exp_binary64_2804` `pow-exp_binary64_2803`
1×	`sqrt-pow1_binary64_2753` `pow1/2_binary64_2815` `rem-sqrt-square_binary64_2748`

Counts

4 → 82

Calls

8 calls:

6.0ms	(.f64 2/3 (.f64 x x))
6.0ms	(*.f64 1/5 (pow.f64 x 4))
6.0ms	(*.f64 1/21 (pow.f64 x 6))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 (.f64 2/3 (.f64 x x)) (*.f64 1/5 (pow.f64 x 4)))

series105.0ms (3.3%)

Counts

4 → 9

Calls

4 calls:

45.0ms	(*.f64 1/21 (pow.f64 x 6))
33.0ms	(*.f64 1/5 (pow.f64 x 4))
26.0ms	(.f64 2/3 (.f64 x x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 468 to 402 computations (14.1% saved)

simplify51.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5031	773

prune146.0ms (4.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	91	2	93

Error

0.0b

Counts

93 → 2

Compiler

Compiled 2750 to 1836 computations (33.2% saved)

localize31.0ms (0.9%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.0b	(.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))
0.0b	(+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))
0.0b	(+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))
0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite50.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64_2796`
41×	`add-cbrt-cube_binary64_2771`
35×	`add-exp-log_binary64_2773`
18×	`prod-exp_binary64_2784` `cbrt-unprod_binary64_2768`
17×	`add-sqr-sqrt_binary64_2757`
15×	`associate-l_binary64_2676`
14×	`*-un-lft-identity_binary64_2735` `add-cube-cbrt_binary64_2770`
12×	`pow-prod-up_binary64_2805` `pow-plus_binary64_2798` `pow-prod-down_binary64_2806`
9×	`times-frac_binary64_2741`
7×	`associate-r_binary64_2675`
4×	`pow-sqr_binary64_2708` `pow2_binary64_2816` `add-log-exp_binary64_2774`
3×	`sqrt-prod_binary64_2751` `cbrt-undiv_binary64_2769` `div-exp_binary64_2786` `*-commutative_binary64_2666`
2×	`rem-3cbrt-lft_binary64_2760` `unswap-sqr_binary64_2703` `pow3_binary64_2818`
1×	`associate-*l/_binary64_2678` `sqrt-pow1_binary64_2753` `div-inv_binary64_2732` `pow1/2_binary64_2815` `rem-sqrt-square_binary64_2748`

Counts

4 → 109

Calls

8 calls:

13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))

series144.0ms (4.5%)

Counts

4 → 9

Calls

4 calls:

61.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
42.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
41.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 1122 to 606 computations (46% saved)

simplify70.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4907	885
1	4907	885

prune325.0ms (10.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	118	2	120

Error

0.0b

Counts

120 → 2

Compiler

Compiled 7802 to 3005 computations (61.5% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	133	578
1	133	578

regimes33.0ms (1%)

Accuracy

Total 0.0b remaining (25.1%)

Threshold costs 0.0b (25.1%)

Compiler

Compiled 362 to 213 computations (41.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	41
1	30	41

end0.0ms (0%)

sample1.9s (59.8%)

Algorithm

1×

intervals

Results

828.0ms	8000×	body	128	valid
102.0ms	8000×	pre	128	true

Compiler

Compiled 1150 to 667 computations (42% saved)

Pareto

0.6239760288227555

Details

analyze6.0ms (0.2%)

sample51.0ms (1.6%)

simplify214.0ms (6.6%)

prune10.0ms (0.3%)

localize23.0ms (0.7%)

rewrite28.0ms (0.9%)

series105.0ms (3.3%)

simplify51.0ms (1.6%)

prune146.0ms (4.5%)

localize31.0ms (0.9%)

rewrite50.0ms (1.5%)

series144.0ms (4.5%)

simplify70.0ms (2.2%)

prune325.0ms (10.1%)

simplify7.0ms (0.2%)

regimes33.0ms (1%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.9s (59.8%)

Profiling