Details

analyze763.0ms (13.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	207×	body	128	valid
4.0ms	256×	pre	128	true
4.0ms	16×	body	2048	valid
3.0ms	9×	body	4096	valid
2.0ms	12×	body	1024	valid
1.0ms	9×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify99.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 10.5b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.6b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
16.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_2806`
21×	`add-sqr-sqrt_binary64_2828`
20×	`add-cube-cbrt_binary64_2841`
18×	`times-frac_binary64_2812`
15×	`sqrt-prod_binary64_2822`
8×	`add-log-exp_binary64_2845`
6×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/r*_binary64_2750`
5×	`pow1_binary64_2867`
4×	`sqrt-div_binary64_2823` `flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`associate-/l*_binary64_2751`
2×	`sum-log_binary64_2897` `associate-/r/_binary64_2752` `+-commutative_binary64_2736`
1×	`pow1/2_binary64_2886` `div-inv_binary64_2803` `div-exp_binary64_2857` `distribute-lft-out_binary64_2757` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `clear-num_binary64_2805` `frac-2neg_binary64_2817`

Counts

4 → 79

Calls

4 calls:

13.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
8.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
5.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series124.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
31.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
25.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
22.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

simplify87.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4921	2082
1	4921	2082

prune132.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	81	10	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 10.2b

Counts

92 → 10

Compiler

Compiled 2566 to 1683 computations (34.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
3.8b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite53.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-cube-cbrt_binary64_2841`
6×	`add-log-exp_binary64_2845` `sqrt-prod_binary64_2822` `pow1_binary64_2867`
4×	`sqrt-div_binary64_2823` `flip-+_binary64_2780` `flip3-+_binary64_2809`
3×	`times-frac_binary64_2812` `associate-/r*_binary64_2750`
2×	`pow1/2_binary64_2886` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `distribute-lft-out_binary64_2757` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `sum-log_binary64_2897` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817` `+-commutative_binary64_2736`

Counts

4 → 65

Calls

4 calls:

25.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
9.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series127.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
29.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
23.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5051	1543

prune182.0ms (3.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	77	10	87

Merged error: 10.2b

Counts

87 → 10

Compiler

Compiled 4458 to 2727 computations (38.8% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))) 3))))
3.8b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
10×	`add-cube-cbrt_binary64_2841`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
7×	`pow1_binary64_2867`
6×	`sqrt-prod_binary64_2822`
5×	`log-pow_binary64_2895`
4×	`sqrt-div_binary64_2823` `exp-prod_binary64_2858` `add-log-exp_binary64_2845` `log-prod_binary64_2892`
3×	`times-frac_binary64_2812` `associate-/r*_binary64_2750` `flip-+_binary64_2780` `flip3-+_binary64_2809`
2×	`pow1/2_binary64_2886` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819` `associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `exp-sum_binary64_2852` `distribute-lft-out_binary64_2757` `prod-exp_binary64_2855` `rem-log-exp_binary64_2847` `cbrt-unprod_binary64_2839` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 70

Calls

4 calls:

25.0ms	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))) 3))))
11.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series147.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(log.f64 (exp.f64 (+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))) 3))))
29.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5010	1640

prune213.0ms (3.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 10.2b

Counts

92 → 12

Compiler

Compiled 5048 to 3151 computations (37.6% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

3.8b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
16.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_2828`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `*-un-lft-identity_binary64_2806` `add-cube-cbrt_binary64_2841` `sqrt-prod_binary64_2822`
7×	`pow1_binary64_2867`
6×	`sqrt-div_binary64_2823`
4×	`flip-+_binary64_2780` `add-log-exp_binary64_2845` `flip3-+_binary64_2809`
3×	`pow1/2_binary64_2886` `times-frac_binary64_2812` `associate-/r*_binary64_2750` `sqrt-pow1_binary64_2824` `rem-sqrt-square_binary64_2819`
2×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `associate-/r/_binary64_2752`
1×	`div-inv_binary64_2803` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `clear-num_binary64_2805` `associate-/l*_binary64_2751` `frac-2neg_binary64_2817`

Counts

4 → 68

Calls

4 calls:

9.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series100.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
24.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
23.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4943	1456
1	4943	1456

prune290.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 10.2b

Counts

92 → 9

Compiler

Compiled 6089 to 3925 computations (35.5% saved)

regimes630.0ms (11.3%)

Compiler: Compiled 10850 to 7615 computations (29.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	111
1	48	111

end0.0ms (0%)

sample2.2s (39.1%)

Algorithm

1×

intervals

Results

306.0ms	6087×	body	128	valid
198.0ms	778×	body	2048	valid
138.0ms	8000×	pre	128	true
97.0ms	500×	body	1024	valid
97.0ms	279×	body	4096	valid
35.0ms	245×	body	512	valid
11.0ms	111×	body	256	valid

Compiler

Compiled 1598 to 1114 computations (30.3% saved)

Details

analyze763.0ms (13.7%)

sample34.0ms (0.6%)

simplify99.0ms (1.8%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite39.0ms (0.7%)

series124.0ms (2.2%)

simplify87.0ms (1.6%)

prune132.0ms (2.4%)

localize17.0ms (0.3%)

rewrite53.0ms (1%)

series127.0ms (2.3%)

simplify57.0ms (1%)

prune182.0ms (3.3%)

localize25.0ms (0.4%)

rewrite56.0ms (1%)

series147.0ms (2.6%)

simplify66.0ms (1.2%)

prune213.0ms (3.8%)

localize28.0ms (0.5%)

rewrite40.0ms (0.7%)

series100.0ms (1.8%)

simplify63.0ms (1.1%)

prune290.0ms (5.2%)

regimes630.0ms (11.3%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (39.1%)

Profiling