Details

analyze788.0ms (12.2%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	197×	body	128	valid
7.0ms	27×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	15×	body	1024	valid
2.0ms	7×	body	4096	valid
1.0ms	5×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify174.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (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: 12.7b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
0.0b	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
14.0b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite50.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_2504` `pow1_binary64_2526`
7×	`*-un-lft-identity_binary64_2465`
6×	`add-sqr-sqrt_binary64_2487`
5×	`add-cube-cbrt_binary64_2500`
4×	`flip3-+_binary64_2468` `sqrt-prod_binary64_2481` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `sqrt-div_binary64_2482`
3×	`sqrt-pow1_binary64_2483`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `associate-*r/_binary64_2407`
1×	`rem-sqrt-square_binary64_2478` `pow-prod-down_binary64_2536` `distribute-lft-out_binary64_2416`

Counts

4 → 51

Calls

4 calls:

18.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series376.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
76.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
48.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
42.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5278	1285

prune111.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	52	11	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	11	64

Merged error: 12.4b

Counts

64 → 11

Compiler

Compiled 1711 to 1174 computations (31.4% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
3.7b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite57.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-cube-cbrt_binary64_2500`
6×	`add-log-exp_binary64_2504` `sqrt-prod_binary64_2481` `pow1_binary64_2526`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `sqrt-div_binary64_2482`
3×	`times-frac_binary64_2471` `associate-/r*_binary64_2409`
2×	`pow1/2_binary64_2545` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `rem-sqrt-square_binary64_2478` `associate-/r/_binary64_2411` `sqrt-pow1_binary64_2483`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `clear-num_binary64_2464` `div-inv_binary64_2462` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `distribute-lft-out_binary64_2416` `associate-/l*_binary64_2410` `cbrt-unprod_binary64_2498`

Counts

4 → 65

Calls

4 calls:

24.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
10.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series242.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(+.f64 1 (pow.f64 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))) 3))
58.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
52.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
44.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4987	1543
1	4987	1543

prune199.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	74	3	77
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	76	12	88

Merged error: 12.4b

Counts

88 → 12

Compiler

Compiled 4534 to 2786 computations (38.6% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`sqrt-prod_binary64_2481` `add-sqr-sqrt_binary64_2487`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `pow1_binary64_2526` `sqrt-div_binary64_2482`
4×	`flip3-+_binary64_2468` `add-log-exp_binary64_2504` `pow1/2_binary64_2545` `flip-+_binary64_2439` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `rem-sqrt-square_binary64_2478` `sqrt-pow1_binary64_2483`

Counts

4 → 60

Calls

4 calls:

8.0ms	(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 p 4)) (*.f64 x x)))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series204.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

56.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
53.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
49.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
46.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify105.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4681	1232
1	4681	1232

prune319.0ms (4.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	71	13	84

Merged error: 12.4b

Counts

84 → 13

Compiler

Compiled 6839 to 4287 computations (37.3% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.6b	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
14.0b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64_2465`
8×	`add-log-exp_binary64_2504` `add-sqr-sqrt_binary64_2487`
7×	`add-cube-cbrt_binary64_2500`
6×	`pow1_binary64_2526`
5×	`log-pow_binary64_2554`
4×	`sqrt-prod_binary64_2481` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `exp-prod_binary64_2517`
3×	`flip3-+_binary64_2468` `log-prod_binary64_2551` `flip-+_binary64_2439`
2×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `sqrt-div_binary64_2482`
1×	`pow1/2_binary64_2545` `rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `sqrt-pow1_binary64_2483` `rem-log-exp_binary64_2506`

Counts

4 → 54

Calls

4 calls:

15.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
2.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))

series430.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(log.f64 (exp.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
91.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
48.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
40.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4879	1410
1	4879	1410

prune88.0ms (1.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	65	14	79

Merged error: 12.4b

Counts

79 → 14

Compiler

Compiled 1604 to 1119 computations (30.2% saved)

regimes686.0ms (10.6%)

Compiler: Compiled 9906 to 7314 computations (26.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	73
1	44	73

end0.0ms (0%)

sample2.2s (33.9%)

Algorithm

1×

intervals

Results

320.0ms	6109×	body	128	valid
203.0ms	756×	body	2048	valid
153.0ms	8000×	pre	128	true
105.0ms	506×	body	1024	valid
82.0ms	255×	body	4096	valid
38.0ms	257×	body	512	valid
12.0ms	117×	body	256	valid

Compiler

Compiled 1438 to 1049 computations (27.1% saved)

Details

analyze788.0ms (12.2%)

sample38.0ms (0.6%)

simplify174.0ms (2.7%)

prune3.0ms (0%)

localize11.0ms (0.2%)

rewrite50.0ms (0.8%)

series376.0ms (5.8%)

simplify77.0ms (1.2%)

prune111.0ms (1.7%)

localize27.0ms (0.4%)

rewrite57.0ms (0.9%)

series242.0ms (3.8%)

simplify61.0ms (0.9%)

prune199.0ms (3.1%)

localize33.0ms (0.5%)

rewrite40.0ms (0.6%)

series204.0ms (3.2%)

simplify105.0ms (1.6%)

prune319.0ms (4.9%)

localize17.0ms (0.3%)

rewrite34.0ms (0.5%)

series430.0ms (6.7%)

simplify93.0ms (1.4%)

prune88.0ms (1.4%)

regimes686.0ms (10.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (33.9%)

Profiling