Details

analyze767.0ms (13.4%)

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 (0.7%)

Algorithm

1×

intervals

Results

10.0ms	197×	body	128	valid
7.0ms	26×	body	2048	valid
5.0ms	256×	pre	128	true
3.0ms	10×	body	4096	valid
2.0ms	12×	body	1024	valid
2.0ms	9×	body	512	valid
0.0ms	2×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify99.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	26
1	38	26

prune3.0ms (0.1%)

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: 12.1b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (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 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
0.2b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
17.8b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite56.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_3147`
21×	`add-sqr-sqrt_binary64_3169`
20×	`add-cube-cbrt_binary64_3182`
18×	`times-frac_binary64_3153`
16×	`sqrt-prod_binary64_3163`
8×	`pow1_binary64_3208`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091` `add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
3×	`sqrt-pow1_binary64_3165` `associate-/l*_binary64_3092`
2×	`pow1/2_binary64_3227` `associate-/r/_binary64_3093` `associate-*r/_binary64_3089`
1×	`clear-num_binary64_3146` `pow-prod-down_binary64_3218` `frac-2neg_binary64_3158` `distribute-lft-out_binary64_3098` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 81

Calls

4 calls:

19.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
14.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
9.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
6.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series213.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

108.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
42.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
34.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
28.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	5604	2228

prune147.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	9	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Merged error: 12.0b

Counts

94 → 9

Compiler

Compiled 2531 to 1657 computations (34.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
3.2b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
17.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64_3169`
24×	`associate-r_binary64_3087`
22×	`times-frac_binary64_3153`
21×	`*-un-lft-identity_binary64_3147`
19×	`add-cube-cbrt_binary64_3182`
15×	`sqrt-prod_binary64_3163`
13×	`add-exp-log_binary64_3185`
10×	`pow1_binary64_3208`
9×	`add-cbrt-cube_binary64_3183`
6×	`add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
5×	`unswap-sqr_binary64_3115`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `prod-exp_binary64_3196`
3×	`sqrt-pow1_binary64_3165` `associate-l_binary64_3088` `associate-*r/_binary64_3089`
2×	`pow-prod-down_binary64_3218` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `associate-/r/_binary64_3093`
1×	`*-commutative_binary64_3078` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `cbrt-undiv_binary64_3181` `un-div-inv_binary64_3145` `1-exp_binary64_3191` `rec-exp_binary64_3197` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 88

Calls

4 calls:

18.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
5.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
4.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))

series216.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
44.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
36.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
31.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5050	2092

prune139.0ms (2.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 12.0b

Counts

109 → 10

Compiler

Compiled 2824 to 1916 computations (32.2% saved)

localize28.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
8.5b	(+.f64 1 (.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
17.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
17.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`sqrt-prod_binary64_3163`
37×	`add-sqr-sqrt_binary64_3169`
27×	`associate-r_binary64_3087`
23×	`*-un-lft-identity_binary64_3147`
22×	`times-frac_binary64_3153`
21×	`add-cube-cbrt_binary64_3182`
8×	`pow1_binary64_3208`
7×	`sqrt-div_binary64_3164`
6×	`unswap-sqr_binary64_3115` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `add-log-exp_binary64_3186`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
3×	`associate-l_binary64_3088`
2×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `associate-/r/_binary64_3093`
1×	`-commutative_binary64_3078` `pow-prod-down_binary64_3218` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `associate-r/_binary64_3089` `div-inv_binary64_3144` `sum-log_binary64_3238`

Counts

4 → 89

Calls

4 calls:

19.0ms	(.f64 x (sqrt.f64 (/.f64 1 (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)))
3.0ms	(+.f64 1 (.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))

series187.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

83.0ms	(.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x))))))
53.0ms	(+.f64 1 (.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
26.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
25.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4991	2234
1	4991	2234

prune206.0ms (3.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	100	11	111

Merged error: 12.0b

Counts

111 → 11

Compiler

Compiled 4383 to 2993 computations (31.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

8.5b	(+.f64 1 (.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3)) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
15.6b	(cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3))
17.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
17.8b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_3169`
8×	`cbrt-prod_binary64_3178`
7×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
6×	`pow1_binary64_3208` `add-log-exp_binary64_3186` `sqrt-prod_binary64_3163`
5×	`sqrt-div_binary64_3164`
4×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
3×	`flip-+_binary64_3121` `flip3-+_binary64_3150`
2×	`rem-sqrt-square_binary64_3160` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227`
1×	`rem-cbrt-cube_binary64_3171` `unpow-prod-down_binary64_3226` `cbrt-div_binary64_3179` `pow1/3_binary64_3229` `cube-prod_binary64_3175` `sqr-pow_binary64_3119` `+-commutative_binary64_3077` `cube-mult_binary64_3177` `cube-div_binary64_3176` `unpow3_binary64_3213` `associate-*r/_binary64_3089` `sum-log_binary64_3238`

Counts

4 → 59

Calls

4 calls:

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)))
3.0ms	(+.f64 1 (.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3)) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
2.0ms	(cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3))

series204.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3))
57.0ms	(+.f64 1 (.f64 (cbrt.f64 (pow.f64 (.f64 x (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (.f64 x x)))))) 3)) (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))
29.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
28.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify104.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4898	1560
1	4898	1560

prune281.0ms (4.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	2	6	8
Picked	1	0	1
Done	0	2	2
Total	72	10	82

Merged error: 12.0b

Counts

82 → 10

Compiler

Compiled 2766 to 1927 computations (30.3% saved)

regimes580.0ms (10.1%)

Compiler: Compiled 8240 to 6341 computations (23% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	29
1	23	29

end0.0ms (0%)

sample2.0s (35.2%)

Algorithm

1×

intervals

Results

318.0ms	6089×	body	128	valid
201.0ms	774×	body	2048	valid
160.0ms	8000×	pre	128	true
101.0ms	503×	body	1024	valid
86.0ms	259×	body	4096	valid
37.0ms	248×	body	512	valid
13.0ms	127×	body	256	valid

Compiler

Compiled 1171 to 895 computations (23.6% saved)

Details

analyze767.0ms (13.4%)

sample38.0ms (0.7%)

simplify99.0ms (1.7%)

prune3.0ms (0.1%)

localize12.0ms (0.2%)

rewrite56.0ms (1%)

series213.0ms (3.7%)

simplify103.0ms (1.8%)

prune147.0ms (2.6%)

localize13.0ms (0.2%)

rewrite40.0ms (0.7%)

series216.0ms (3.8%)

simplify98.0ms (1.7%)

prune139.0ms (2.4%)

localize28.0ms (0.5%)

rewrite46.0ms (0.8%)

series187.0ms (3.3%)

simplify83.0ms (1.4%)

prune206.0ms (3.6%)

localize25.0ms (0.4%)

rewrite24.0ms (0.4%)

series204.0ms (3.6%)

simplify104.0ms (1.8%)

prune281.0ms (4.9%)

regimes580.0ms (10.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.0s (35.2%)

Profiling