Details

analyze919.0ms (10.3%)

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)

sample39.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	201×	body	128	valid
6.0ms	23×	body	2048	valid
5.0ms	256×	pre	128	true
2.0ms	7×	body	4096	valid
2.0ms	11×	body	1024	valid
2.0ms	11×	body	512	valid
0.0ms	3×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify101.0ms (1.1%)

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

Error

12.6b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.1b	(+.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))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
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))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
17.1b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite41.0ms (0.5%)

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`
15×	`sqrt-prod_binary64_3163`
8×	`add-log-exp_binary64_3186`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `associate-/r*_binary64_3091`
5×	`pow1_binary64_3208`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `sqrt-div_binary64_3164`
3×	`associate-/l*_binary64_3092`
2×	`+-commutative_binary64_3077` `associate-/r/_binary64_3093` `sum-log_binary64_3238`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `distribute-lft-out_binary64_3098` `rem-sqrt-square_binary64_3160` `cbrt-undiv_binary64_3181` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `div-exp_binary64_3198` `div-inv_binary64_3144`

Counts

4 → 79

Calls

8 calls:

14.0ms	(+.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	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))
6.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
0.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))

series421.0ms (4.7%)

Counts

4 → 46

Calls

4 calls:

121.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
108.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
103.0ms	(+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))
88.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 1168 to 1090 computations (6.7% saved)

simplify93.0ms (1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4929	2505
1	4929	2505

prune248.0ms (2.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	120	5	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	121	5	126

Error

5.0b

Counts

126 → 5

Compiler

Compiled 2835 to 1852 computations (34.7% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.0b	(sqrt.f64 (.f64 1/2 (.f64 (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))))))
0.0b	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
0.0b	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
1.1b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
17.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
17.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite48.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_3147`
8×	`add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186`
6×	`pow1_binary64_3208` `add-cube-cbrt_binary64_3182` `sqrt-prod_binary64_3163`
4×	`add-exp-log_binary64_3185` `flip-+_binary64_3121` `add-cbrt-cube_binary64_3183` `flip3-+_binary64_3150` `sqrt-div_binary64_3164`
2×	`distribute-lft-out_binary64_3098` `rem-sqrt-square_binary64_3160` `+-commutative_binary64_3077` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `sum-log_binary64_3238`

Counts

4 → 54

Calls

8 calls:

16.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.0ms	(+.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)))
5.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
0.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))

series374.0ms (4.2%)

Counts

4 → 44

Calls

4 calls:

97.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
95.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
93.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
88.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))

Compiler

Compiled 2240 to 1816 computations (18.9% saved)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4958	1668
1	4958	1668

prune167.0ms (1.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	98	5	103

Error

5.0b

Counts

103 → 5

Compiler

Compiled 3638 to 2395 computations (34.2% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.0b	(sqrt.f64 (.f64 1/2 (+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))))
0.0b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.0b	(+.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)))))
2.8b	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
17.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite41.0ms (0.5%)

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`
14×	`sqrt-prod_binary64_3163`
13×	`add-exp-log_binary64_3185`
9×	`add-cbrt-cube_binary64_3183`
8×	`add-log-exp_binary64_3186`
7×	`pow1_binary64_3208`
5×	`unswap-sqr_binary64_3115`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `prod-exp_binary64_3196` `sqrt-div_binary64_3164`
3×	`associate-l_binary64_3088`
2×	`+-commutative_binary64_3077` `cbrt-unprod_binary64_3180` `div-exp_binary64_3198` `associate-/r/_binary64_3093` `sum-log_binary64_3238`
1×	`-commutative_binary64_3078` `pow-prod-down_binary64_3218` `rem-sqrt-square_binary64_3160` `cbrt-undiv_binary64_3181` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `un-div-inv_binary64_3145` `1-exp_binary64_3191` `rec-exp_binary64_3197` `associate-r/_binary64_3089` `div-inv_binary64_3144`

Counts

4 → 86

Calls

8 calls:

17.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
6.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
5.0ms	(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))))))
0.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))

series418.0ms (4.7%)

Counts

4 → 46

Calls

4 calls:

117.0ms	(.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))))
114.0ms	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
99.0ms	(+.f64 1 (.f64 x (/.f64 1 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))
88.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

Compiler

Compiled 1242 to 1164 computations (6.3% saved)

simplify85.0ms (1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4931	2348
1	4931	2348

prune155.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	133	4	137

Error

4.8b

Counts

137 → 4

Compiler

Compiled 3101 to 2112 computations (31.9% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))
0.0b	(/.f64 (-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x))))))
0.0b	(sqrt.f64 (.f64 1/2 (/.f64 (-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))))
0.7b	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
1.8b	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))
3.3b	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
17.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite58.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_3169`
33×	`cancel-sign-sub-inv_binary64_3113`
31×	`*-un-lft-identity_binary64_3147`
30×	`times-frac_binary64_3153`
22×	`add-cube-cbrt_binary64_3182`
14×	`sqrt-prod_binary64_3163`
10×	`difference-of-squares_binary64_3116`
9×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
8×	`add-log-exp_binary64_3186`
6×	`associate-/r/_binary64_3093`
5×	`pow1_binary64_3208`
4×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `sqrt-div_binary64_3164`
3×	`associate-/r*_binary64_3091` `div-inv_binary64_3144`
2×	`flip--_binary64_3122` `flip3--_binary64_3151` `sub-neg_binary64_3140` `distribute-lft-out--_binary64_3099` `cbrt-undiv_binary64_3181` `div-exp_binary64_3198` `diff-log_binary64_3239`
1×	`clear-num_binary64_3146` `frac-2neg_binary64_3158` `rem-sqrt-square_binary64_3160` `prod-exp_binary64_3196` `sqrt-pow1_binary64_3165` `pow1/2_binary64_3227` `cbrt-unprod_binary64_3180` `associate-/l*_binary64_3092`

Counts

4 → 105

Calls

8 calls:

16.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))
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)))
0.0ms	(sqrt.f64 (.f64 1/2 (/.f64 (-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))))))

series533.0ms (6%)

Counts

4 → 52

Calls

4 calls:

182.0ms	(-.f64 1 (/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))
158.0ms	(/.f64 (.f64 x x) (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))
97.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
95.0ms	(-.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))

Compiler

Compiled 2644 to 2086 computations (21.1% saved)

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4985	3801
1	4985	3801

prune275.0ms (3.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	156	1	157
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	157	4	161

Error

4.8b

Counts

161 → 4

Compiler

Compiled 5970 to 3559 computations (40.4% saved)

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	460	1565
1	460	1565

regimes178.0ms (2%)

Accuracy

Total 7.5b remaining (56.8%)

Threshold costs 0b (0%)

Compiler

Compiled 2030 to 1556 computations (23.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	23	53
1	23	53

end0.0ms (0%)

sample4.5s (50.2%)

Algorithm

1×

intervals

Results

336.0ms	6070×	body	128	valid
220.0ms	799×	body	2048	valid
157.0ms	8000×	pre	128	true
109.0ms	510×	body	1024	valid
90.0ms	266×	body	4096	valid
40.0ms	243×	body	512	valid
14.0ms	112×	body	256	valid

Compiler

Compiled 3075 to 2355 computations (23.4% saved)

Pareto

0.15206040037513058

Details

analyze919.0ms (10.3%)

sample39.0ms (0.4%)

simplify101.0ms (1.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite41.0ms (0.5%)

series421.0ms (4.7%)

simplify93.0ms (1%)

prune248.0ms (2.8%)

localize16.0ms (0.2%)

rewrite48.0ms (0.5%)

series374.0ms (4.2%)

simplify69.0ms (0.8%)

prune167.0ms (1.9%)

localize16.0ms (0.2%)

rewrite41.0ms (0.5%)

series418.0ms (4.7%)

simplify85.0ms (1%)

prune155.0ms (1.7%)

localize16.0ms (0.2%)

rewrite58.0ms (0.7%)

series533.0ms (6%)

simplify88.0ms (1%)

prune275.0ms (3.1%)

simplify24.0ms (0.3%)

regimes178.0ms (2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample4.5s (50.2%)

Profiling