Details

analyze1.1s (12.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	52
1	67	52
0	2	2
1	2	2

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)

sample41.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	198×	body	128	valid
6.0ms	21×	body	2048	valid
4.0ms	256×	pre	128	true
3.0ms	8×	body	4096	valid
3.0ms	13×	body	1024	valid
2.0ms	11×	body	512	valid
1.0ms	5×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify11.0ms (0.1%)

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

12.2b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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)))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.3b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite183.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

12.0b

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-log-exp_binary64_3186` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164` `associate-/r*_binary64_3091`
4×	`flip3-+_binary64_3150` `flip-+_binary64_3121`
3×	`sqrt-pow1_binary64_3165` `associate-/l*_binary64_3092`
2×	`pow1/2_binary64_3227` `associate-*r/_binary64_3089` `associate-/r/_binary64_3093`
1×	`rem-sqrt-square_binary64_3160` `sum-log_binary64_3238` `distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `pow-prod-down_binary64_3218` `div-exp_binary64_3198` `cbrt-undiv_binary64_3181` `frac-2neg_binary64_3158` `clear-num_binary64_3146` `div-inv_binary64_3144`

Counts

4 → 81

Calls

4 calls:

14.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
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))))
5.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2495 to 1576 computations (36.8% saved)

series618.0ms (6.9%)

Error

3.2b

Counts

4 → 63

Calls

4 calls:

183.0ms	(sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (.f64 x x)))))))
148.0ms	(/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x))))
115.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
107.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

Compiler

Compiled 2590 to 2279 computations (12% saved)

simplify54.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5079	3304

prune175.0ms (2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	139	5	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	5	145

Error

2.0b

Counts

145 → 5

Compiler

Compiled 3233 to 2134 computations (34% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3))
0.5b	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3)
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite184.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

14×	`cbrt-prod_binary64_3178`
13×	`*-un-lft-identity_binary64_3147`
12×	`add-sqr-sqrt_binary64_3169`
11×	`add-cube-cbrt_binary64_3182`
9×	`pow1_binary64_3208`
8×	`unpow-prod-down_binary64_3226` `cube-prod_binary64_3175`
7×	`sqrt-prod_binary64_3163`
6×	`add-log-exp_binary64_3186` `sqrt-div_binary64_3164`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
4×	`flip3-+_binary64_3150` `flip-+_binary64_3121` `pow-pow_binary64_3219` `associate-*r/_binary64_3089` `cube-div_binary64_3176`
3×	`sqrt-pow1_binary64_3165` `pow-unpow_binary64_3224`
2×	`pow1/2_binary64_3227` `unpow3_binary64_3213` `cube-mult_binary64_3177` `sqr-pow_binary64_3119` `cbrt-div_binary64_3179`
1×	`rem-sqrt-square_binary64_3160` `sum-log_binary64_3238` `distribute-lft-out_binary64_3098` `+-commutative_binary64_3077` `pow-prod-down_binary64_3218` `pow-to-exp_binary64_3216` `pow-exp_binary64_3215` `rem-cube-cbrt_binary64_3170` `sqrt-pow2_binary64_3166` `pow1/3_binary64_3229` `rem-cbrt-cube_binary64_3171`

Counts

4 → 83

Calls

4 calls:

15.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3)
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
6.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 3012 to 2109 computations (30% saved)

series813.0ms (9.1%)

Error

2.0b

Counts

4 → 64

Calls

4 calls:

328.0ms	(pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3)
182.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (.f64 1/2 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4)))))))) 3))
116.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
114.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 3106 to 2823 computations (9.1% saved)

simplify79.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5049	3901

prune183.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	146	6	152

Error

2.0b

Counts

152 → 6

Compiler

Compiled 3615 to 2562 computations (29.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))))
0.3b	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))))))
1.0b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
13.3b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

rewrite155.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

20×	`add-sqr-sqrt_binary64_3169`
18×	`sqrt-prod_binary64_3163`
16×	`*-un-lft-identity_binary64_3147`
10×	`pow1_binary64_3208` `add-cube-cbrt_binary64_3182`
7×	`associate-r_binary64_3087`
6×	`add-log-exp_binary64_3186` `add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `sqrt-div_binary64_3164` `associate-l_binary64_3088`
4×	`pow1/2_binary64_3227` `sqrt-pow1_binary64_3165` `flip3-+_binary64_3150` `flip-+_binary64_3121` `unswap-sqr_binary64_3115`
3×	`distribute-lft-out_binary64_3098` `pow-prod-down_binary64_3218`
2×	`rem-sqrt-square_binary64_3160` `associate-*r/_binary64_3089`
1×	`sum-log_binary64_3238` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sqrt-unprod_binary64_3167` `*-commutative_binary64_3078`

Counts

4 → 76

Calls

4 calls:

18.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))))))
12.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))))
12.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2421 to 1632 computations (32.6% saved)

series619.0ms (7%)

Error

2.0b

Counts

4 → 64

Calls

4 calls:

192.0ms	(.f64 (sqrt.f64 1/2) (sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (.f64 p 4))))))))
146.0ms	(sqrt.f64 (+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4)))))))
111.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))))
110.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 p (*.f64 p 4))))

Compiler

Compiled 2602 to 2311 computations (11.2% saved)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5037	3230

prune162.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Error

2.0b

Counts

146 → 6

Compiler

Compiled 3104 to 2118 computations (31.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
0.2b	(/.f64 p (/.f64 (*.f64 x x) p))
0.2b	(/.f64 (*.f64 x x) p)
21.7b	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

rewrite152.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

2.0b

Rules

69×	`times-frac_binary64_3153`
45×	`add-sqr-sqrt_binary64_3169`
37×	`add-cube-cbrt_binary64_3182` `*-un-lft-identity_binary64_3147`
32×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183`
26×	`associate-r_binary64_3087`
12×	`pow1_binary64_3208` `div-exp_binary64_3198` `cbrt-undiv_binary64_3181`
10×	`div-inv_binary64_3144` `associate-/r*_binary64_3091`
7×	`prod-exp_binary64_3196` `cbrt-unprod_binary64_3180`
4×	`add-log-exp_binary64_3186` `pow-prod-down_binary64_3218` `associate-/l*_binary64_3092`
3×	`sqrt-pow1_binary64_3165` `associate-r/_binary64_3089` `unswap-sqr_binary64_3115` `associate-l*_binary64_3088`
2×	`frac-2neg_binary64_3158` `clear-num_binary64_3146` `associate-/r/_binary64_3093`
1×	`pow1/2_binary64_3227` `sqrt-div_binary64_3164` `sqrt-prod_binary64_3163` `*-commutative_binary64_3078`

Counts

4 → 132

Calls

4 calls:

13.0ms	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
8.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))
6.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
5.0ms	(/.f64 (*.f64 x x) p)

Compiler

Compiled 2638 to 1100 computations (58.3% saved)

series297.0ms (3.3%)

Error

Counts

4 → 24

Calls

4 calls:

95.0ms	(.f64 2 (/.f64 p (/.f64 (.f64 x x) p)))
82.0ms	(/.f64 p (/.f64 (*.f64 x x) p))
63.0ms	(/.f64 (*.f64 x x) p)
41.0ms	(sqrt.f64 (.f64 1/2 (.f64 2 (/.f64 p (/.f64 (*.f64 x x) p)))))

Compiler

Compiled 714 to 645 computations (9.7% saved)

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4940	1917
1	4940	1917

prune114.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	3	0	3
Picked	1	0	1
Done	0	2	2
Total	158	4	162

Error

Counts

162 → 4

Compiler

Compiled 2412 to 1076 computations (55.4% saved)

regimes1.1s (11.9%)

Accuracy

Total 5.9b remaining (99.1%)

Threshold costs 0b (0%)

Compiler

Compiled 10976 to 8731 computations (20.5% saved)

bsearch4.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	71
1	36	71

end0.0ms (0%)

sample2.6s (29.7%)

Algorithm

1×

intervals

Results

321.0ms	6080×	body	128	valid
217.0ms	805×	body	2048	valid
146.0ms	8000×	pre	128	true
103.0ms	497×	body	1024	valid
86.0ms	265×	body	4096	valid
39.0ms	238×	body	512	valid
11.0ms	115×	body	256	valid

Compiler

Compiled 1575 to 1246 computations (20.9% saved)

Details

analyze1.1s (12.8%)

sample41.0ms (0.5%)

simplify11.0ms (0.1%)

prune3.0ms (0%)

localize12.0ms (0.1%)

rewrite183.0ms (2.1%)

series618.0ms (6.9%)

simplify54.0ms (0.6%)

prune175.0ms (2%)

localize15.0ms (0.2%)

rewrite184.0ms (2.1%)

series813.0ms (9.1%)

simplify79.0ms (0.9%)

prune183.0ms (2.1%)

localize16.0ms (0.2%)

rewrite155.0ms (1.7%)

series619.0ms (7%)

simplify69.0ms (0.8%)

prune162.0ms (1.8%)

localize9.0ms (0.1%)

rewrite152.0ms (1.7%)

series297.0ms (3.3%)

simplify90.0ms (1%)

prune114.0ms (1.3%)

regimes1.1s (11.9%)

bsearch4.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (29.7%)

Profiling