Details

analyze193.0ms (2.3%)

Algorithm

2×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	84
1	22	84
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14
99.8%	0.1%	0.1%	14

Symmetry

(sort x y z)

Compiler

Compiled 30 to 24 computations (20% saved)

sample193.0ms (2.3%)

Algorithm

2×

intervals

Results

23.0ms

512×

body

128

valid

Compiler

Compiled 3884 to 3881 computations (0.1% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

prune5.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

36.2b

Counts

2 → 1

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
33.4b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite113.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

36.1b

Rules

21×	`add-sqr-sqrt_binary64_21583`
19×	`times-frac_binary64_21567`
18×	`add-cube-cbrt_binary64_21596` `*-un-lft-identity_binary64_21561`
13×	`sqrt-prod_binary64_21577`
8×	`add-log-exp_binary64_21600`
5×	`add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597`
4×	`pow1_binary64_21622`
3×	`associate-/l_binary64_21506` `associate-/r_binary64_21505` `sum-log_binary64_21652`
2×	`div-inv_binary64_21558` `rem-sqrt-square_binary64_21574` `flip3-+_binary64_21564` `associate-/l/_binary64_21508` `flip-+_binary64_21535`
1×	`pow1/2_binary64_21641` `sqrt-pow1_binary64_21579` `sqrt-div_binary64_21578` `div-exp_binary64_21612` `cbrt-undiv_binary64_21595` `frac-2neg_binary64_21572` `clear-num_binary64_21560` `associate-+l+_binary64_21494` `+-commutative_binary64_21491`

Counts

3 → 67

Calls

3 calls:

9.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
6.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

Compiler

Compiled 1822 to 489 computations (73.2% saved)

series1.0s (12.1%)

Error

0.6b

Counts

3 → 51

Calls

3 calls:

363.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
351.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
254.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

Compiler

Compiled 2191 to 2036 computations (7.1% saved)

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5051	2748

prune129.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	4	119

Error

0.6b

Counts

119 → 4

Compiler

Compiled 2309 to 739 computations (68% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.4b	(*.f64 (sqrt.f64 1/3) x)

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

8×	`add-sqr-sqrt_binary64_21583`
6×	`associate-l_binary64_21502`
4×	`add-cube-cbrt_binary64_21596` `*-un-lft-identity_binary64_21561` `sqrt-prod_binary64_21577`
3×	`pow1_binary64_21622` `add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597` `associate-r_binary64_21501`
2×	`unswap-sqr_binary64_21529`
1×	`pow-prod-down_binary64_21632` `prod-exp_binary64_21610` `add-log-exp_binary64_21600` `cbrt-unprod_binary64_21594` `*-commutative_binary64_21492`

Counts

1 → 22

Calls

1 calls:

6.0ms

(*.f64 (sqrt.f64 1/3) x)

Compiler

Compiled 228 to 190 computations (16.7% saved)

series53.0ms (0.6%)

Error

0.6b

Counts

1 → 3

Calls

1 calls:

51.0ms

(*.f64 (sqrt.f64 1/3) x)

Compiler

Compiled 45 to 57 computations (-26.7% saved)

simplify69.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4865	216
1	4865	216

prune27.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	22	3	25
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	22	7	29

Error

0.5b

Counts

29 → 7

Compiler

Compiled 293 to 254 computations (13.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
0.3b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))

rewrite86.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

21×	`sqrt-prod_binary64_21577`
15×	`add-sqr-sqrt_binary64_21583`
12×	`associate-l_binary64_21502`
10×	`associate-r_binary64_21501`
9×	`pow1_binary64_21622` `add-exp-log_binary64_21599` `add-cbrt-cube_binary64_21597` `add-cube-cbrt_binary64_21596` `*-un-lft-identity_binary64_21561`
4×	`pow-prod-down_binary64_21632` `prod-exp_binary64_21610` `cbrt-unprod_binary64_21594`
3×	`unswap-sqr_binary64_21529`
2×	`add-log-exp_binary64_21600` `*-commutative_binary64_21492`

Counts

2 → 50

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))
6.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))

Compiler

Compiled 836 to 755 computations (9.7% saved)

series122.0ms (1.4%)

Error

0.5b

Counts

2 → 6

Calls

2 calls:

65.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
53.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))

Compiler

Compiled 135 to 156 computations (-15.6% saved)

simplify60.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4878	567
1	4878	567

prune71.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	55	8	63

Error

0.5b

Counts

63 → 8

Compiler

Compiled 803 to 735 computations (8.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))))
0.4b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3)))))
1.0b	(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

rewrite309.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

0.5b

Rules

36×	`add-sqr-sqrt_binary64_21583`
32×	`sqrt-prod_binary64_21577`
28×	`associate-r_binary64_21501`
27×	`pow1_binary64_21622`
22×	`add-exp-log_binary64_21599` `add-cube-cbrt_binary64_21596` `*-un-lft-identity_binary64_21561`
20×	`add-cbrt-cube_binary64_21597`
19×	`cbrt-prod_binary64_21592`
17×	`associate-l_binary64_21502`
12×	`pow-prod-down_binary64_21632`
11×	`prod-exp_binary64_21610` `cbrt-unprod_binary64_21594`
7×	`unswap-sqr_binary64_21529`
6×	`pow1/3_binary64_21643` `swap-sqr_binary64_21528`
4×	`add-log-exp_binary64_21600` `*-commutative_binary64_21492`
2×	`pow-prod-up_binary64_21631` `pow-sqr_binary64_21534`
1×	`pow2_binary64_21642` `pow-plus_binary64_21624`

Counts

4 → 118

Calls

4 calls:

19.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3)))))
11.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))))
9.0ms	(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))
7.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))

Compiler

Compiled 3144 to 2981 computations (5.2% saved)

series638.0ms (7.5%)

Error

0.5b

Counts

4 → 9

Calls

4 calls:

306.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 (cbrt.f64 1/3) (cbrt.f64 1/3)))) (.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3)))))
239.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))))
81.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
0.0ms	(*.f64 (cbrt.f64 1/3) (cbrt.f64 1/3))

Compiler

Compiled 459 to 489 computations (-6.5% saved)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5086	1883

prune232.0ms (2.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	127	8	135

Error

0.5b

Counts

135 → 8

Compiler

Compiled 2832 to 2684 computations (5.2% saved)

regimes2.4s (28.4%)

Accuracy

Total 11.1b remaining (94.3%)

Threshold costs 0b (0%)

Compiler

Compiled 13543 to 11655 computations (13.9% saved)

bsearch128.0ms (1.5%)

Steps

Iters	Range		Point
8	1.0793265465716688e+145	9.261795095599924e+147	1.9982784290001902e+146
7	1.5130522040947306e+44	2.585095881511769e+46	1.5389623186968813e+44
7	7.581629087803451e+30	2.0231118093172926e+32	1.9929948001661953e+32
9	8.197955732331857e-137	1.869130470151144e-129	8.300356615998216e-137

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify24.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	122
1	112	122

Compiler

Compiled 154 to 112 computations (27.3% saved)

end0.0ms (0%)

sample2.4s (28.5%)

Algorithm

1×

intervals

Results

415.0ms

8000×

body

128

valid

Compiler

Compiled 1206 to 1059 computations (12.2% saved)

Details

analyze193.0ms (2.3%)

sample193.0ms (2.3%)

simplify16.0ms (0.2%)

prune5.0ms (0.1%)

localize10.0ms (0.1%)

rewrite113.0ms (1.3%)

series1.0s (12.1%)

simplify51.0ms (0.6%)

prune129.0ms (1.5%)

localize4.0ms (0%)

rewrite26.0ms (0.3%)

series53.0ms (0.6%)

simplify69.0ms (0.8%)

prune27.0ms (0.3%)

localize6.0ms (0.1%)

rewrite86.0ms (1%)

series122.0ms (1.4%)

simplify60.0ms (0.7%)

prune71.0ms (0.8%)

localize13.0ms (0.2%)

rewrite309.0ms (3.6%)

series638.0ms (7.5%)

simplify67.0ms (0.8%)

prune232.0ms (2.7%)

regimes2.4s (28.4%)

bsearch128.0ms (1.5%)

simplify24.0ms (0.3%)

end0.0ms (0%)

sample2.4s (28.5%)

Profiling