Details

analyze165.0ms (1.6%)

Algorithm

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

Symmetry

(sort x y z)

Compiler

Compiled 15 to 12 computations (20% saved)

sample34.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

prune3.0ms (0%)

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

37.7b

Counts

2 → 1

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
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)
35.0b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite149.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

37.6b

Rules

22×	`add-sqr-sqrt_binary64_20219`
19×	`add-cube-cbrt_binary64_20232` `times-frac_binary64_20203` `*-un-lft-identity_binary64_20197`
13×	`sqrt-prod_binary64_20213`
11×	`add-log-exp_binary64_20236`
6×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
5×	`pow1_binary64_20258`
4×	`sum-log_binary64_20288`
3×	`flip3-+_binary64_20200` `flip-+_binary64_20171` `associate-/l_binary64_20142` `associate-/r_binary64_20141`
2×	`div-inv_binary64_20194` `rem-sqrt-square_binary64_20210` `associate-/l/_binary64_20144` `+-commutative_binary64_20127`
1×	`pow1/2_binary64_20277` `sqrt-pow1_binary64_20215` `sqrt-div_binary64_20214` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-+l+_binary64_20130`

Counts

4 → 78

Calls

4 calls:

17.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
9.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 2077 to 563 computations (72.9% saved)

series1.2s (11.4%)

Error

0.8b

Counts

4 → 68

Calls

4 calls:

413.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
315.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
213.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
107.0ms	(+.f64 (.f64 x x) (.f64 y y))

Compiler

Compiled 3177 to 2867 computations (9.8% saved)

simplify81.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5054	3483

prune189.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	141	6	147

Error

0.8b

Counts

147 → 6

Compiler

Compiled 3017 to 1062 computations (64.8% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

rewrite52.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

8×	`add-sqr-sqrt_binary64_20219`
6×	`associate-l_binary64_20138`
4×	`add-cube-cbrt_binary64_20232` `*-un-lft-identity_binary64_20197` `sqrt-prod_binary64_20213`
3×	`pow1_binary64_20258` `add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `associate-r_binary64_20137`
2×	`unswap-sqr_binary64_20165`
1×	`pow-prod-down_binary64_20268` `prod-exp_binary64_20246` `add-log-exp_binary64_20236` `cbrt-unprod_binary64_20230` `*-commutative_binary64_20128`

Counts

1 → 22

Calls

1 calls:

10.0ms

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

Compiler

Compiled 228 to 190 computations (16.7% saved)

series49.0ms (0.5%)

Error

0.8b

Counts

1 → 3

Calls

1 calls:

46.0ms

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

Compiler

Compiled 45 to 57 computations (-26.7% saved)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4865	216
1	4865	216

prune27.0ms (0.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	21	4	25
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	21	10	31

Error

0.7b

Counts

31 → 10

Compiler

Compiled 332 to 291 computations (12.3% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
0.2b	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))

rewrite90.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

21×	`sqrt-prod_binary64_20213`
15×	`add-sqr-sqrt_binary64_20219`
12×	`associate-l_binary64_20138`
10×	`associate-r_binary64_20137`
9×	`pow1_binary64_20258` `add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `add-cube-cbrt_binary64_20232` `*-un-lft-identity_binary64_20197`
4×	`pow-prod-down_binary64_20268` `prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
3×	`unswap-sqr_binary64_20165`
2×	`add-log-exp_binary64_20236` `*-commutative_binary64_20128`

Counts

2 → 50

Calls

2 calls:

10.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))
7.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))

Compiler

Compiled 836 to 755 computations (9.7% saved)

series96.0ms (1%)

Error

0.7b

Counts

2 → 6

Calls

2 calls:

55.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 1/3)))
38.0ms	(.f64 (sqrt.f64 (sqrt.f64 1/3)) (.f64 x (sqrt.f64 (sqrt.f64 1/3))))

Compiler

Compiled 135 to 156 computations (-15.6% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4878	567
1	4878	567

prune81.0ms (0.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	2	5	7
Picked	0	1	1
Done	1	1	2
Total	56	10	66

Error

0.6b

Counts

66 → 10

Compiler

Compiled 831 to 757 computations (8.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.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))))
0.3b	(.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))

rewrite317.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Error

0.6b

Rules

36×	`add-sqr-sqrt_binary64_20219`
32×	`sqrt-prod_binary64_20213`
28×	`associate-r_binary64_20137`
27×	`pow1_binary64_20258`
22×	`add-exp-log_binary64_20235` `add-cube-cbrt_binary64_20232` `*-un-lft-identity_binary64_20197`
20×	`add-cbrt-cube_binary64_20233`
19×	`cbrt-prod_binary64_20228`
17×	`associate-l_binary64_20138`
12×	`pow-prod-down_binary64_20268`
11×	`prod-exp_binary64_20246` `cbrt-unprod_binary64_20230`
7×	`unswap-sqr_binary64_20165`
6×	`pow1/3_binary64_20279` `swap-sqr_binary64_20164`
4×	`add-log-exp_binary64_20236` `*-commutative_binary64_20128`
2×	`pow-prod-up_binary64_20267` `pow-sqr_binary64_20170`
1×	`pow2_binary64_20278` `pow-plus_binary64_20260`

Counts

4 → 118

Calls

4 calls:

33.0ms	(.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))))
7.0ms	(*.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)

series451.0ms (4.5%)

Error

0.6b

Counts

4 → 9

Calls

4 calls:

218.0ms	(.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)))))
152.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 1/3))) (sqrt.f64 (sqrt.f64 (cbrt.f64 1/3))))
70.0ms	(*.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)

simplify89.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5086	1883

prune272.0ms (2.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	124	3	127
Fresh	3	4	7
Picked	1	0	1
Done	0	2	2
Total	128	9	137

Error

0.6b

Counts

137 → 9

Compiler

Compiled 2832 to 2684 computations (5.2% saved)

regimes3.1s (30.5%)

Accuracy

Total 10.2b remaining (94%)

Threshold costs 0b (0%)

Compiler

Compiled 19971 to 17012 computations (14.8% saved)

bsearch27.0ms (0.3%)

Steps

Iters	Range		Point
4	-7.063145158942761e-61	-4.294454075858151e-61	-4.367848642812645e-61
3	-1.1049780562537373e+138	-7.801486740724005e+137	-9.222615287767356e+137

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	56
1	64	56

Compiler

Compiled 72 to 58 computations (19.4% saved)

end0.0ms (0%)

sample3.5s (34.3%)

Algorithm

1×

intervals

Results

464.0ms

8000×

body

128

valid

Compiler

Compiled 1695 to 1492 computations (12% saved)

Details

analyze165.0ms (1.6%)

sample34.0ms (0.3%)

simplify14.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite149.0ms (1.5%)

series1.2s (11.4%)

simplify81.0ms (0.8%)

prune189.0ms (1.9%)

localize6.0ms (0.1%)

rewrite52.0ms (0.5%)

series49.0ms (0.5%)

simplify76.0ms (0.8%)

prune27.0ms (0.3%)

localize12.0ms (0.1%)

rewrite90.0ms (0.9%)

series96.0ms (1%)

simplify72.0ms (0.7%)

prune81.0ms (0.8%)

localize14.0ms (0.1%)

rewrite317.0ms (3.1%)

series451.0ms (4.5%)

simplify89.0ms (0.9%)

prune272.0ms (2.7%)

regimes3.1s (30.5%)

bsearch27.0ms (0.3%)

simplify24.0ms (0.2%)

end0.0ms (0%)

sample3.5s (34.3%)

Profiling