Details

analyze14.0ms (0.3%)

Algorithm

1×

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

Compiler

Compiled 15 to 12 computations (20% saved)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms

256×

body

128

valid

Compiler

Compiled 29 to 26 computations (10.3% saved)

simplify99.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	21
1	22	21

prune3.0ms (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

38.5b

Counts

2 → 1

Compiler

Compiled 28 to 22 computations (21.4% saved)

localize10.0ms (0.2%)

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)
35.9b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite27.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_22606`
19×	`times-frac_binary64_22590`
18×	`*-un-lft-identity_binary64_22584` `add-cube-cbrt_binary64_22619`
13×	`sqrt-prod_binary64_22600`
8×	`add-log-exp_binary64_22623`
5×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
4×	`pow1_binary64_22645`
3×	`associate-/l_binary64_22529` `associate-/r_binary64_22528` `sum-log_binary64_22675`
2×	`flip3-+_binary64_22587` `associate-/l/_binary64_22531` `div-inv_binary64_22581` `rem-sqrt-square_binary64_22597` `flip-+_binary64_22558`
1×	`cbrt-undiv_binary64_22618` `div-exp_binary64_22635` `sqrt-pow1_binary64_22602` `clear-num_binary64_22583` `+-commutative_binary64_22514` `sqrt-div_binary64_22601` `pow1/2_binary64_22664` `associate-+l+_binary64_22517` `frac-2neg_binary64_22595`

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))

series179.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))
44.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
32.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4955	2002
1	4955	2002

prune86.0ms (2.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	70	6	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	6	77

Error

17.9b

Counts

77 → 6

Compiler

Compiled 1779 to 532 computations (70.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
35.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite30.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`sqrt-prod_binary64_22600`
36×	`times-frac_binary64_22590`
33×	`add-sqr-sqrt_binary64_22606`
32×	`*-un-lft-identity_binary64_22584` `add-cube-cbrt_binary64_22619`
8×	`add-log-exp_binary64_22623`
6×	`associate-/l_binary64_22529` `associate-/r_binary64_22528`
5×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
4×	`sqrt-div_binary64_22601` `pow1_binary64_22645`
3×	`flip3-+_binary64_22587` `sum-log_binary64_22675` `flip-+_binary64_22558`
2×	`associate-/l/_binary64_22531`
1×	`cbrt-undiv_binary64_22618` `div-exp_binary64_22635` `sqrt-pow1_binary64_22602` `div-inv_binary64_22581` `clear-num_binary64_22583` `+-commutative_binary64_22514` `rem-sqrt-square_binary64_22597` `pow1/2_binary64_22664` `sqrt-undiv_binary64_22605` `associate-+l+_binary64_22517` `frac-2neg_binary64_22595`

Counts

3 → 91

Calls

3 calls:

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

series242.0ms (5.8%)

Counts

3 → 9

Calls

3 calls:

133.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
76.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
34.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

simplify93.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5196	3169

prune92.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	97	9	106

Error

17.7b

Counts

106 → 9

Compiler

Compiled 2594 to 746 computations (71.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.4b	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
35.8b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_22606`
13×	`sqrt-prod_binary64_22600`
8×	`*-un-lft-identity_binary64_22584` `add-log-exp_binary64_22623` `pow1_binary64_22645` `add-cube-cbrt_binary64_22619`
6×	`associate-r_binary64_22524` `associate-l_binary64_22525`
5×	`add-cbrt-cube_binary64_22620` `add-exp-log_binary64_22622`
4×	`sqrt-div_binary64_22601` `unswap-sqr_binary64_22552`
3×	`flip3-+_binary64_22587` `sqrt-pow1_binary64_22602` `sum-log_binary64_22675` `pow1/2_binary64_22664` `flip-+_binary64_22558` `pow-prod-down_binary64_22655`
2×	`associate-*l/_binary64_22527`
1×	`cbrt-unprod_binary64_22617` `+-commutative_binary64_22514` `prod-exp_binary64_22633` `rem-sqrt-square_binary64_22597` `associate-+l+_binary64_22517` `*-commutative_binary64_22515` `sqrt-unprod_binary64_22604`

Counts

3 → 60

Calls

3 calls:

12.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
8.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

series207.0ms (5%)

Counts

3 → 9

Calls

3 calls:

107.0ms	(.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z))) (sqrt.f64 1/3))
67.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))
33.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))

simplify63.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4932	1631
1	4932	1631

prune62.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	69	9	78

Error

17.7b

Counts

78 → 9

Compiler

Compiled 1586 to 474 computations (70.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3))
0.3b	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 3))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (sqrt.f64 3))))
1.0b	(/.f64 1 (sqrt.f64 3))
35.8b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3)))

rewrite78.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

170×	`sqrt-prod_binary64_22600`
148×	`add-sqr-sqrt_binary64_22606`
120×	`times-frac_binary64_22590`
83×	`*-un-lft-identity_binary64_22584`
75×	`add-cube-cbrt_binary64_22619`
25×	`associate-r_binary64_22524` `associate-l_binary64_22525`
24×	`unswap-sqr_binary64_22552`
12×	`associate-/r*_binary64_22528` `add-exp-log_binary64_22622`
11×	`pow1_binary64_22645`
10×	`add-cbrt-cube_binary64_22620`
6×	`associate-/l*_binary64_22529`
5×	`div-inv_binary64_22581` `sqrt-div_binary64_22601`
4×	`sqrt-pow1_binary64_22602` `add-log-exp_binary64_22623` `pow1/2_binary64_22664`
3×	`div-exp_binary64_22635` `pow-flip_binary64_22658` `rem-sqrt-square_binary64_22597` `pow-prod-down_binary64_22655`
2×	`associate-/l/_binary64_22531` `cbrt-undiv_binary64_22618` `clear-num_binary64_22583` `frac-2neg_binary64_22595`
1×	`associate-r/_binary64_22526` `flip3-+_binary64_22587` `cbrt-unprod_binary64_22617` `1-exp_binary64_22628` `prod-exp_binary64_22633` `frac-times_binary64_22594` `-commutative_binary64_22515` `inv-pow_binary64_22669` `rec-exp_binary64_22634` `flip-+_binary64_22558` `associate-*l/_binary64_22527` `sqrt-unprod_binary64_22604`

Counts

4 → 212

Calls

4 calls:

32.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 3))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (sqrt.f64 3))))
9.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3))
7.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3)))
4.0ms	(/.f64 1 (sqrt.f64 3))

series381.0ms (9.1%)

Counts

4 → 10

Calls

4 calls:

189.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3)))
128.0ms	(.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 3))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) (sqrt.f64 3))))
65.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (sqrt.f64 3))
0.0ms	(/.f64 1 (sqrt.f64 3))

simplify121.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4909	7323
1	4909	7323

prune330.0ms (7.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	218	4	222
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	219	12	231

Error

17.7b

Counts

231 → 12

Compiler

Compiled 7090 to 3554 computations (49.9% saved)

regimes797.0ms (19.1%)

Accuracy

Total 7.3b remaining (28.8%)

Threshold costs 0b (0%)

Compiler

Compiled 7362 to 5450 computations (26% saved)

bsearch30.0ms (0.7%)

Steps

Iters	Range		Point
9	1.5867353562277276e+73	7.431087739947706e+80	5.427644600415484e+80
5	-6.500267094506816e+117	-3.0872243938781714e+117	-4.387595707132531e+117

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	47
1	38	47

end0.0ms (0%)

sample1.1s (25.6%)

Algorithm

1×

intervals

Results

363.0ms

8000×

body

128

valid

Compiler

Compiled 581 to 443 computations (23.8% saved)

Details

analyze14.0ms (0.3%)

sample19.0ms (0.4%)

simplify99.0ms (2.4%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite27.0ms (0.7%)

series179.0ms (4.3%)

simplify71.0ms (1.7%)

prune86.0ms (2.1%)

localize10.0ms (0.2%)

rewrite30.0ms (0.7%)

series242.0ms (5.8%)

simplify93.0ms (2.2%)

prune92.0ms (2.2%)

localize10.0ms (0.2%)

rewrite32.0ms (0.8%)

series207.0ms (5%)

simplify63.0ms (1.5%)

prune62.0ms (1.5%)

localize13.0ms (0.3%)

rewrite78.0ms (1.9%)

series381.0ms (9.1%)

simplify121.0ms (2.9%)

prune330.0ms (7.9%)

regimes797.0ms (19.1%)

bsearch30.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (25.6%)

Profiling