Details

analyze1.1s (15.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
6.0ms	98×	body	128	invalid

Compiler

Compiled 27 to 27 computations (0% saved)

simplify199.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	704	19
1	704	19

prune4.0ms (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

6.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize24.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 z z) t)
0.0b	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
5.7b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cancel-sign-sub-inv_binary64_10615`
11×	`add-sqr-sqrt_binary64_10671`
9×	`*-un-lft-identity_binary64_10649` `add-cube-cbrt_binary64_10684`
8×	`pow1_binary64_10710` `add-cbrt-cube_binary64_10685` `associate--r+_binary64_10585` `add-exp-log_binary64_10687` `distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598`
7×	`add-log-exp_binary64_10688`
6×	`sub-neg_binary64_10642`
4×	`associate-r_binary64_10589`
3×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `pow-prod-down_binary64_10720` `flip3--_binary64_10653` `flip--_binary64_10624`
2×	`difference-of-squares_binary64_10618` `associate-*r/_binary64_10591` `diff-log_binary64_10741`
1×	`-commutative_binary64_10580` `associate-l*_binary64_10590`

Counts

3 → 64

Calls

3 calls:

18.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
10.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
5.0ms	(-.f64 (*.f64 z z) t)

series219.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

124.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
78.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
17.0ms	(-.f64 (*.f64 z z) t)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4904	1145
1	4904	1145

prune99.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	67	6	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	7	74

Error

2.5b

Counts

74 → 7

Compiler

Compiled 1429 to 601 computations (57.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
0.1b	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
5.7b	(sqrt.f64 (-.f64 (*.f64 z z) t))
5.7b	(sqrt.f64 (-.f64 (*.f64 z z) t))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64_10710`
18×	`add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687` `sqrt-div_binary64_10666`
16×	`add-sqr-sqrt_binary64_10671` `sqrt-prod_binary64_10665`
14×	`associate-r_binary64_10589`
10×	`-un-lft-identity_binary64_10649` `add-cube-cbrt_binary64_10684` `associate-r/_binary64_10591`
9×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `pow-prod-down_binary64_10720` `flip3--_binary64_10653` `flip--_binary64_10624`
4×	`add-log-exp_binary64_10688` `difference-of-squares_binary64_10618` `frac-times_binary64_10659`
2×	`associate-l/_binary64_10592` `sqrt-pow1_binary64_10667` `pow1/2_binary64_10729` `-commutative_binary64_10580` `rem-sqrt-square_binary64_10662` `associate-l_binary64_10590`

Counts

4 → 89

Calls

4 calls:

16.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
10.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
5.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
4.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

series277.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
87.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
53.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
34.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5168	1705

prune145.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	101	7	108

Error

2.5b

Counts

108 → 7

Compiler

Compiled 2624 to 860 computations (67.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
1.2b	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
5.7b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
5.7b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`pow1_binary64_10710` `add-sqr-sqrt_binary64_10671`
14×	`add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687`
12×	`cancel-sign-sub-inv_binary64_10615` `*-un-lft-identity_binary64_10649` `add-cube-cbrt_binary64_10684`
8×	`distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598` `associate-r_binary64_10589`
6×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `pow-prod-down_binary64_10720` `sqrt-prod_binary64_10665`
4×	`add-log-exp_binary64_10688` `sub-neg_binary64_10642` `flip3--_binary64_10653` `flip--_binary64_10624` `associate-*r/_binary64_10591` `sqrt-div_binary64_10666`
2×	`difference-of-squares_binary64_10618` `sqrt-pow1_binary64_10667` `pow1/2_binary64_10729` `-commutative_binary64_10580` `rem-sqrt-square_binary64_10662` `associate-l*_binary64_10590`

Counts

4 → 88

Calls

4 calls:

15.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
13.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
7.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
4.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))

series551.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

237.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
188.0ms	(sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t))))
64.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
62.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4930	1844
1	4930	1844

prune170.0ms (2.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	100	7	107

Error

2.5b

Counts

107 → 7

Compiler

Compiled 3497 to 1477 computations (57.8% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
3.0b	(-.f64 (pow.f64 z 4) (*.f64 t t))
8.1b	(.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (*.f64 t t)))
24.4b	(/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (.f64 z z) t))

rewrite75.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_10685` `add-exp-log_binary64_10687`
14×	`add-sqr-sqrt_binary64_10671`
12×	`cancel-sign-sub-inv_binary64_10615`
9×	`pow1_binary64_10710` `*-un-lft-identity_binary64_10649` `add-cube-cbrt_binary64_10684`
8×	`add-log-exp_binary64_10688`
7×	`difference-of-squares_binary64_10618`
6×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682` `times-frac_binary64_10655` `associate-r_binary64_10589`
4×	`sub-neg_binary64_10642` `associate-/r/_binary64_10595` `flip3--_binary64_10653` `flip--_binary64_10624` `associate-*r/_binary64_10591`
3×	`associate-/r*_binary64_10593` `pow-prod-down_binary64_10720` `div-exp_binary64_10700` `cbrt-undiv_binary64_10683`
2×	`sqr-pow_binary64_10621` `distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598` `flip-+_binary64_10623` `div-inv_binary64_10646` `unpow-prod-down_binary64_10728` `flip3-+_binary64_10652` `associate-/l/_binary64_10596` `diff-log_binary64_10741`
1×	`clear-num_binary64_10648` `associate-/l_binary64_10594` `-commutative_binary64_10580` `frac-2neg_binary64_10660` `associate-l_binary64_10590`

Counts

4 → 90

Calls

4 calls:

26.0ms	(/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (.f64 z z) t))
14.0ms	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
9.0ms	(.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (*.f64 t t)))
5.0ms	(-.f64 (pow.f64 z 4) (*.f64 t t))

series761.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

333.0ms	(-.f64 (.f64 x x) (/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (*.f64 z z) t)))
254.0ms	(/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (.f64 z z) t))
126.0ms	(.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (*.f64 t t)))
48.0ms	(-.f64 (pow.f64 z 4) (*.f64 t t))

simplify112.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4938	2071
1	4938	2071

prune163.0ms (2.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	1	2	3
Picked	0	1	1
Done	0	3	3
Total	102	7	109

Error

2.4b

Counts

109 → 7

Compiler

Compiled 2491 to 1085 computations (56.4% saved)

regimes793.0ms (11.6%)

Accuracy

Total 0.6b remaining (19.6%)

Threshold costs 0.6b (19.6%)

Compiler

Compiled 3702 to 2894 computations (21.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	326	54
1	326	54

end0.0ms (0%)

sample1.6s (23.8%)

Algorithm

1×

intervals

Results

465.0ms	8000×	body	128	valid
183.0ms	3133×	body	128	invalid

Compiler

Compiled 357 to 273 computations (23.5% saved)

Details

analyze1.1s (15.7%)

sample39.0ms (0.6%)

simplify199.0ms (2.9%)

prune4.0ms (0.1%)

localize24.0ms (0.3%)

rewrite38.0ms (0.6%)

series219.0ms (3.2%)

simplify80.0ms (1.2%)

prune99.0ms (1.4%)

localize12.0ms (0.2%)

rewrite48.0ms (0.7%)

series277.0ms (4.1%)

simplify109.0ms (1.6%)

prune145.0ms (2.1%)

localize12.0ms (0.2%)

rewrite48.0ms (0.7%)

series551.0ms (8.1%)

simplify109.0ms (1.6%)

prune170.0ms (2.5%)

localize29.0ms (0.4%)

rewrite75.0ms (1.1%)

series761.0ms (11.1%)

simplify112.0ms (1.6%)

prune163.0ms (2.4%)

regimes793.0ms (11.6%)

bsearch2.0ms (0%)

simplify15.0ms (0.2%)

end0.0ms (0%)

sample1.6s (23.8%)

Profiling