Details

analyze653.0ms (15.4%)

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)

sample28.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
3.0ms	96×	body	128	invalid

Compiler

Compiled 27 to 27 computations (0% saved)

simplify131.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	704	19
1	704	19

prune2.0ms (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

5.1b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize8.0ms (0.2%)

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)))
4.8b	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`cancel-sign-sub-inv_binary64_16412`
11×	`add-sqr-sqrt_binary64_16468`
9×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
8×	`add-exp-log_binary64_16484` `pow1_binary64_16507` `distribute-rgt-in_binary64_16396` `associate--r+_binary64_16382` `distribute-lft-in_binary64_16395` `add-cbrt-cube_binary64_16482`
7×	`add-log-exp_binary64_16485`
6×	`sub-neg_binary64_16439`
4×	`associate-r_binary64_16386`
3×	`pow-prod-down_binary64_16517` `cbrt-unprod_binary64_16479` `prod-exp_binary64_16495` `flip3--_binary64_16450` `flip--_binary64_16421`
2×	`associate-*r/_binary64_16388` `diff-log_binary64_16538` `difference-of-squares_binary64_16415`
1×	`-commutative_binary64_16377` `associate-l*_binary64_16387`

Counts

3 → 64

Calls

3 calls:

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

series142.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

72.0ms	(-.f64 (.f64 x x) (.f64 (.f64 y 4) (-.f64 (.f64 z z) t)))
55.0ms	(.f64 (.f64 y 4) (-.f64 (*.f64 z z) t))
15.0ms	(-.f64 (*.f64 z z) t)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4904	1145
1	4904	1145

prune70.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	68	6	74

Error

3.0b

Counts

74 → 6

Compiler

Compiled 1400 to 583 computations (58.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
0.2b	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
4.7b	(sqrt.f64 (-.f64 (*.f64 z z) t))
4.7b	(sqrt.f64 (-.f64 (*.f64 z z) t))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64_16507`
18×	`add-exp-log_binary64_16484` `sqrt-div_binary64_16463` `add-cbrt-cube_binary64_16482`
16×	`sqrt-prod_binary64_16462` `add-sqr-sqrt_binary64_16468`
14×	`associate-r_binary64_16386`
10×	`associate-r/_binary64_16388` `add-cube-cbrt_binary64_16481` `-un-lft-identity_binary64_16446`
9×	`pow-prod-down_binary64_16517` `cbrt-unprod_binary64_16479` `prod-exp_binary64_16495` `flip3--_binary64_16450` `flip--_binary64_16421`
4×	`add-log-exp_binary64_16485` `difference-of-squares_binary64_16415` `frac-times_binary64_16456`
2×	`rem-sqrt-square_binary64_16459` `sqrt-pow1_binary64_16464` `-commutative_binary64_16377` `associate-l/_binary64_16389` `pow1/2_binary64_16526` `associate-l_binary64_16387`

Counts

4 → 89

Calls

4 calls:

17.0ms	(.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)))
4.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
4.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

series169.0ms (4%)

Counts

4 → 12

Calls

4 calls:

59.0ms	(.f64 (.f64 (.f64 y 4) (sqrt.f64 (-.f64 (.f64 z z) t))) (sqrt.f64 (-.f64 (*.f64 z z) t)))
55.0ms	(.f64 (.f64 y 4) (sqrt.f64 (-.f64 (*.f64 z z) t)))
29.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))
26.0ms	(sqrt.f64 (-.f64 (*.f64 z z) t))

simplify70.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5168	1705

prune92.0ms (2.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Error

3.0b

Counts

107 → 7

Compiler

Compiled 2622 to 863 computations (67.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (*.f64 z z) t)
2.9b	(-.f64 (pow.f64 z 4) (*.f64 t t))
7.7b	(.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (*.f64 t t)))
19.9b	(/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (.f64 z z) t))

rewrite37.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
11×	`add-sqr-sqrt_binary64_16468`
9×	`pow1_binary64_16507`
8×	`add-log-exp_binary64_16485`
7×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
6×	`cbrt-unprod_binary64_16479` `prod-exp_binary64_16495` `associate-r_binary64_16386` `difference-of-squares_binary64_16415`
4×	`associate-*r/_binary64_16388`
3×	`times-frac_binary64_16452` `cbrt-undiv_binary64_16480` `pow-prod-down_binary64_16517` `sub-neg_binary64_16439` `cancel-sign-sub-inv_binary64_16412` `flip3--_binary64_16450` `div-exp_binary64_16497` `flip--_binary64_16421` `associate-/r*_binary64_16390`
2×	`associate-/l/_binary64_16393` `unpow-prod-down_binary64_16525` `flip3-+_binary64_16449` `distribute-rgt-in_binary64_16396` `distribute-lft-in_binary64_16395` `flip-+_binary64_16420` `associate-/r/_binary64_16392` `sqr-pow_binary64_16418`
1×	`+-commutative_binary64_16376` `clear-num_binary64_16445` `-commutative_binary64_16377` `div-inv_binary64_16443` `diff-log_binary64_16538` `associate-/l_binary64_16391` `sum-log_binary64_16537` `frac-2neg_binary64_16457` `associate-l_binary64_16387`

Counts

4 → 80

Calls

4 calls:

13.0ms	(/.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))
4.0ms	(+.f64 (*.f64 z z) t)

series285.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (.f64 t t))) (+.f64 (.f64 z z) t))
93.0ms	(.f64 (.f64 y 4) (-.f64 (pow.f64 z 4) (*.f64 t t)))
27.0ms	(-.f64 (pow.f64 z 4) (*.f64 t t))
15.0ms	(+.f64 (*.f64 z z) t)

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5043	1481

prune99.0ms (2.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	92	7	99

Error

3.0b

Counts

99 → 7

Compiler

Compiled 2305 to 999 computations (56.7% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 z z) t)
0.2b	(/.f64 1 (-.f64 (*.f64 z z) t))
0.5b	(/.f64 1 (.f64 (/.f64 (/.f64 1 (-.f64 (.f64 z z) t)) y) 1/4))
4.7b	(/.f64 (/.f64 1 (-.f64 (*.f64 z z) t)) y)

rewrite54.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`times-frac_binary64_16452`
84×	`add-sqr-sqrt_binary64_16468`
71×	`add-exp-log_binary64_16484`
67×	`add-cube-cbrt_binary64_16481` `*-un-lft-identity_binary64_16446`
38×	`div-exp_binary64_16497`
25×	`add-cbrt-cube_binary64_16482`
24×	`associate-/l*_binary64_16391`
17×	`difference-of-squares_binary64_16415`
15×	`prod-exp_binary64_16495`
11×	`cbrt-undiv_binary64_16480` `1-exp_binary64_16490` `rec-exp_binary64_16496` `associate-/r/_binary64_16392`
8×	`pow1_binary64_16507` `associate-/r*_binary64_16390`
7×	`div-inv_binary64_16443`
6×	`add-log-exp_binary64_16485` `flip3--_binary64_16450` `flip--_binary64_16421`
3×	`clear-num_binary64_16445` `pow-flip_binary64_16520` `cbrt-unprod_binary64_16479` `cancel-sign-sub-inv_binary64_16412` `frac-2neg_binary64_16457`
2×	`inv-pow_binary64_16531`
1×	`associate-/l/_binary64_16393` `pow-prod-down_binary64_16517` `diff-log_binary64_16538` `sub-neg_binary64_16439` `associate-*l/_binary64_16389`

Counts

4 → 187

Calls

4 calls:

16.0ms	(/.f64 1 (.f64 (/.f64 (/.f64 1 (-.f64 (.f64 z z) t)) y) 1/4))
10.0ms	(/.f64 (/.f64 1 (-.f64 (*.f64 z z) t)) y)
7.0ms	(/.f64 1 (-.f64 (*.f64 z z) t))
4.0ms	(-.f64 (*.f64 z z) t)

series102.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(/.f64 1 (.f64 (/.f64 (/.f64 1 (-.f64 (.f64 z z) t)) y) 1/4))
34.0ms	(/.f64 (/.f64 1 (-.f64 (*.f64 z z) t)) y)
15.0ms	(-.f64 (*.f64 z z) t)
13.0ms	(/.f64 1 (-.f64 (*.f64 z z) t))

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	3708
1	4966	3708

prune200.0ms (4.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	198	1	199
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	198	8	206

Error

3.0b

Counts

206 → 8

Compiler

Compiled 4577 to 2000 computations (56.3% saved)

regimes594.0ms (14%)

Accuracy

Total 0.9b remaining (25.5%)

Threshold costs 0.9b (25.5%)

Compiler

Compiled 5851 to 4620 computations (21% saved)

bsearch2.0ms (0%)

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

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	326	54
1	326	54

end0.0ms (0%)

sample1.2s (27.5%)

Algorithm

1×

intervals

Results

295.0ms	8000×	body	128	valid
116.0ms	3044×	body	128	invalid

Compiler

Compiled 560 to 435 computations (22.3% saved)

Details

analyze653.0ms (15.4%)

sample28.0ms (0.7%)

simplify131.0ms (3.1%)

prune2.0ms (0%)

localize8.0ms (0.2%)

rewrite24.0ms (0.6%)

series142.0ms (3.3%)

simplify67.0ms (1.6%)

prune70.0ms (1.7%)

localize11.0ms (0.3%)

rewrite44.0ms (1%)

series169.0ms (4%)

simplify70.0ms (1.7%)

prune92.0ms (2.2%)

localize13.0ms (0.3%)

rewrite37.0ms (0.9%)

series285.0ms (6.7%)

simplify65.0ms (1.5%)

prune99.0ms (2.3%)

localize11.0ms (0.3%)

rewrite54.0ms (1.3%)

series102.0ms (2.4%)

simplify96.0ms (2.3%)

prune200.0ms (4.7%)

regimes594.0ms (14%)

bsearch2.0ms (0%)

simplify9.0ms (0.2%)

end0.0ms (0%)

sample1.2s (27.5%)

Profiling