Details

analyze112.0ms (1.7%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	53.1%	22%	7
25%	46.8%	28.2%	8
25%	33.6%	41.5%	9
28.1%	18%	54%	10
31.6%	12.1%	56.3%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 30 to 20 computations (33.3% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 47 to 34 computations (27.7% saved)

simplify37.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5126	25

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

2.4b

Counts

2 → 1

Compiler

Compiled 34 to 24 computations (29.4% saved)

localize13.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 4 (.f64 b b))
0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
0.0b	(.f64 4 (.f64 b b))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`add-log-exp_binary64_117` `*-un-lft-identity_binary64_78`
10×	`add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-cbrt-cube_binary64_114`
8×	`add-cube-cbrt_binary64_113`
3×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unpow-prod-down_binary64_157` `pow-prod-down_binary64_149` `pow-unpow_binary64_155` `cancel-sign-sub-inv_binary64_44`
2×	`diff-log_binary64_170` `difference-of-squares_binary64_47` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate--l+_binary64_15` `associate-r*_binary64_18` `pow-pow_binary64_150` `flip--_binary64_53` `unswap-sqr_binary64_46` `difference-of-sqr-1_binary64_48` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 68

Calls

8 calls:

10.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
5.0ms	(.f64 4 (.f64 b b))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
4.0ms	(+.f64 (.f64 a a) (.f64 b b))
0.0ms	(+.f64 (.f64 a a) (.f64 b b))

series643.0ms (9.7%)

Counts

4 → 51

Calls

4 calls:

369.0ms	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (.f64 b b))) 1)
169.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
80.0ms	(+.f64 (.f64 a a) (.f64 b b))
24.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1310 to 1149 computations (12.3% saved)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4998	1957
1	4998	1957

prune166.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	10	119
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	10	120

Error

2.2b

Counts

120 → 10

Compiler

Compiled 2602 to 1306 computations (49.8% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

2.5b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
0.0b	(.f64 4 (.f64 b b))
0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b))) 1)
0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
0.0b	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
0.0b	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b))) 1)
0.0b	(.f64 4 (.f64 b b))
2.5b	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
27×	`add-log-exp_binary64_117`
18×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
12×	`sum-log_binary64_169`
11×	`add-sqr-sqrt_binary64_100`
9×	`*-un-lft-identity_binary64_78`
6×	`add-cube-cbrt_binary64_113`
4×	`associate-l_binary64_19` `diff-log_binary64_170`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`-commutative_binary64_9` `associate-r*_binary64_18` `difference-of-squares_binary64_47`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `associate--l+_binary64_15` `associate-+l+_binary64_11` `flip--_binary64_53` `unswap-sqr_binary64_46` `difference-of-sqr-1_binary64_48` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 83

Calls

8 calls:

15.0ms	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b))) 1)
12.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
10.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
5.0ms	(.f64 4 (.f64 b b))
0.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))

series827.0ms (12.4%)

Counts

4 → 45

Calls

4 calls:

364.0ms	(-.f64 (+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b))) 1)
352.0ms	(+.f64 (+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 (.f64 a a) (.f64 b (.f64 b 2))))) (.f64 4 (.f64 b b)))
88.0ms	(.f64 (.f64 a a) (.f64 b (.f64 b 2)))
24.0ms	(.f64 4 (.f64 b b))

Compiler

Compiled 1334 to 1174 computations (12% saved)

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5152	2680

prune153.0ms (2.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	128	10	138

Error

2.2b

Counts

138 → 10

Compiler

Compiled 3437 to 2106 computations (38.7% saved)

localize15.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
13.6b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
13.6b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`pow1_binary64_139`
6×	`sqrt-prod_binary64_94` `unpow-prod-down_binary64_157` `add-exp-log_binary64_116` `pow-unpow_binary64_155`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-div_binary64_95`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow1/2_binary64_158` `flip3-+_binary64_81`

Counts

4 → 66

Calls

8 calls:

9.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(+.f64 1 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))))

series687.0ms (10.3%)

Counts

4 → 63

Calls

4 calls:

193.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
183.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
181.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
129.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))

Compiler

Compiled 3552 to 2668 computations (24.9% saved)

simplify50.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5265	2496

prune242.0ms (3.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	129	10	139

Error

2.1b

Counts

139 → 10

Compiler

Compiled 5475 to 2667 computations (51.3% saved)

localize14.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 1 (+.f64 (.f64 a a) (.f64 b b)))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(.f64 (.f64 b b) 4)
0.2b	(.f64 (+.f64 1 (+.f64 (.f64 a a) (.f64 b b))) (+.f64 -1 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
13.6b	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
13×	`pow1_binary64_139`
12×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114`
10×	`add-cube-cbrt_binary64_113`
7×	`flip-+_binary64_52` `associate-r_binary64_18` `flip3-+_binary64_81`
5×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-times_binary64_88` `pow-prod-down_binary64_149`
3×	`sqrt-prod_binary64_94` `unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`-commutative_binary64_9` `associate-l/_binary64_21` `unswap-sqr_binary64_46` `sqrt-div_binary64_95` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`distribute-lft-in_binary64_27` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `unpow2_binary64_143` `distribute-rgt-in_binary64_28` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow1/2_binary64_158`

Counts

4 → 82

Calls

8 calls:

17.0ms	(.f64 (+.f64 1 (+.f64 (.f64 a a) (.f64 b b))) (+.f64 -1 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))
7.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
5.0ms	(.f64 (.f64 b b) 4)
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
0.0ms	(+.f64 (.f64 a a) (.f64 b b))

series816.0ms (12.3%)

Counts

4 → 54

Calls

4 calls:

428.0ms	(.f64 (+.f64 1 (+.f64 (.f64 a a) (.f64 b b))) (+.f64 -1 (sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (*.f64 b b) 4)))))
186.0ms	(sqrt.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 (.f64 b b) 4)))
179.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
23.0ms	(.f64 (.f64 b b) 4)

Compiler

Compiled 2769 to 2216 computations (20% saved)

simplify79.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5071	3738

prune180.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	136	10	146

Error

2.1b

Counts

146 → 10

Compiler

Compiled 4591 to 2058 computations (55.2% saved)

regimes701.0ms (10.5%)

Accuracy

Total -2.3b remaining (-6250.9%)

Threshold costs -2.3b (-6250.9%)

Compiler

Compiled 8933 to 5737 computations (35.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	37
1	35	37

end4.0ms (0.1%)

Compiler: Compiled 89 to 62 computations (30.3% saved)

sample1.6s (23.6%)

Algorithm

1×

intervals

Results

460.0ms	8000×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 1361 to 888 computations (34.8% saved)

Pareto

-0.33802945985230737

Details

analyze112.0ms (1.7%)

sample23.0ms (0.3%)

simplify37.0ms (0.6%)

prune2.0ms (0%)

localize13.0ms (0.2%)

rewrite29.0ms (0.4%)

series643.0ms (9.7%)

simplify80.0ms (1.2%)

prune166.0ms (2.5%)

localize15.0ms (0.2%)

rewrite51.0ms (0.8%)

series827.0ms (12.4%)

simplify64.0ms (1%)

prune153.0ms (2.3%)

localize15.0ms (0.2%)

rewrite33.0ms (0.5%)

series687.0ms (10.3%)

simplify50.0ms (0.7%)

prune242.0ms (3.6%)

localize14.0ms (0.2%)

rewrite43.0ms (0.6%)

series816.0ms (12.3%)

simplify79.0ms (1.2%)

prune180.0ms (2.7%)

regimes701.0ms (10.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end4.0ms (0.1%)

sample1.6s (23.6%)

Profiling