Details

sample40.0ms

Algorithm

intervals

Results

25.0ms

643×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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

Merged error: 0.2b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

7.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(+ (* a a) (* b b))
5.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series224.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
32.0ms	(+ (* a a) (* b b))
24.0ms	(* 4.0 (* b b))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5001	385

prune230.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 0.0b

Counts

87 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0b	(* 2 (pow a 2))
0.9b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity`
24×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
12×	`prod-diff`
11×	`add-log-exp`
9×	`add-exp-log`
8×	`associate-r`
6×	`add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `fma-neg` `log1p-expm1-u` `unswap-sqr`
3×	`fma-def` `associate-l` `prod-exp`
2×	`diff-log` `sum-log` `fma-udef` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `associate-+l+` `flip3--` `flip3-+` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

4 → 92

Calls

4 calls:

8.0ms	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
5.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
6.0ms	(* 2 (pow a 2))
1.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series206.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(- (+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4)) 1.0)
53.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
24.0ms	(* 2 (pow a 2))
74.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	322	886
1	1427	748
2	5001	748

prune286.0ms

Filtered

104 candidates to 67 candidates (64.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	103	5	108

Merged error: 0b

Counts

108 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
0.0b	(* 2 (pow a 2))
0.0b	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
13×	`add-cube-cbrt`
9×	`prod-diff`
8×	`add-exp-log` `associate-r`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-neg` `associate-l` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 68

Calls

3 calls:

4.0ms	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
6.0ms	(* 2 (pow a 2))
1.0ms	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

series183.0ms

Counts

3 → 9

Calls

3 calls:

89.0ms	(- (fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4)) 1.0)
24.0ms	(* 2 (pow a 2))
70.0ms	(fma (pow b 2) (+ 4.0 (* 2 (pow a 2))) (pow a 4))

simplify49.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	259	614
1	1045	483
2	5001	476

prune201.0ms

Filtered

77 candidates to 53 candidates (68.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	77	5	82

Merged error: 0b

Counts

82 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.0b	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.9b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`*-commutative` `fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

5.0ms	(* 2.0 (pow a 2))
3.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series202.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 2.0 (pow a 2))
60.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
31.0ms	(* 4.0 (* b b))
82.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify42.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	291	467
1	1199	418
2	5002	407

prune235.0ms

Filtered

89 candidates to 61 candidates (68.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	89	5	94

Merged error: 0b

Counts

94 → 5

regimes160.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	8
1	15	8

end0.0ms

sample1.2s

Algorithm

intervals

Results

833.0ms

20683×

body

valid