Details

sample54.0ms

Algorithm

intervals

Results

36.0ms

664×

body

valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	55	15
1	179	14
2	561	13
3	1824	13
4	5002	13

prune7.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.2b

Counts

2 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`pow-to-exp` `flip3--` `pow-pow` `associate-l` `pow-exp` `*-commutative` `flip--` `unswap-sqr` `sqr-pow`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series303.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(fma 4.0 (fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
49.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
52.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	391	706
1	1680	606
2	5002	592

prune226.0ms

Filtered

84 candidates to 63 candidates (75.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 0.0b

Counts

85 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
12×	`pow1` `add-exp-log`
9×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `associate-r` `pow-prod-down` `pow-exp` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series350.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
99.0ms	(pow (+ (* a a) (* b b)) 2.0)
99.0ms	(pow (+ (* a a) (* b b)) 2.0)
101.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	304	643
1	1350	575
2	5002	555

prune398.0ms

Filtered

102 candidates to 77 candidates (75.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	102	6	108

Merged error: 0.0b

Counts

108 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.1b	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
0.6b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`associate-r` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
6×	`prod-diff` `prod-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `associate-l` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`sub-neg` `associate-r/` `-commutative` `fma-udef` `unpow2` `sqr-pow`
1×	`pow-to-exp` `flip3--` `pow-exp` `flip--`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* 2.0 (pow a 2))
1.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series199.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 2.0 (pow a 2))
52.0ms	(fma (* a a) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a))))
50.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
73.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify53.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	389	579
1	1731	492
2	5001	484

prune275.0ms

Filtered

94 candidates to 62 candidates (66.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	94	6	100

Merged error: 0.0b

Counts

100 → 6

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
24.4b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod` `add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
12×	`add-exp-log`
10×	`pow1` `add-cbrt-cube`
7×	`sqr-pow`
6×	`pow-unpow` `prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in` `pow-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cube-mult` `sub-neg` `pow-pow` `unpow3` `associate-*r/`
1×	`flip3--` `pow1/3` `associate-l` `*-commutative` `flip--` `rem-cbrt-cube` `rem-cube-cbrt` `unswap-sqr`

Counts

4 → 118

Calls

4 calls:

6.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
7.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
6.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

series431.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
105.0ms	(pow (+ (* a a) (* b b)) 2.0)
154.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	484	933
1	2071	873
2	5001	849

prune320.0ms

Filtered

130 candidates to 78 candidates (60.0%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	130	6	136

Merged error: 0.0b

Counts

136 → 6

regimes97.0ms

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	21	13
1	21	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

20463×

body

valid