Details

sample53.0ms

Algorithm

intervals

Results

34.0ms

664×

body

valid

simplify78.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	53	14
1	173	13
2	532	12
3	1681	12
4	4278	12
5	5001	12

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

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.0b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
0.5b	(* (* b b) (+ 3.0 a))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

1.0ms	(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
1.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(* (* b b) (+ 3.0 a))

series274.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(fma 4.0 (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
46.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
100.0ms	(pow (+ (* a a) (* b b)) 2.0)
32.0ms	(* (* b b) (+ 3.0 a))

simplify45.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	335	551
1	1554	479
2	5001	471

prune230.0ms

Filtered

77 candidates to 61 candidates (79.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	71	6	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	6	78

Merged error: 0.0b

Counts

78 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 4.0 (fma (* b 3.0) b (* (* a a) (- 1.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
0.1b	(* (* a a) (- 1.0 a))
0.2b	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`pow1` `add-exp-log`
9×	`add-cbrt-cube`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `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--` `distribute-lft-out--` `difference-of-squares` `unswap-sqr` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

1.0ms	(fma 4.0 (fma (* b 3.0) b (* (* a a) (- 1.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
9.0ms	(* (* a a) (- 1.0 a))
1.0ms	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series283.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(fma 4.0 (fma (* b 3.0) b (* (* a a) (- 1.0 a))) (- (pow (+ (* a a) (* b b)) 2.0) 1.0))
48.0ms	(* (* a a) (- 1.0 a))
46.0ms	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
102.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	442	827
1	2120	631
2	5003	624

prune222.0ms

Filtered

98 candidates to 62 candidates (63.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	5	0	5
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Merged error: 0.0b

Counts

104 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.1b	(* (* a a) (- 1.0 a))
0.2b	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
0.6b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
14×	`add-exp-log`
13×	`associate-r`
11×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
9×	`pow1`
6×	`prod-exp`
5×	`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--` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* 2.0 (pow a 2))
9.0ms	(* (* a a) (- 1.0 a))
1.0ms	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
1.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series198.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* 2.0 (pow a 2))
48.0ms	(* (* a a) (- 1.0 a))
47.0ms	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
73.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify62.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	434	726
1	2321	535
2	5002	535

prune257.0ms

Filtered

108 candidates to 61 candidates (56.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	108	5	113

Merged error: 0.0b

Counts

113 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`unpow-prod-down`
20×	`cbrt-prod`
16×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
14×	`cube-prod`
7×	`add-exp-log` `sqr-pow`
6×	`pow-unpow`
5×	`pow1` `pow-exp` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp`
2×	`cube-mult` `pow-pow` `unpow3`
1×	`pow1/3` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 95

Calls

4 calls:

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

series410.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma (* b 3.0) b (* (* a a) (- 1.0 a)))
116.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
100.0ms	(pow (+ (* a a) (* b b)) 2.0)
146.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify43.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	323	769
1	1197	733
2	5001	687

prune260.0ms

Filtered

107 candidates to 68 candidates (63.6%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

regimes53.0ms

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	19	11
1	19	11

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

20463×

body

valid