Details

sample51.0ms

Algorithm

intervals

Results

34.0ms

683×

body

valid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

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

prune6.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.3b	(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:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (* a a) (* b b))
63.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
32.0ms	(* 4.0 (* b b))
110.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5002	385

prune193.0ms

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: 0b

Counts

87 → 4

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (pow a 2))
0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.7b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 57

Calls

3 calls:

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

series159.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(* 2 (pow a 2))
49.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
78.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify39.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	215	372
1	971	344
2	5001	343

prune186.0ms

Filtered

66 candidates to 46 candidates (69.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	66	4	70

Merged error: 0b

Counts

70 → 4

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (fma a a (* b b)) (* 2 2.0))
33.5b	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-exp-log`
6×	`pow1` `unpow-prod-down` `add-cbrt-cube`
4×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r/` `sqr-pow`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `fma-udef` `div-inv`

Counts

4 → 77

Calls

4 calls:

1.0ms	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
2.0ms	(pow (fma a a (* b b)) (* 2 2.0))
8.0ms	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series442.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
109.0ms	(pow (+ (* a a) (* b b)) 2.0)
110.0ms	(pow (fma a a (* b b)) (* 2 2.0))
147.0ms	(/ (fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify66.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	331	1143
1	1391	1040
2	5002	1005

prune323.0ms

Filtered

89 candidates to 74 candidates (83.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	89	4	93

Merged error: 0b

Counts

93 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (fma a a (* b b)) (* 2 2.0))
43.6b	(/ (fma (pow 4.0 3) (pow b 6) (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (fma (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)) (pow (fma a a (* b b)) (* 2 2.0))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`add-exp-log` `unpow-prod-down` `times-frac`
7×	`pow1` `pow-unpow`
6×	`add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `associate-/r` `associate-/l` `sqr-pow`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 84

Calls

4 calls:

5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
2.0ms	(pow (fma a a (* b b)) (* 2 2.0))
3.0ms	(/ (fma (pow 4.0 3) (pow b 6) (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (fma (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)) (pow (fma a a (* b b)) (* 2 2.0))))

series514.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(pow (+ (* a a) (* b b)) 2.0)
105.0ms	(pow (+ (* a a) (* b b)) 2.0)
114.0ms	(pow (fma a a (* b b)) (* 2 2.0))
191.0ms	(/ (fma (pow 4.0 3) (pow b 6) (pow (pow (+ (* a a) (* b b)) 2.0) 3)) (fma (* 4.0 (* b b)) (- (* 4.0 (* b b)) (pow (+ (* a a) (* b b)) 2.0)) (pow (fma a a (* b b)) (* 2 2.0))))

simplify49.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	292	1408
1	1197	1291
2	5001	1267

prune440.0ms

Filtered

96 candidates to 80 candidates (83.3%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	96	4	100

Merged error: 0b

Counts

100 → 4

regimes146.0ms

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

sample1.3s

Algorithm

intervals

Results

942.0ms

20368×

body

valid