Details

sample47.0ms

Algorithm

intervals

Results

31.0ms

676×

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

prune9.0ms

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

localize9.0ms

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)

rewrite22.0ms

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)

series226.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (* a a) (* b b))
70.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
24.0ms	(* 4.0 (* b b))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify255.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (38.0ms)

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

prune189.0ms

Filtered

86 candidates to 66 candidates (76.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	3	87

Merged error: 0.0b

Counts

87 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0b	(* 2 (pow a 2))
2.2b	(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:

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

series146.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
24.0ms	(* 2 (pow a 2))
72.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify36.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	215	372
1	947	344
2	5002	343

prune164.0ms

Filtered

66 candidates to 46 candidates (69.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	66	3	69

Merged error: 0.0b

Counts

69 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.2b	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
22.5b	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 106

Calls

4 calls:

8.0ms	(* 4.0 (* b b))
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))

series386.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 4.0 (* b b))
118.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
100.0ms	(pow (+ (* a a) (* b b)) 2.0)
143.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify47.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	362	755
1	1347	721
2	5001	675

prune224.0ms

Filtered

118 candidates to 74 candidates (62.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	118	3	121

Merged error: 0.0b

Counts

121 → 3

localize23.0ms

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))
35.2b	(/ (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))))

series421.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(fma (- (* 4.0 4.0)) (pow b 4) (pow (fma a a (* b b)) (* 2 2.0)))
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
110.0ms	(pow (fma a a (* b b)) (* 2 2.0))
129.0ms	(/ (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))))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune310.0ms

Filtered

89 candidates to 74 candidates (83.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	89	3	92

Merged error: 0b

Counts

92 → 3

regimes76.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

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

957.0ms

20540×

body

valid