Details

sample77.0ms

Algorithm

intervals

Results

53.0ms

658×

body

valid

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	8
1	41	8
2	67	8
3	119	8
4	309	8
5	1494	8
6	5001	8

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(+ (* a a) (* b b))
6.0ms	(+ (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)

series219.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ (* a a) (* b b))
60.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
29.0ms	(* 4.0 (* b b))
99.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify41.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	322	413
1	1353	379
2	5001	379

prune137.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0.0b

Counts

71 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log`
28×	`prod-exp`
25×	`add-sqr-sqrt`
16×	`unswap-sqr`
14×	`unpow-prod-down`
12×	`pow-to-exp` `pow-exp`
11×	`-un-lft-identity` `associate-l*` `add-cbrt-cube` `add-log-exp`
10×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `associate-r`
6×	`pow1`
4×	`sum-log` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `pow-prod-down` `*-commutative` `flip-+`
1×	`associate-+r+` `distribute-lft-out`

Counts

4 → 101

Calls

4 calls:

8.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
4.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

series171.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2)))))
55.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
36.0ms	(* 2 (* (pow a 2) (pow b 2)))
32.0ms	(* (pow a 2) (pow b 2))

simplify61.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	375	699
1	1613	622
2	5001	616

prune200.0ms

Filtered

113 candidates to 60 candidates (53.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	113	3	116

Merged error: 0.0b

Counts

116 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
2.2b	(* (pow a 2) (pow b 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-exp-log`
31×	`prod-exp`
27×	`add-sqr-sqrt`
17×	`unswap-sqr`
16×	`add-cbrt-cube`
14×	`unpow-prod-down` `associate-l`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r*` `unpow2` `sqr-pow`
9×	`add-log-exp`
7×	`cbrt-unprod`
5×	`pow-prod-down`
3×	`sum-log` `*-commutative`
1×	`+-commutative` `associate-+l+` `flip3-+` `flip-+`

Counts

4 → 108

Calls

4 calls:

7.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
7.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
5.0ms	(* 4.0 (* b b))
7.0ms	(* (pow a 2) (pow b 2))

series155.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
62.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
28.0ms	(* 4.0 (* b b))
30.0ms	(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	400	683
1	1741	575
2	5002	568

prune185.0ms

Filtered

120 candidates to 61 candidates (50.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0)))
0.3b	(pow (+ (* a a) (* b b)) (* 2 2.0))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
35.3b	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite36.0ms

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` `add-log-exp`
4×	`pow-unpow`
3×	`associate-/r` `associate-/l`
2×	`pow-to-exp` `pow-pow` `flip3-+` `pow-exp` `associate-/r/` `flip-+` `associate-/l/` `sqr-pow`
1×	`cbrt-undiv` `+-commutative` `flip3--` `frac-2neg` `div-exp` `clear-num` `sum-log` `flip--` `div-inv`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0)))
4.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
15.0ms	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series604.0ms

Counts

4 → 12

Calls

4 calls:

238.0ms	(+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0)))
99.0ms	(pow (+ (* a a) (* b b)) (* 2 2.0))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)
163.0ms	(/ (+ (* (- (* 4.0 4.0)) (pow b 4)) (pow (+ (* a a) (* b b)) (* 2 2.0))) (- (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify64.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	417	1350
1	2090	1213
2	5002	1147

prune254.0ms

Filtered

86 candidates to 69 candidates (80.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	86	3	89

Merged error: 0.0b

Counts

89 → 3

regimes74.0ms

Accuracy

76.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	20
1	34	20

end0.0ms

sample1.3s

Algorithm

intervals

Results

950.0ms

20498×

body

valid