Details

sample47.0ms

Algorithm

intervals

Results

31.0ms

679×

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

localize12.0ms

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))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite22.0ms

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

series216.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a a) (* b b))
66.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
24.0ms	(* 4.0 (* b b))
100.0ms	(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

prune148.0ms

Filtered

70 candidates to 49 candidates (70.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

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))))) 1.0)
0.0b	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
0.0b	(* 2 (* (pow a 2) (pow b 2)))
3.4b	(* (pow a 2) (pow b 2))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

11.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
5.0ms	(+ (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))

series173.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (+ (pow a 4) (+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))) 1.0)
54.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
34.0ms	(* 2 (* (pow a 2) (pow b 2)))
35.0ms	(* (pow a 2) (pow b 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	382	781
1	1594	689
2	5001	676

prune207.0ms

Filtered

117 candidates to 61 candidates (52.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	0	117
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	117	4	121

Merged error: 0b

Counts

121 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.4b	(pow (+ (* a a) (* b b)) 2.0)
4.3b	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
15.4b	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1`
11×	`add-exp-log` `add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-cbrt-cube`
6×	`log-prod`
4×	`log-div` `exp-prod` `add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `associate-l` `exp-sum` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3-+` `exp-diff` `log-pow` `flip-+`
1×	`pow-to-exp` `pow-pow` `rem-log-exp` `associate-r` `pow-exp` `*-commutative` `rem-exp-log` `unswap-sqr` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

6.0ms	(* 4.0 (* b b))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
7.0ms	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
6.0ms	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series275.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* 4.0 (* b b))
109.0ms	(pow (+ (* a a) (* b b)) 2.0)
62.0ms	(exp (log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
78.0ms	(log (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify112.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	309	643
1	1037	584
2	3639	571
3	5001	567

prune165.0ms

Filtered

79 candidates to 54 candidates (68.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	79	4	83

Merged error: 0b

Counts

83 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
0.0b	(* 2.0 (* (pow a 2) (pow b 2)))
0.0b	(* 4.0 (* b b))
3.4b	(* (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	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
7.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
5.0ms	(* 4.0 (* b b))
7.0ms	(* (pow a 2) (pow b 2))

series157.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(+ (+ (pow b 4) (* 2.0 (* (pow a 2) (pow b 2)))) (* 4.0 (* b b)))
35.0ms	(* 2.0 (* (pow a 2) (pow b 2)))
29.0ms	(* 4.0 (* b b))
31.0ms	(* (pow a 2) (pow b 2))

simplify58.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (48.0ms)

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

prune193.0ms

Filtered

120 candidates to 61 candidates (50.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	120	4	124

Merged error: 0b

Counts

124 → 4

regimes146.0ms

Accuracy

95.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 1.0b

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

948.0ms

20618×

body

valid