Details

sample56.0ms

Algorithm

intervals

Results

34.0ms

691×

body

valid

simplify62.0ms

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

prune3.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
6.0ms	(+ (* a a) (* b b))
3.0ms	(* 4.0 (* b b))
24.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify49.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	382	507
1	1541	465
2	5002	450

prune112.0ms

Filtered

51 candidates to 75 candidates (-47.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	72	3	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	3	76

Merged error: 0.0b

Counts

76 → 3

localize14.0ms

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)
24.8b	(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×	`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 → 98

Calls

4 calls:

5.0ms	(* 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))

series93.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 4.0 (* b b))
33.0ms	(pow (pow (+ (* a a) (* b b)) 2.0) 3)
23.0ms	(pow (+ (* a a) (* b b)) 2.0)
35.0ms	(cbrt (pow (pow (+ (* a a) (* b b)) 2.0) 3))

simplify56.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	348	760
1	1290	740
2	5002	712

prune149.0ms

Filtered

63 candidates to 110 candidates (-74.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	110	0	110
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	110	3	113

Merged error: 0.0b

Counts

113 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

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))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 87

Calls

3 calls:

5.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
7.0ms	(* 2 (* (pow a 2) (pow b 2)))
8.0ms	(* (pow a 2) (pow b 2))

series28.0ms

Counts

3 → 9

Calls

3 calls:

13.0ms	(+ (pow b 4) (* 2 (* (pow a 2) (pow b 2))))
8.0ms	(* 2 (* (pow a 2) (pow b 2)))
7.0ms	(* (pow a 2) (pow b 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	297	518
1	1270	444
2	5001	432

prune132.0ms

Filtered

47 candidates to 96 candidates (-104.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
0.2b	(* (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
35×	`sqrt-prod`
33×	`*-un-lft-identity`
22×	`pow1`
17×	`add-cube-cbrt`
14×	`sqrt-div`
12×	`swap-sqr`
9×	`sqrt-pow1` `pow1/2`
8×	`add-exp-log` `associate-r` `associate-l`
7×	`flip3--` `flip--` `distribute-lft-out--`
6×	`unpow-prod-down` `pow-unpow` `add-cbrt-cube`
5×	`pow-prod-up` `difference-of-squares`
4×	`frac-times` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`pow-to-exp` `pow-pow` `associate-r/` `associate-l/` `pow-exp` `sqr-pow`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 116

Calls

4 calls:

8.0ms	(sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
22.0ms	(* (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
5.0ms	(pow (+ (* a a) (* b b)) 2.0)
5.0ms	(pow (+ (* a a) (* b b)) 2.0)

series88.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0))
18.0ms	(* (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)) (sqrt (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)))
22.0ms	(pow (+ (* a a) (* b b)) 2.0)
25.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify73.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	355	1641
1	1553	1494
2	5003	1445

prune236.0ms

Filtered

75 candidates to 128 candidates (-70.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	127	4	131

Merged error: 0.0b

Counts

131 → 4

regimes474.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.8b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	25
1	37	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

1.0s

20575×

body

valid

Details

sample56.0ms

simplify62.0ms

prune3.0ms

localize11.0ms

rewrite29.0ms

series49.0ms

simplify49.0ms

prune112.0ms

localize14.0ms

rewrite28.0ms

series93.0ms

simplify56.0ms

prune149.0ms

localize13.0ms

rewrite24.0ms

series28.0ms

simplify53.0ms

prune132.0ms

localize14.0ms

rewrite44.0ms

series88.0ms

simplify73.0ms

prune236.0ms

regimes474.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample1.6s

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