Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

307×

body

valid

simplify38.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

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: 14.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
5.5b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
47×	`times-frac`
39×	`*-un-lft-identity`
36×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
30×	`associate-r`
14×	`frac-times` `associate-l`
13×	`prod-exp` `cbrt-unprod`
12×	`difference-of-squares`
11×	`pow1`
9×	`cbrt-undiv` `div-exp`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num`

Counts

4 → 153

Calls

4 calls:

14.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
97.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342

prune340.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 7.8b

Counts

166 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.0b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

15.0ms	(- (/ 1.0 a) (/ 1.0 b))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
41.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
36.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
47.0ms	(/ (/ 1.0 (+ b a)) (- b a))
65.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
97.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify64.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune689.0ms

Filtered

359 candidates to 229 candidates (63.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	358	8	366

Merged error: 0.0b

Counts

366 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(* PI (/ 1.0 (+ b a)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
47×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
34×	`times-frac`
30×	`associate-r`
21×	`prod-exp` `cbrt-unprod`
18×	`add-cube-cbrt`
17×	`associate-*r/`
12×	`cbrt-undiv` `div-exp`
11×	`pow1`
10×	`distribute-lft-out--`
8×	`difference-of-squares`
7×	`associate-/l/`
6×	`frac-times` `flip3--` `flip--` `div-inv` `add-log-exp`
5×	`frac-sub`
4×	`associate-l` `pow-prod-down` `associate-/r/`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-l/` `-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 137

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
30.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
21.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
10.0ms	(* PI (/ 1.0 (+ b a)))

series282.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
101.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* PI (/ 1.0 (+ b a)))

simplify233.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	762	1319
1	4686	1036
2	5001	1036

prune295.0ms

Filtered

149 candidates to 97 candidates (65.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	147	10	157

Merged error: 0b

Counts

157 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
0.3b	(/ (* PI 1.0) (+ b a))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
39×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
29×	`times-frac`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
13×	`add-cube-cbrt`
12×	`associate-r`
10×	`associate-l` `distribute-lft-out--`
8×	`associate-*r/` `difference-of-squares`
7×	`div-inv` `associate-/l/`
6×	`pow1` `frac-times` `flip3--` `associate-/r/` `flip--` `add-log-exp`
5×	`associate-/r*` `frac-sub`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `clear-num` `flip-+` `associate-/l`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
24.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
25.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
6.0ms	(/ (* PI 1.0) (+ b a))

series279.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
100.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))
53.0ms	(/ (* PI 1.0) (+ b a))

simplify97.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	742	1334
1	4357	1050
2	5001	1050

prune243.0ms

Filtered

146 candidates to 95 candidates (65.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	146	10	156

Merged error: 0b

Counts

156 → 10

regimes68.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

sample684.0ms

Algorithm

intervals

Results

521.0ms

9660×

body

valid