Details

sample30.0ms

Algorithm

intervals

Results

19.0ms

329×

body

valid

simplify39.0ms

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

prune6.0ms

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: 15.7b

Counts

2 → 1

localize13.0ms

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)))
4.4b	(- (* b b) (* a a))
10.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite51.0ms

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:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
15.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify111.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune240.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	157	8	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Merged error: 10.3b

Counts

166 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
34.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
29.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
11.0ms	(/ (/ PI 2.0) (+ b a))
13.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune385.0ms

Filtered

194 candidates to 285 candidates (-46.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	280	5	285
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	284	9	293

Merged error: 0.0b

Counts

293 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (/ PI 2.0) (/ 1.0 (- b a)))
0.5b	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
53×	`*-un-lft-identity`
52×	`times-frac`
33×	`associate-r`
27×	`frac-times` `add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
13×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/` `unswap-sqr`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative` `distribute-lft-out`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 180

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
14.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
7.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))
9.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify40.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	975	1762
1	5001	1452

prune376.0ms

Filtered

132 candidates to 192 candidates (-45.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	188	4	192
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	191	10	201

Merged error: 0b

Counts

201 → 10

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (/ PI (* a b)))
0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
1.1b	(/ PI (* a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `add-cube-cbrt` `times-frac` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*r/` `clear-num` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`

Counts

3 → 78

Calls

3 calls:

7.0ms	(* 0.5 (/ PI (* a b)))
9.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
4.0ms	(/ PI (* a b))

series18.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(* 0.5 (/ PI (* a b)))
10.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
3.0ms	(/ PI (* a b))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	333	455
1	1752	363
2	5001	363

prune77.0ms

Filtered

54 candidates to 87 candidates (-61.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	83	4	87
Fresh	6	2	8
Picked	1	0	1
Done	1	0	1
Total	91	6	97

Merged error: 0b

Counts

97 → 6

regimes84.0ms

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	16	6
1	16	6

end0.0ms

sample789.0ms

Algorithm

intervals

Results

551.0ms

9566×

body

valid

Details

sample30.0ms

simplify39.0ms

prune6.0ms

localize13.0ms

rewrite51.0ms

series35.0ms

simplify111.0ms

prune240.0ms

localize13.0ms

rewrite98.0ms

series37.0ms

simplify53.0ms

prune385.0ms

localize12.0ms

rewrite87.0ms

series36.0ms

simplify40.0ms

prune376.0ms

localize7.0ms

rewrite22.0ms

series18.0ms

simplify45.0ms

prune77.0ms

regimes84.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample789.0ms

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