Details

sample37.0ms

Algorithm

intervals

Results

17.0ms

308×

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 13.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
3.6b	(- (* b b) (* a a))
8.6b	(* (* (/ 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:

16.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
50.0ms	(/ 1.0 (- (* b b) (* a a)))
39.0ms	(- (* b b) (* a a))
104.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify107.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune1.0s

Filtered

165 candidates to 119 candidates (27.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	10	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 8.4b

Counts

166 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (sqrt 1.0) (+ b a))
0.2b	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
0.4b	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
8.6b	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-exp-log` `add-cbrt-cube`
109×	`*-un-lft-identity`
106×	`add-sqr-sqrt`
104×	`times-frac`
78×	`associate-r`
63×	`add-cube-cbrt`
51×	`prod-exp` `cbrt-unprod`
47×	`frac-times`
44×	`sqrt-prod`
33×	`associate-*l/`
31×	`cbrt-undiv` `div-exp`
20×	`pow1`
19×	`associate-*r/`
15×	`associate-l`
13×	`distribute-lft-out`
11×	`distribute-lft-out--`
10×	`pow-prod-down` `difference-of-squares`
9×	`flip3--` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `div-inv` `associate-/l*` `unswap-sqr`
4×	`associate-/r*` `add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`
1×	`frac-2neg` `clear-num`

Counts

4 → 272

Calls

4 calls:

8.0ms	(/ (sqrt 1.0) (+ b a))
19.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
16.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
33.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series858.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (sqrt 1.0) (+ b a))
245.0ms	(* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a)))
177.0ms	(* (/ PI 2.0) (/ (sqrt 1.0) (+ b a)))
344.0ms	(* (* (* (/ PI 2.0) (/ (sqrt 1.0) (+ b a))) (/ (sqrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify62.0ms

Algorithm

egg-herbie

Counts

284 → 284

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1325	3218
1	5001	2763

prune2.6s

Filtered

284 candidates to 178 candidates (37.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	281	3	284
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	288	6	294

Merged error: 0.0b

Counts

294 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
23.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
6.0ms	(/ (* PI 1.0) (- b a))
21.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (/ 1.0 a) (/ 1.0 b))
110.0ms	(/ (* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a))) (* 2.0 (+ b a)))
67.0ms	(/ (* PI 1.0) (- b a))
88.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) (/ (* PI 1.0) (- b a)))

simplify92.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	695	1331
1	4083	1048
2	5002	1048

prune682.0ms

Filtered

145 candidates to 98 candidates (32.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	143	8	151

Merged error: 0.0b

Counts

151 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.4b	(/ PI (* a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `times-frac` `associate-/l`
3×	`associate-*r/`
2×	`pow1` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 53

Calls

2 calls:

10.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
4.0ms	(/ PI (* a b))

series109.0ms

Counts

2 → 6

Calls

2 calls:

81.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
28.0ms	(/ PI (* a b))

simplify51.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	390	416
1	2377	290
2	5003	290

prune109.0ms

Filtered

59 candidates to 33 candidates (44.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	55	4	59
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	60	7	67

Merged error: 0.0b

Counts

67 → 7

regimes105.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	6
1	14	6

end0.0ms

sample1.0s

Algorithm

intervals

Results

736.0ms

9647×

body

valid

Details

sample37.0ms

simplify38.0ms

prune4.0ms

localize13.0ms

rewrite52.0ms

series260.0ms

simplify107.0ms

prune1.0s

localize18.0ms

rewrite90.0ms

series858.0ms

simplify62.0ms

prune2.6s

localize15.0ms

rewrite71.0ms

series308.0ms

simplify92.0ms

prune682.0ms

localize8.0ms

rewrite16.0ms

series109.0ms

simplify51.0ms

prune109.0ms

regimes105.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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