Details

sample31.0ms

Algorithm

intervals

Results

19.0ms

295×

body

valid

simplify40.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	10
1	90	10
2	384	10
3	1828	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: 13.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
6.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

12.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
38.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
86.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify163.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (48.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune838.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	506	7	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	507	7	514

Merged error: 6.7b

Counts

514 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ b a))
0.1b	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
0.3b	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
6.8b	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

533×	`times-frac`
439×	`add-sqr-sqrt`
434×	`*-un-lft-identity`
404×	`add-cube-cbrt`
338×	`prod-diff`
196×	`add-exp-log`
171×	`distribute-rgt-in` `distribute-lft-in`
112×	`add-cbrt-cube`
95×	`prod-exp`
60×	`div-exp`
58×	`div-inv`
51×	`cbrt-unprod`
47×	`frac-times`
34×	`associate-r`
32×	`associate-l`
31×	`cbrt-undiv`
29×	`associate-*r/`
23×	`associate-*l/`
21×	`pow1`
11×	`rec-exp` `1-exp`
10×	`pow-prod-down`
9×	`flip3--` `flip--`
8×	`frac-sub` `distribute-lft-out--`
7×	`distribute-lft-out` `difference-of-squares`
6×	`associate-/r/` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`sub-neg` `flip3-+` `flip-+`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 600

Calls

4 calls:

5.0ms	(/ 1 (+ b a))
16.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
23.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
42.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(/ 1 (+ b a))
62.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
45.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
92.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify183.0ms

Algorithm

egg-herbie

Counts

612 → 612

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	2992	16756
1	5002	15654

prune837.0ms

Filtered

612 candidates to 255 candidates (41.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	609	3	612
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	611	8	619

Merged error: 0.0b

Counts

619 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite281.0ms

Algorithm

rewrite-expression-head

Rules

1446×	`times-frac`
1150×	`add-sqr-sqrt`
1141×	`*-un-lft-identity`
1119×	`add-cube-cbrt`
1014×	`prod-diff`
855×	`distribute-rgt-in` `distribute-lft-in`
161×	`div-inv`
52×	`add-exp-log` `add-cbrt-cube`
25×	`associate-*r/`
24×	`associate-l`
21×	`prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp` `associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`frac-times`
8×	`flip3--` `flip--`
7×	`associate-/l/`
6×	`sub-neg` `associate-/r*` `associate-/r/` `frac-sub`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`associate-*l/`
2×	`frac-2neg` `clear-num` `*-commutative` `unswap-sqr`
1×	`flip3-+` `flip-+`

Counts

4 → 1191

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
68.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (+ b a)))
38.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
46.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))

series396.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (- b a))
92.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (+ b a)))
55.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
208.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))

simplify352.0ms

Algorithm

egg-herbie

Counts

1203 → 1203

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4299	35096
1	5001	32664

prune1.3s

Filtered

1203 candidates to 348 candidates (28.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1199	4	1203
Fresh	3	3	6
Picked	0	1	1
Done	0	1	1
Total	1202	9	1211

Merged error: 0b

Counts

1211 → 9

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
0.8b	(/ PI (* a b))

rewrite20.0ms

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` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r*` `associate-/r/` `log1p-expm1-u` `div-inv` `add-log-exp`
1×	`flip3-+` `flip-+` `associate-/l/`

Counts

2 → 57

Calls

2 calls:

14.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
4.0ms	(/ PI (* a b))

series86.0ms

Counts

2 → 6

Calls

2 calls:

67.0ms	(/ (* 1.0 (/ PI (* a b))) (* 2.0 (+ b a)))
19.0ms	(/ PI (* a b))

simplify52.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	395	436
1	2396	310
2	5002	310

prune82.0ms

Filtered

63 candidates to 37 candidates (58.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	64	8	72

Merged error: 0b

Counts

72 → 8

regimes62.0ms

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

sample697.0ms

Algorithm

intervals

Results

538.0ms

9555×

body

valid