Details

sample27.0ms

Algorithm

intervals

Results

17.0ms

310×

body

valid

simplify39.0ms

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: 14.5b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
3.3b	(- (* b b) (* a a))
10.7b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite98.0ms

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:

13.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
8.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
34.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series227.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
42.0ms	(/ 1.0 (- (* b b) (* a a)))
35.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify166.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (52.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune763.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	507	6	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	508	6	514

Merged error: 10.6b

Counts

514 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
10.7b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
34.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
44.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (- b a))
65.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
48.0ms	(/ (/ PI 2.0) (+ b a))
99.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify188.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (57.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.1s

Filtered

646 candidates to 303 candidates (46.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	641	5	646
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	645	7	652

Merged error: 0.0b

Counts

652 → 7

localize16.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
0.3b	(/ (/ PI 2.0) (+ b a))
0.4b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

580×	`times-frac`
461×	`*-un-lft-identity`
437×	`add-sqr-sqrt`
421×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`div-inv`
42×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r`
10×	`associate-*l/`
9×	`associate-/r*`
8×	`pow1` `associate-/l/`
7×	`distribute-lft-out--`
6×	`frac-times` `associate-*r/` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`associate-/r/` `frac-sub`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 512

Calls

3 calls:

51.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
38.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series254.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
50.0ms	(/ (/ PI 2.0) (+ b a))
104.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify162.0ms

Algorithm

egg-herbie

Counts

521 → 521

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2559	13775
1	5001	11776

prune762.0ms

Filtered

521 candidates to 215 candidates (41.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	517	4	521
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	518	10	528

Merged error: 0b

Counts

528 → 10

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite148.0ms

Algorithm

rewrite-expression-head

Rules

556×	`times-frac`
441×	`*-un-lft-identity`
429×	`add-sqr-sqrt`
395×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
62×	`div-inv`
46×	`add-exp-log` `add-cbrt-cube`
16×	`cbrt-undiv` `div-exp` `associate-/r/` `distribute-lft-out--`
15×	`prod-exp` `cbrt-unprod` `difference-of-squares`
12×	`associate-r`
11×	`associate-/l*`
10×	`associate-*l/`
9×	`associate-/r*`
8×	`pow1` `associate-/l/` `distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`frac-times` `associate-*r/`
5×	`flip3--` `flip--`
4×	`frac-sub`
3×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `clear-num`
1×	`associate-l` `*-commutative`

Counts

3 → 508

Calls

3 calls:

25.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
45.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
32.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series273.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
108.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
70.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify157.0ms

Algorithm

egg-herbie

Counts

517 → 517

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2551	12897
1	5002	11726

prune730.0ms

Filtered

517 candidates to 213 candidates (41.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	515	2	517
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	520	7	527

Merged error: 0b

Counts

527 → 7

regimes55.0ms

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	14	8
1	14	8

end0.0ms

sample589.0ms

Algorithm

intervals

Results

428.0ms

9605×

body

valid