Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

312×

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: 15.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
5.3b	(- (* b b) (* a a))
9.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite118.0ms

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:

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))
43.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
45.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify170.0ms

Algorithm

egg-herbie

Counts

513 → 513

Iterations

Useful iterations: 1 (50.0ms)

Iter	Nodes	Cost
0	2481	15016
1	5002	13008

prune808.0ms

Filtered

513 candidates to 220 candidates (42.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	504	9	513
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	505	9	514

Merged error: 9.3b

Counts

514 → 9

localize16.0ms

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)))
0.2b	(/ (/ PI 2.0) (+ b a))
9.4b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite161.0ms

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))
37.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
45.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (- b a))
64.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
49.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify186.0ms

Algorithm

egg-herbie

Counts

646 → 646

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	2933	16072
1	5002	14991

prune1.0s

Filtered

646 candidates to 303 candidates (46.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	639	7	646
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	645	10	655

Merged error: 0.0b

Counts

655 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite204.0ms

Algorithm

rewrite-expression-head

Rules

833×	`times-frac`
661×	`*-un-lft-identity`
641×	`add-sqr-sqrt`
613×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
90×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
13×	`fma-neg`
12×	`associate-r` `distribute-lft-out--`
10×	`associate-*l/` `difference-of-squares`
9×	`pow1` `associate-/r*`
8×	`associate-/l/`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`sub-neg` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 718

Calls

4 calls:

21.0ms	(- (/ 1.0 a) (/ 1.0 b))
52.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
46.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
240.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
56.0ms	(/ (/ PI 2.0) (+ b a))
105.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify205.0ms

Algorithm

egg-herbie

Counts

730 → 730

Iterations

Useful iterations: 1 (53.0ms)

Iter	Nodes	Cost
0	2586	18289
1	5001	15335

prune1.2s

Filtered

730 candidates to 320 candidates (43.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	727	3	730
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	731	9	740

Merged error: 0b

Counts

740 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

757×	`times-frac`
609×	`add-sqr-sqrt`
569×	`*-un-lft-identity`
331×	`add-cube-cbrt`
169×	`prod-diff`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
71×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
13×	`fma-neg`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `expm1-log1p-u` `frac-sub` `log1p-expm1-u` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 556

Calls

4 calls:

19.0ms	(- (/ 1.0 a) (/ 1.0 b))
40.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
20.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(/ (/ PI 2.0) (+ b a))

series235.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
97.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
55.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))
51.0ms	(/ (/ PI 2.0) (+ b a))

simplify125.0ms

Algorithm

egg-herbie

Counts

568 → 568

Iterations

Useful iterations: 1 (43.0ms)

Iter	Nodes	Cost
0	2064	8678
1	5002	7331

prune1.1s

Filtered

568 candidates to 329 candidates (57.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	566	2	568
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	570	7	577

Merged error: 0b

Counts

577 → 7

regimes52.0ms

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	16	7
1	16	7

end0.0ms

sample590.0ms

Algorithm

intervals

Results

428.0ms

9677×

body

valid