Details

sample26.0ms

Algorithm

intervals

Results

16.0ms

309×

body

valid

simplify37.0ms

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

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: 15.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.4b	(/ 1.0 (- (* b b) (* a a)))
4.9b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite53.0ms

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)))
6.0ms	(- (* b b) (* a a))
22.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
85.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify110.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342

prune337.0ms

Filtered

165 candidates to 119 candidates (72.1%)

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: 8.9b

Counts

166 → 8

localize12.0ms

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

rewrite96.0ms

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))
33.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
28.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (/ 1.0 a) (/ 1.0 b))
62.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
51.0ms	(/ (/ PI 2.0) (+ b a))
90.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune541.0ms

Filtered

285 candidates to 194 candidates (68.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	280	5	285
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	286	7	293

Merged error: 0.0b

Counts

293 → 7

localize12.0ms

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

122×	`times-frac`
108×	`*-un-lft-identity`
88×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
43×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r` `distribute-lft-out--`
11×	`div-inv`
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×	`associate-/r/`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `diff-log` `associate-l` `*-commutative` `flip-+`

Counts

4 → 190

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
29.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series278.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
48.0ms	(/ (/ PI 2.0) (+ b a))
103.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5001	1596

prune371.0ms

Filtered

202 candidates to 137 candidates (67.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	200	9	209

Merged error: 0.0b

Counts

209 → 9

localize12.0ms

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

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
308×	`add-sqr-sqrt`
288×	`*-un-lft-identity`
114×	`add-cube-cbrt`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
43×	`add-exp-log` `add-cbrt-cube`
32×	`div-inv`
25×	`associate-/l*`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`pow-prod-down` `associate-*l/`
2×	`frac-2neg` `clear-num` `frac-sub`
1×	`frac-times` `sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r/` `associate-l` `-commutative` `flip-+`

Counts

4 → 299

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
35.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
11.0ms	(/ (/ PI 2.0) (+ b a))
18.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series223.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
94.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
54.0ms	(/ (/ PI 2.0) (+ b a))
45.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify64.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1245	3083
1	5002	2836

prune697.0ms

Filtered

311 candidates to 207 candidates (66.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	310	10	320

Merged error: 0b

Counts

320 → 10

regimes99.0ms

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	18	10
1	18	10

end0.0ms

sample673.0ms

Algorithm

intervals

Results

519.0ms

9532×

body

valid