Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

311×

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

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: 14.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.4b	(- (* b b) (* a a))
9.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite55.0ms

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:

17.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
89.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune408.0ms

Filtered

165 candidates to 119 candidates (72.1%)

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: 9.6b

Counts

166 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
0.1b	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
0.3b	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
9.8b	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

176×	`add-exp-log`
140×	`add-cbrt-cube`
84×	`prod-exp` `cbrt-unprod`
69×	`add-sqr-sqrt`
61×	`*-un-lft-identity` `times-frac`
58×	`associate-r`
51×	`cbrt-undiv` `div-exp`
47×	`frac-times`
35×	`add-cube-cbrt`
33×	`associate-*l/`
20×	`pow1`
19×	`associate-*r/`
15×	`cbrt-prod` `associate-l`
11×	`distribute-lft-out--`
10×	`pow-prod-down` `difference-of-squares`
9×	`flip3--` `flip--`
8×	`frac-sub`
6×	`associate-/r/` `div-inv`
4×	`associate-/r*` `add-log-exp` `unswap-sqr`
3×	`*-commutative` `distribute-lft-out`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`
1×	`frac-2neg` `clear-num` `associate-/l*`

Counts

4 → 247

Calls

4 calls:

8.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
21.0ms	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
14.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
39.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
123.0ms	(* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a)))
371.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))
151.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (/ (cbrt 1.0) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify67.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1394	3895
1	5001	3238

prune781.0ms

Filtered

259 candidates to 167 candidates (64.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	250	9	259
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	259	10	269

Merged error: 0.0b

Counts

269 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm

rewrite-expression-head

Rules

116×	`add-exp-log`
88×	`add-cbrt-cube`
55×	`prod-exp` `cbrt-unprod`
46×	`add-sqr-sqrt`
39×	`associate-*l/`
38×	`*-un-lft-identity`
36×	`times-frac`
32×	`cbrt-undiv` `div-exp`
27×	`frac-times`
22×	`associate-r`
20×	`add-cube-cbrt`
15×	`pow1` `associate-*r/` `associate-/l/`
14×	`associate-l`
9×	`flip3--` `associate-/r*` `flip--`
8×	`frac-sub`
7×	`pow-prod-down` `distribute-lft-out--`
6×	`associate-/r/` `div-inv` `difference-of-squares`
4×	`add-log-exp` `unswap-sqr`
3×	`distribute-lft-out`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `-commutative` `flip-+` `associate-/l`

Counts

4 → 191

Calls

4 calls:

14.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
56.0ms	(/ (* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
29.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
14.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

series680.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))
146.0ms	(/ (* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
175.0ms	(* (* (* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))
223.0ms	(* (/ PI 2.0) (/ (* (cbrt 1.0) (cbrt 1.0)) (+ b a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

203 → 203

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1096	2777
1	5002	2253

prune532.0ms

Filtered

203 candidates to 133 candidates (65.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	195	8	203
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	202	11	213

Merged error: 0b

Counts

213 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-exp-log`
95×	`add-cbrt-cube`
63×	`add-sqr-sqrt`
62×	`times-frac`
60×	`prod-exp` `cbrt-unprod`
55×	`*-un-lft-identity`
31×	`cbrt-undiv` `div-exp`
23×	`add-cube-cbrt`
20×	`associate-*r/`
18×	`pow1` `distribute-lft-out--`
16×	`associate-/r/` `difference-of-squares`
12×	`associate-r` `div-inv`
10×	`pow-prod-down`
8×	`associate-/l*`
7×	`flip3-+` `flip-+`
6×	`associate-/r*` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`sub-neg` `frac-sub`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 182

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(/ (/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
33.0ms	(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
25.0ms	(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
155.0ms	(/ (/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a))) (- b a))
177.0ms	(/ (* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (+ b a)))
117.0ms	(* (* (* PI (* (cbrt 1.0) (cbrt 1.0))) (cbrt 1.0)) (- (/ 1.0 a) (/ 1.0 b)))

simplify56.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1003	3381
1	5001	2593

prune515.0ms

Filtered

194 candidates to 121 candidates (62.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	196	9	205

Merged error: 0b

Counts

205 → 9

regimes83.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	33	17
2	39	17
3	39	17

end0.0ms

sample584.0ms

Algorithm

intervals

Results

423.0ms

9580×

body

valid