Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

299×

body

valid

simplify39.0ms

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: 14.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
4.3b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite56.0ms

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)))
4.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
88.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify111.0ms

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

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	9	166

Merged error: 8.9b

Counts

166 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
9.0b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite114.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `flip--` `unswap-sqr`
4×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
14.0ms	(/ (/ 1.0 (+ b a)) (- b a))
39.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
35.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1.0 (+ b a))
53.0ms	(/ (/ 1.0 (+ b a)) (- b a))
66.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
95.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify68.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169

prune829.0ms

Filtered

370 candidates to 235 candidates (63.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	367	3	370
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	369	10	379

Merged error: 0.0b

Counts

379 → 10

localize12.0ms

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
30×	`associate-r`
25×	`add-cube-cbrt`
21×	`prod-exp` `cbrt-unprod`
17×	`associate-*r/`
13×	`cbrt-undiv` `div-exp`
11×	`pow1`
7×	`associate-/l/` `distribute-lft-out`
6×	`frac-times` `associate-/r/`
5×	`flip3--` `associate-/r*` `flip--` `div-inv` `distribute-lft-out--`
4×	`associate-l` `pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `associate-l/` `clear-num` `-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
26.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
25.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(* PI (/ 1.0 (+ b a)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (+ b a))
91.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
98.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
53.0ms	(* PI (/ 1.0 (+ b a)))

simplify112.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	738	1318
1	4740	1036
2	5001	1036

prune286.0ms

Filtered

160 candidates to 102 candidates (63.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	155	5	160
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	160	10	170

Merged error: 0b

Counts

170 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

120×	`times-frac`
89×	`add-sqr-sqrt`
82×	`*-un-lft-identity`
52×	`add-exp-log` `add-cbrt-cube`
36×	`add-cube-cbrt`
35×	`associate-/r*`
22×	`cbrt-undiv` `div-exp`
20×	`distribute-lft-out--`
18×	`associate-r`
16×	`difference-of-squares`
14×	`associate-/r/` `div-inv`
12×	`prod-exp` `cbrt-unprod`
7×	`distribute-lft-out`
6×	`pow1`
5×	`associate-/l*`
4×	`flip3--` `associate-*r/` `flip--` `add-log-exp`
3×	`frac-2neg` `associate-l` `clear-num` `frac-sub` `associate-/l/`
2×	`flip3-+` `flip-+` `unswap-sqr`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 183

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
25.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
9.0ms	(* PI (/ 1.0 (+ b a)))
19.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (+ b a))
92.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
53.0ms	(* PI (/ 1.0 (+ b a)))
56.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify118.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	872	1737
1	4840	1451
2	5001	1451

prune342.0ms

Filtered

195 candidates to 135 candidates (69.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	193	2	195
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	195	10	205

Merged error: 0b

Counts

205 → 10

regimes100.0ms

Accuracy

0% (0.2b 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	15	6
1	15	6

end0.0ms

sample562.0ms

Algorithm

intervals

Results

412.0ms

9562×

body

valid