Details

sample23.0ms

Algorithm

intervals

Results

13.0ms

310×

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: 14.5b

Counts

2 → 1

localize15.0ms

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)))

rewrite52.0ms

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:

14.0ms	(* (/ 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)))

series232.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
40.0ms	(/ 1.0 (- (* b b) (* a a)))
34.0ms	(- (* b b) (* a a))
101.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune381.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	6	166

Merged error: 10.6b

Counts

166 → 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)))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
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*`
15×	`div-inv`
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×	`pow-prod-down` `frac-sub` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
32.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
11.0ms	(/ (/ PI 2.0) (+ b a))
30.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (- b a))
64.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
53.0ms	(/ (/ PI 2.0) (+ b a))
108.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune574.0ms

Filtered

300 candidates to 204 candidates (68.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	299	7	306

Merged error: 0.0b

Counts

306 → 7

localize12.0ms

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)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
97×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
57×	`add-cube-cbrt`
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*` `div-inv`
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×	`pow-prod-down` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 168

Calls

3 calls:

32.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
25.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
53.0ms	(/ (/ PI 2.0) (+ b a))
101.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify103.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	892	1689
1	4508	1452
2	5001	1452

prune326.0ms

Filtered

177 candidates to 118 candidates (66.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	174	10	184

Merged error: 0b

Counts

184 → 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)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

88×	`times-frac`
77×	`*-un-lft-identity`
65×	`add-sqr-sqrt`
46×	`add-exp-log` `add-cbrt-cube`
31×	`add-cube-cbrt`
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/` `div-inv`
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×	`pow-prod-down` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`associate-l` `*-commutative`

Counts

3 → 164

Calls

3 calls:

25.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
22.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
24.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series411.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
224.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
64.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify43.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	881	2157
1	5002	1887

prune291.0ms

Filtered

173 candidates to 113 candidates (65.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	176	7	183

Merged error: 0b

Counts

183 → 7

regimes52.0ms

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

sample580.0ms

Algorithm

intervals

Results

422.0ms

9605×

body

valid