Details

sample27.0ms

Algorithm

intervals

Results

17.0ms

304×

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: 16.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.0b	(/ 1.0 (- (* b b) (* a a)))
4.5b	(- (* b b) (* a a))
10.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite54.0ms

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)))
3.0ms	(- (* b b) (* a a))
26.0ms	(* (* (/ 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)))
30.0ms	(- (* b b) (* a a))
90.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify112.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune347.0ms

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: 10.1b

Counts

166 → 10

localize17.0ms

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)))
10.2b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite110.0ms

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))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
42.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
30.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (+ b a))
52.0ms	(/ (/ 1.0 (+ b a)) (- b a))
66.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
96.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify71.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1467	3480
1	5002	3169

prune699.0ms

Filtered

370 candidates to 235 candidates (63.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	367	3	370
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	372	8	380

Merged error: 0.1b

Counts

380 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b	(* PI (/ 1.0 (+ b a)))

rewrite65.0ms

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))
24.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
21.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(* PI (/ 1.0 (+ b a)))

series293.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (+ b a))
94.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
101.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
53.0ms	(* PI (/ 1.0 (+ b a)))

simplify108.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	738	1318
1	4740	1036
2	5002	1036

prune300.0ms

Filtered

160 candidates to 103 candidates (64.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	153	7	160
Fresh	3	3	6
Picked	1	0	1
Done	1	0	1
Total	158	10	168

Merged error: 0.0b

Counts

168 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
0.2b	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.4b	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log` `add-cbrt-cube`
42×	`times-frac`
39×	`add-sqr-sqrt` `*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
16×	`prod-exp` `cbrt-unprod`
15×	`add-cube-cbrt`
12×	`associate-r`
11×	`associate-/l*`
10×	`distribute-lft-out--`
9×	`pow1`
8×	`associate-*r/` `associate-/r/` `div-inv` `difference-of-squares`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`flip3--` `flip--` `associate-/l/` `distribute-lft-out`
3×	`sub-neg` `flip3-+` `pow-prod-down` `frac-sub` `flip-+`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 136

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
23.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
24.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
17.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
96.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
102.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
65.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify101.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	723	1440
1	3957	1141
2	5001	1141

prune251.0ms

Filtered

148 candidates to 95 candidates (64.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	149	9	158

Merged error: 0b

Counts

158 → 9

regimes64.0ms

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	17	9
1	17	9

end0.0ms

sample705.0ms

Algorithm

intervals

Results

538.0ms

9581×

body

valid

Details

sample27.0ms

simplify39.0ms

prune2.0ms

localize12.0ms

rewrite54.0ms

series219.0ms

simplify112.0ms

prune347.0ms

localize17.0ms

rewrite110.0ms

series252.0ms

simplify71.0ms

prune699.0ms

localize18.0ms

rewrite65.0ms

series293.0ms

simplify108.0ms

prune300.0ms

localize13.0ms

rewrite81.0ms

series299.0ms

simplify101.0ms

prune251.0ms

regimes64.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample705.0ms

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