Details

sample335.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 96.899414%

Results

17.0ms

299×

body

valid

simplify41.0ms

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

prune3.0ms

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: 14.7b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.5b	(- (* b b) (* a a))
10.6b	(* (* (/ 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)))
3.0ms	(- (* b b) (* a a))
25.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify117.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (23.0ms)

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

prune241.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

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: 10.4b

Counts

166 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
10.6b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
11.0ms	(/ (/ 1.0 (+ b a)) (- b a))
43.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
32.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
7.0ms	(/ (/ 1.0 (+ b a)) (- b a))
14.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
13.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify72.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune462.0ms

Filtered

230 candidates to 359 candidates (-56.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	354	5	359
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	359	9	368

Merged error: 0.1b

Counts

368 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* 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)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 137

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
28.0ms	(/ (* (* 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)))
10.0ms	(* PI (/ 1.0 (+ b a)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
13.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(* PI (/ 1.0 (+ b a)))

simplify111.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	762	1319
1	4686	1036
2	5001	1036

prune189.0ms

Filtered

96 candidates to 149 candidates (-55.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	4	3	7
Picked	1	0	1
Done	1	0	1
Total	150	8	158

Merged error: 0b

Counts

158 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ (* (* 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)))

rewrite80.0ms

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)))
20.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
19.0ms	(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
13.0ms	(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
7.0ms	(* (* 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

prune154.0ms

Filtered

96 candidates to 148 candidates (-54.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	147	1	148
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	149	7	156

Merged error: 0b

Counts

156 → 7

regimes93.0ms

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	17	9
1	17	9

end0.0ms

sample1.1s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 96.899414%

Results

560.0ms

9590×

body

valid

Details

sample335.0ms

simplify41.0ms

prune3.0ms

localize13.0ms

rewrite53.0ms

series33.0ms

simplify117.0ms

prune241.0ms

localize13.0ms

rewrite119.0ms

series39.0ms

simplify72.0ms

prune462.0ms

localize13.0ms

rewrite77.0ms

series37.0ms

simplify111.0ms

prune189.0ms

localize13.0ms

rewrite80.0ms

series36.0ms

simplify101.0ms

prune154.0ms

regimes93.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling