Details

analyze224.0ms

Algorithm: search

sample21.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
0.0ms	8×	body	80	invalid

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

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: 14.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
5.2b	(- (* b b) (* a a))
8.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms

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:

15.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
21.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series32.0ms

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)))
5.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify103.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

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

prune240.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

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: 7.8b

Counts

166 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
8.0b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite115.0ms

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:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
10.0ms	(/ (/ 1.0 (+ b a)) (- b a))
38.0ms	(* (/ 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)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
7.0ms	(/ (/ 1.0 (+ b a)) (- b a))
8.0ms	(* (/ 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)))

simplify69.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune457.0ms

Filtered

229 candidates to 359 candidates (-56.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	354	5	359
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	360	9	369

Merged error: 0.0b

Counts

369 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

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:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
23.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
8.0ms	(* PI (/ 1.0 (+ b a)))
20.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))

series35.0ms

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

simplify104.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (19.0ms)

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

prune179.0ms

Filtered

96 candidates to 149 candidates (-55.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	145	4	149
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	151	7	158

Merged error: 0b

Counts

158 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
23.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
8.0ms	(/ (* PI 1.0) (+ b a))
21.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(/ (* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
6.0ms	(/ (* PI 1.0) (+ b a))
12.0ms	(* (/ (* PI 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify97.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	742	1334
1	4357	1050
2	5002	1050

prune150.0ms

Filtered

96 candidates to 146 candidates (-52.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	146	7	153

Merged error: 0b

Counts

153 → 7

regimes95.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	10
1	19	10

end0.0ms

analyze211.0ms

Algorithm: search

sample594.0ms

Algorithm

intervals

Results

446.0ms	8000×	body	80	valid
19.0ms	346×	body	80	invalid

Details

analyze224.0ms

sample21.0ms

simplify37.0ms

prune3.0ms

localize12.0ms

rewrite50.0ms

series32.0ms

simplify103.0ms

prune240.0ms

localize12.0ms

rewrite115.0ms

series33.0ms

simplify69.0ms

prune457.0ms

localize14.0ms

rewrite72.0ms

series35.0ms

simplify104.0ms

prune179.0ms

localize12.0ms

rewrite68.0ms

series38.0ms

simplify97.0ms

prune150.0ms

regimes95.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze211.0ms

sample594.0ms

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