Details

sample28.0ms

Algorithm

intervals

Results

17.0ms

308×

body

valid

simplify46.0ms

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

prune6.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 14.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
3.6b	(- (* b b) (* a a))
9.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite49.0ms

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

series34.0ms

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))
14.0ms	(* (* (/ 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

prune232.0ms

Filtered

165 candidates to 119 candidates (27.9%)

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: 9.4b

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)))
9.5b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite118.0ms

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))
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)))

series31.0ms

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

simplify62.0ms

Algorithm

egg-herbie

Counts

359 → 359

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1498	3481
1	5002	3169

prune451.0ms

Filtered

359 candidates to 229 candidates (36.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	357	2	359
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	360	8	368

Merged error: 0.1b

Counts

368 → 8

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)))

rewrite99.0ms

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))
27.0ms	(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
42.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
12.0ms	(* PI (/ 1.0 (+ b a)))

series38.0ms

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)))
15.0ms	(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
7.0ms	(* PI (/ 1.0 (+ b a)))

simplify107.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 1 (20.0ms)

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

prune193.0ms

Filtered

149 candidates to 97 candidates (34.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	148	9	157

Merged error: 0.0b

Counts

157 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

118×	`times-frac`
94×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
50×	`add-exp-log` `add-cbrt-cube`
31×	`associate-/r*`
29×	`add-cube-cbrt`
25×	`distribute-lft-out--`
21×	`cbrt-undiv` `div-exp`
20×	`difference-of-squares`
18×	`associate-r`
15×	`div-inv`
12×	`prod-exp` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-log-exp`
5×	`flip3--` `flip--`
4×	`associate-*r/` `frac-sub`
3×	`associate-l` `associate-/l/` `distribute-lft-out`
2×	`frac-2neg` `clear-num` `associate-/l*` `unswap-sqr`
1×	`sub-neg` `flip3-+` `diff-log` `pow-prod-down` `*-commutative` `flip-+`

Counts

4 → 172

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
27.0ms	(/ (* PI (/ 1.0 (+ b a))) (/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
18.0ms	(/ (* 2.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
9.0ms	(* PI (/ 1.0 (+ b a)))

series31.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify107.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	872	1738
1	4713	1451
2	5001	1451

prune238.0ms

Filtered

184 candidates to 129 candidates (29.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	184	9	193

Merged error: 0.0b

Counts

193 → 9

regimes227.0ms

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	18	10
1	18	10

end0.0ms

sample824.0ms

Algorithm

intervals

Results

574.0ms

9634×

body

valid

Details

sample28.0ms

simplify46.0ms

prune6.0ms

localize13.0ms

rewrite49.0ms

series34.0ms

simplify103.0ms

prune232.0ms

localize13.0ms

rewrite118.0ms

series31.0ms

simplify62.0ms

prune451.0ms

localize13.0ms

rewrite99.0ms

series38.0ms

simplify107.0ms

prune193.0ms

localize13.0ms

rewrite74.0ms

series31.0ms

simplify107.0ms

prune238.0ms

regimes227.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample824.0ms

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