Details

sample34.0ms

Algorithm

intervals

Results

22.0ms

317×

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

prune3.0ms

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: 14.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b	(/ 1.0 (- (* b b) (* a a)))
4.7b	(- (* b b) (* a a))
8.2b	(* (* (/ 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:

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))
24.0ms	(* (* (/ 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)))

simplify111.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune236.0ms

Filtered

165 candidates to 119 candidates (27.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 8.1b

Counts

166 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
8.2b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

229×	`times-frac`
185×	`*-un-lft-identity`
160×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
59×	`add-exp-log` `associate-l` `add-cbrt-cube`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`div-inv`
14×	`frac-times`
13×	`associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-r/` `associate-l/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`pow-prod-down` `associate-/r*`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `*-commutative` `flip-+`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 273

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
36.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
31.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
9.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
17.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify53.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune377.0ms

Filtered

285 candidates to 194 candidates (31.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	281	4	285
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	284	8	292

Merged error: 0.0b

Counts

292 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
185×	`*-un-lft-identity`
144×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
79×	`associate-l`
50×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `div-inv`
13×	`associate-r` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub`
6×	`associate-/r/` `add-log-exp`
4×	`pow-prod-down` `associate-l/` `associate-/r`
2×	`flip3-+` `*-commutative` `flip-+` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 277

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
37.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
8.0ms	(/ (/ PI 2.0) (+ b a))
25.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
17.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
7.0ms	(/ (/ PI 2.0) (+ b a))
8.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify57.0ms

Algorithm

egg-herbie

Counts

289 → 289

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1236	2823
1	5001	2529

prune405.0ms

Filtered

289 candidates to 194 candidates (32.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	284	5	289
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	288	9	297

Merged error: 0.0b

Counts

297 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

315×	`times-frac`
264×	`*-un-lft-identity`
238×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
58×	`associate-l`
48×	`distribute-lft-out--`
47×	`add-exp-log` `add-cbrt-cube`
41×	`difference-of-squares`
27×	`distribute-lft-out`
26×	`div-inv`
25×	`associate-/l*`
16×	`cbrt-undiv` `div-exp`
15×	`prod-exp` `cbrt-unprod`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`associate-/l/`
3×	`flip3--` `associate-*r/` `pow-prod-down` `flip--`
2×	`frac-2neg` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`frac-times` `sub-neg` `diff-log` `div-sub` `associate-r` `associate-l/` `-commutative`

Counts

4 → 293

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
36.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))
19.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))

series34.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(* (/ (/ PI 2.0) (+ b a)) (* 1.0 (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))))
10.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))

simplify111.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1217	3075
1	4983	2800
2	5001	2800

prune509.0ms

Filtered

305 candidates to 207 candidates (32.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	304	1	305
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	305	9	314

Merged error: 0b

Counts

314 → 9

regimes106.0ms

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

sample818.0ms

Algorithm

intervals

Results

562.0ms

9557×

body

valid

Details

sample34.0ms

simplify39.0ms

prune3.0ms

localize12.0ms

rewrite54.0ms

series33.0ms

simplify111.0ms

prune236.0ms

localize12.0ms

rewrite102.0ms

series36.0ms

simplify53.0ms

prune377.0ms

localize12.0ms

rewrite97.0ms

series36.0ms

simplify57.0ms

prune405.0ms

localize12.0ms

rewrite93.0ms

series34.0ms

simplify111.0ms

prune509.0ms

regimes106.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample818.0ms

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