Details

sample22.0ms

Algorithm

intervals

Results

12.0ms

299×

body

valid

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

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: 13.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.5b	(- (* b b) (* a a))
8.7b	(* (* (/ 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)))
7.0ms	(- (* b b) (* a a))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
43.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
84.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify106.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5002	1342

prune383.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	153	12	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	12	166

Merged error: 8.5b

Counts

166 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.7b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
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` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
32.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
33.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (- b a))
64.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
48.0ms	(/ (/ PI 2.0) (+ b a))
93.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify50.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune699.0ms

Filtered

300 candidates to 202 candidates (67.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	291	9	300
Fresh	11	0	11
Picked	1	0	1
Done	0	0	0
Total	303	9	312

Merged error: 0.0b

Counts

312 → 9

localize17.0ms

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

17.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
27.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series279.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
53.0ms	(/ (/ PI 2.0) (+ b a))
102.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5001	1596

prune609.0ms

Filtered

202 candidates to 137 candidates (67.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	195	7	202
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	201	10	211

Merged error: 0b

Counts

211 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
0.2b	(/ (/ PI 2.0) (+ b a))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
0.5b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log` `add-cbrt-cube`
129×	`times-frac`
108×	`prod-exp` `cbrt-unprod`
105×	`*-un-lft-identity`
88×	`cbrt-undiv` `div-exp`
77×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`pow1`
14×	`div-inv` `distribute-lft-out`
12×	`associate-*r/`
10×	`associate-/r*`
8×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `sub-neg` `associate-/r/` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 269

Calls

4 calls:

29.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
18.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
22.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

series328.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
49.0ms	(/ (/ PI 2.0) (+ b a))
90.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
119.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

simplify58.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1249	3709
1	5001	2766

prune436.0ms

Filtered

281 candidates to 139 candidates (49.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	277	4	281
Fresh	6	2	8
Picked	1	0	1
Done	1	0	1
Total	285	6	291

Merged error: 0b

Counts

291 → 6

regimes46.0ms

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	25	12
1	25	12

end0.0ms

sample564.0ms

Algorithm

intervals

Results

413.0ms

9660×

body

valid