Details

sample25.0ms

Algorithm

intervals

Results

15.0ms

295×

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: 13.1b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.3b	(/ 1.0 (- (* b b) (* a a)))
5.0b	(- (* b b) (* a a))
6.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite66.0ms

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:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
26.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
120.0ms	(* (* (/ 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	5002	1342

prune340.0ms

Filtered

165 candidates to 119 candidates (72.1%)

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: 6.7b

Counts

166 → 7

localize15.0ms

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
6.8b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite90.0ms

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))
34.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
29.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series257.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1.0 (- b a))
61.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
54.0ms	(/ (/ PI 2.0) (+ b a))
97.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify54.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune560.0ms

Filtered

300 candidates to 204 candidates (68.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	301	6	307

Merged error: 0.0b

Counts

307 → 6

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)) (- (/ 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)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

226×	`times-frac`
193×	`*-un-lft-identity`
148×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
79×	`associate-l`
52×	`add-exp-log` `add-cbrt-cube`
27×	`distribute-lft-out`
17×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
16×	`frac-times` `associate-r/` `associate-/l`
15×	`div-inv`
13×	`associate-r`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-/r*`
8×	`flip3--` `associate-/r/` `flip--`
6×	`sub-neg` `frac-sub`
4×	`pow-prod-down` `associate-*l/` `add-log-exp`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`
1×	`associate-/l/`

Counts

4 → 292

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
31.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
8.0ms	(/ (/ PI 2.0) (+ b a))
27.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ 1.0 (- b a))
94.0ms	(* (/ (/ PI 2.0) (+ b a)) (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))
54.0ms	(/ (/ PI 2.0) (+ b a))
51.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify62.0ms

Algorithm

egg-herbie

Counts

304 → 304

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1243	2856
1	5001	2568

prune583.0ms

Filtered

304 candidates to 205 candidates (67.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	303	1	304
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	303	7	310

Merged error: 0.0b

Counts

310 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (- b a) (* a b))
0.3b	(/ (/ PI 2.0) (+ b a))
0.3b	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* (- b a) (* a b)))
0.3b	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

199×	`add-exp-log` `add-cbrt-cube`
102×	`prod-exp` `cbrt-unprod`
98×	`times-frac`
84×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
54×	`cbrt-undiv` `add-cube-cbrt` `div-exp`
21×	`pow1`
14×	`distribute-lft-out` `associate-/l*`
12×	`associate-r/` `associate-l/`
11×	`pow-prod-down`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`div-inv`
6×	`flip3--` `associate-l` `flip--` `associate-/l/`
5×	`associate-/r*`
4×	`frac-times` `sub-neg` `associate-/r/` `add-log-exp`
2×	`frac-2neg` `associate-r` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 225

Calls

4 calls:

10.0ms	(* (- b a) (* a b))
8.0ms	(/ (/ PI 2.0) (+ b a))
26.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* (- b a) (* a b)))
18.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (- b a) (* a b))
51.0ms	(/ (/ PI 2.0) (+ b a))
74.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* (- b a) (* a b)))
93.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

237 → 237

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1123	2792
1	5001	1981

prune313.0ms

Filtered

237 candidates to 116 candidates (48.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	236	1	237
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	237	7	244

Merged error: 0b

Counts

244 → 7

regimes54.0ms

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

sample675.0ms

Algorithm

intervals

Results

517.0ms

9555×

body

valid