Details

sample30.0ms

Algorithm

intervals

Results

20.0ms

300×

body

valid

simplify41.0ms

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: 15.5b

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)))
2.8b	(- (* b b) (* a a))
11.8b	(* (* (/ 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:

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))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series216.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
88.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune357.0ms

Filtered

165 candidates to 119 candidates (72.1%)

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: 11.7b

Counts

166 → 9

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))
11.8b	(* (* (/ (/ 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))
31.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
34.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ 1.0 (- b a))
63.0ms	(* (/ (/ 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)))

simplify54.0ms

Algorithm

egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1260	2632
1	5001	2332

prune582.0ms

Filtered

300 candidates to 204 candidates (68.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	302	7	309

Merged error: 0.0b

Counts

309 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (* (* (/ (/ 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)))

rewrite87.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
29.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
11.0ms	(/ (/ PI 2.0) (+ b a))
25.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series288.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
93.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
55.0ms	(/ (/ PI 2.0) (+ b a))
104.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify108.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5002	1596

prune381.0ms

Filtered

202 candidates to 137 candidates (67.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	199	10	209

Merged error: 0.0b

Counts

209 → 10

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

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

514×	`times-frac`
420×	`add-sqr-sqrt`
380×	`*-un-lft-identity`
142×	`add-cube-cbrt`
122×	`distribute-lft-out--`
105×	`difference-of-squares`
83×	`associate-/r*`
44×	`div-inv`
43×	`add-exp-log` `add-cbrt-cube`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`flip3--` `flip--`
4×	`pow1` `frac-sub` `associate-/l/`
3×	`frac-2neg` `clear-num`
1×	`sub-neg` `flip3-+` `diff-log` `div-sub` `associate-*l/` `flip-+`

Counts

4 → 366

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
12.0ms	(/ (/ PI 2.0) (+ b a))
17.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (/ 1.0 a) (/ 1.0 b))
92.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
55.0ms	(/ (/ PI 2.0) (+ b a))
48.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

simplify205.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1498	4278
1	5001	4025

prune719.0ms

Filtered

378 candidates to 254 candidates (67.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	376	2	378
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	378	10	388

Merged error: 0b

Counts

388 → 10

regimes67.0ms

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	17	10
1	17	10

end0.0ms

sample690.0ms

Algorithm

intervals

Results

526.0ms

9602×

body

valid

Details

sample30.0ms

simplify41.0ms

prune2.0ms

localize12.0ms

rewrite54.0ms

series216.0ms

simplify109.0ms

prune357.0ms

localize12.0ms

rewrite96.0ms

series248.0ms

simplify54.0ms

prune582.0ms

localize12.0ms

rewrite87.0ms

series288.0ms

simplify108.0ms

prune381.0ms

localize12.0ms

rewrite104.0ms

series226.0ms

simplify205.0ms

prune719.0ms

regimes67.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample690.0ms

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