Details

sample27.0ms

Algorithm

intervals

Results

17.0ms

312×

body

valid

simplify38.0ms

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: 15.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
5.2b	(- (* b b) (* a a))
8.9b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite57.0ms

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))))
9.0ms	(/ 1.0 (- (* b b) (* a a)))
4.0ms	(- (* b b) (* a a))
24.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series222.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
46.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
91.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify113.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune380.0ms

Filtered

165 candidates to 119 candidates (72.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	10	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	10	166

Merged error: 8.7b

Counts

166 → 10

localize13.0ms

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 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.9b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite107.0ms

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))
37.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
32.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series261.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
70.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
58.0ms	(/ (/ PI 2.0) (+ b a))
100.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify62.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune694.0ms

Filtered

285 candidates to 194 candidates (68.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	279	6	285
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	286	9	295

Merged error: 0.0b

Counts

295 → 9

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)))

rewrite93.0ms

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:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
31.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
31.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (/ 1.0 a) (/ 1.0 b))
99.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
54.0ms	(/ (/ PI 2.0) (+ b a))
111.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify116.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (25.0ms)

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

prune407.0ms

Filtered

202 candidates to 137 candidates (67.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	202	9	211

Merged error: 0b

Counts

211 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
0.2b	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.3b	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac`
88×	`*-un-lft-identity`
80×	`add-sqr-sqrt`
47×	`add-exp-log` `add-cbrt-cube`
34×	`add-cube-cbrt`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
16×	`cbrt-undiv` `div-exp` `associate-/r/`
15×	`prod-exp` `cbrt-unprod`
12×	`associate-r` `div-inv`
11×	`associate-/l*`
10×	`associate-*l/`
9×	`pow1` `associate-/r*`
8×	`associate-/l/` `distribute-lft-out`
7×	`flip3-+` `flip-+`
6×	`frac-times` `flip3--` `associate-*r/` `flip--` `add-log-exp`
5×	`frac-sub`
3×	`sub-neg` `pow-prod-down`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`diff-log` `associate-l` `*-commutative`

Counts

4 → 186

Calls

4 calls:

13.0ms	(- (/ 1.0 a) (/ 1.0 b))
32.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
23.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
20.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series303.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (/ 1.0 a) (/ 1.0 b))
98.0ms	(/ (/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (- b a))
104.0ms	(/ (* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
69.0ms	(* (* (/ PI 2.0) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	920	2312
1	5002	2031

prune347.0ms

Filtered

198 candidates to 133 candidates (67.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	198	9	207

Merged error: 0b

Counts

207 → 9

regimes65.0ms

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

sample689.0ms

Algorithm

intervals

Results

529.0ms

9537×

body

valid

Details

sample27.0ms

simplify38.0ms

prune2.0ms

localize12.0ms

rewrite57.0ms

series222.0ms

simplify113.0ms

prune380.0ms

localize13.0ms

rewrite107.0ms

series261.0ms

simplify62.0ms

prune694.0ms

localize12.0ms

rewrite93.0ms

series300.0ms

simplify116.0ms

prune407.0ms

localize15.0ms

rewrite98.0ms

series303.0ms

simplify51.0ms

prune347.0ms

regimes65.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample689.0ms

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