Details

sample41.0ms

Algorithm

intervals

Results

24.0ms

314×

body

valid

simplify57.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	30	10
1	89	10
2	377	10
3	1779	10
4	5001	10

prune4.0ms

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: 15.9b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.5b	(/ 1.0 (- (* b b) (* a a)))
4.4b	(- (* b b) (* a a))
10.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite83.0ms

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:

18.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
9.0ms	(/ 1.0 (- (* b b) (* a a)))
6.0ms	(- (* b b) (* a a))
44.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series215.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
44.0ms	(/ 1.0 (- (* b b) (* a a)))
29.0ms	(- (* b b) (* a a))
86.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify105.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

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

prune343.0ms

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: 10.6b

Counts

166 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
0.2b	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
10.8b	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

192×	`add-exp-log`
110×	`add-cbrt-cube`
95×	`prod-exp`
80×	`add-sqr-sqrt`
63×	`*-un-lft-identity` `times-frac`
58×	`div-exp`
51×	`cbrt-unprod`
47×	`frac-times`
34×	`associate-r`
33×	`add-cube-cbrt`
32×	`associate-l`
30×	`cbrt-undiv`
29×	`associate-*r/`
23×	`associate-*l/`
20×	`pow1`
13×	`distribute-lft-out--`
11×	`difference-of-squares`
10×	`rec-exp` `flip3--` `1-exp` `pow-prod-down` `flip--`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp` `unswap-sqr`
4×	`associate-/r/`
3×	`sub-neg` `*-commutative` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in`
1×	`flip3-+` `diff-log` `flip-+`

Counts

4 → 239

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
23.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
34.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(- (/ 1.0 a) (/ 1.0 b))
62.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
50.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
92.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1329	2628
1	5002	2194

prune587.0ms

Filtered

251 candidates to 156 candidates (62.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	244	7	251
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	251	9	260

Merged error: 0.0b

Counts

260 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
50×	`add-exp-log` `add-cbrt-cube`
41×	`*-un-lft-identity`
37×	`times-frac`
25×	`associate-*r/`
24×	`associate-l`
21×	`prod-exp` `cbrt-unprod`
19×	`add-cube-cbrt`
13×	`associate-r` `distribute-lft-out--`
12×	`cbrt-undiv` `div-exp`
11×	`pow1` `difference-of-squares`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`frac-times`
8×	`flip3--` `flip--`
7×	`sub-neg` `frac-sub` `associate-/l/`
6×	`div-inv` `add-log-exp`
4×	`pow-prod-down` `associate-/r/`
3×	`associate-*l/`
2×	`*-commutative` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r` `flip-+` `associate-/l`

Counts

4 → 154

Calls

4 calls:

15.0ms	(- (/ 1.0 a) (/ 1.0 b))
26.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (+ b a)))
23.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
23.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))

series244.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (/ 1.0 a) (/ 1.0 b))
89.0ms	(/ (* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (+ b a)))
54.0ms	(* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b)))
68.0ms	(* PI (* (/ 1.0 (- b a)) (- (/ 1.0 a) (/ 1.0 b))))

simplify103.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	801	1596
1	4674	1292
2	5001	1292

prune287.0ms

Filtered

166 candidates to 106 candidates (63.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	165	10	175

Merged error: 0b

Counts

175 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* PI (/ 1.0 (* a b))) (* 2.0 (+ b a)))
0.3b	(* PI (/ 1.0 (* a b)))
0.4b	(/ 1.0 (* a b))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-exp-log` `add-cbrt-cube`
17×	`prod-exp` `cbrt-unprod`
16×	`cbrt-undiv` `div-exp`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`times-frac` `associate-r`
5×	`pow1`
4×	`associate-r/` `associate-/l`
3×	`associate-l` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/r*` `associate-/r/`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`

Counts

3 → 80

Calls

3 calls:

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

series123.0ms

Counts

3 → 9

Calls

3 calls:

66.0ms	(/ (* PI (/ 1.0 (* a b))) (* 2.0 (+ b a)))
36.0ms	(* PI (/ 1.0 (* a b)))
21.0ms	(/ 1.0 (* a b))

simplify64.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	434	555
1	2878	403
2	5003	403

prune117.0ms

Filtered

89 candidates to 54 candidates (60.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	3	89
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	91	8	99

Merged error: 0b

Counts

99 → 8

regimes51.0ms

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	19	10
1	19	10

end0.0ms

sample623.0ms

Algorithm

intervals

Results

452.0ms

9646×

body

valid

Details

sample41.0ms

simplify57.0ms

prune4.0ms

localize21.0ms

rewrite83.0ms

series215.0ms

simplify105.0ms

prune343.0ms

localize24.0ms

rewrite97.0ms

series234.0ms

simplify52.0ms

prune587.0ms

localize12.0ms

rewrite94.0ms

series244.0ms

simplify103.0ms

prune287.0ms

localize8.0ms

rewrite24.0ms

series123.0ms

simplify64.0ms

prune117.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample623.0ms

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