Details

sample29.0ms

Algorithm

intervals

Results

17.0ms

315×

body

valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5046	21

prune8.0ms

Filtered

1 candidates to 1 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: 13.5b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b	(/ 1.0 (- (* b b) (* a a)))
5.3b	(- (* b b) (* a a))
6.8b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite49.0ms

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

series37.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
7.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
13.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify52.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5073	2682

prune244.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	156	9	165
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 6.6b

Counts

167 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
0.3b	(/ PI (* (+ b a) 2.0))
6.8b	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
52×	`*-un-lft-identity`
47×	`times-frac`
33×	`associate-r`
30×	`add-cube-cbrt`
24×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`frac-times`
12×	`associate-*l/` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`associate-l`
8×	`associate-*r/` `associate-/r/`
6×	`flip3--` `associate-/r` `flip--` `div-inv` `associate-/l`
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-+` `unswap-sqr`

Counts

4 → 172

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
18.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
6.0ms	(/ PI (* (+ b a) 2.0))
26.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
10.0ms	(* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a)))
7.0ms	(/ PI (* (+ b a) 2.0))
14.0ms	(* (* (/ PI (* (+ b a) 2.0)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify42.0ms

Algorithm

egg-herbie

Counts

184 → 184

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5407	2696

prune224.0ms

Filtered

122 candidates to 184 candidates (-50.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	177	7	184
Fresh	7	2	9
Picked	0	1	1
Done	0	0	0
Total	184	10	194

Merged error: 0.0b

Counts

194 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

211×	`add-exp-log` `add-cbrt-cube`
99×	`prod-exp` `cbrt-unprod`
69×	`cbrt-undiv` `div-exp`
39×	`add-sqr-sqrt` `*-un-lft-identity`
34×	`times-frac`
25×	`add-cube-cbrt`
23×	`associate-*r/`
21×	`associate-l`
11×	`frac-times` `associate-/l/`
9×	`pow1`
8×	`distribute-rgt-in` `flip3--` `distribute-lft-in` `flip--`
7×	`associate-/r` `associate-/l` `distribute-lft-out--` `difference-of-squares`
6×	`associate-*l/` `associate-/r/`
4×	`sub-neg` `div-inv` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
1×	`flip3-+` `associate-r` `*-commutative` `flip-+`

Counts

4 → 201

Calls

4 calls:

7.0ms	(/ 1.0 (- b a))
12.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
24.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
6.0ms	(/ PI (* (+ b a) 2.0))

series23.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
1.0ms	(* (/ 1.0 (- b a)) (* 1.0 (- b a)))
9.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* (/ 1.0 (- b a)) (* 1.0 (- b a)))) (* a b))
7.0ms	(/ PI (* (+ b a) 2.0))

simplify46.0ms

Algorithm

egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5931	2479

prune169.0ms

Filtered

107 candidates to 213 candidates (-99.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	209	4	213
Fresh	6	2	8
Picked	0	1	1
Done	1	0	1
Total	216	7	223

Merged error: 0.0b

Counts

223 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`prod-exp` `cbrt-unprod`
21×	`times-frac`
18×	`associate-*r/`
17×	`cbrt-undiv` `div-exp`
12×	`add-cube-cbrt`
9×	`pow1` `associate-l`
8×	`distribute-rgt-in` `distribute-lft-in`
7×	`associate-/l/` `distribute-lft-out--`
6×	`frac-times` `flip3--` `associate-l/` `associate-/r` `associate-/r/` `flip--` `add-log-exp` `difference-of-squares`
5×	`sub-neg` `frac-sub` `div-inv`
4×	`associate-/l*`
3×	`pow-prod-down`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`diff-log` `associate-r` `*-commutative`

Counts

4 → 136

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
27.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
6.0ms	(/ PI (* (+ b a) 2.0))
21.0ms	(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
12.0ms	(/ (* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b)))) (- b a))
7.0ms	(/ PI (* (+ b a) 2.0))
13.0ms	(* (/ PI (* (+ b a) 2.0)) (* 1.0 (- (/ 1.0 a) (/ 1.0 b))))

simplify35.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5361	2385

prune142.0ms

Filtered

93 candidates to 148 candidates (-59.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	0	5	5
Picked	0	1	1
Done	1	0	1
Total	147	8	155

Merged error: 0b

Counts

155 → 8

regimes98.0ms

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	21
1	19	21

end0.0ms

sample789.0ms

Algorithm

intervals

Results

541.0ms

9558×

body

valid

Details

sample29.0ms

simplify22.0ms

prune8.0ms

localize16.0ms

rewrite49.0ms

series37.0ms

simplify52.0ms

prune244.0ms

localize13.0ms

rewrite62.0ms

series36.0ms

simplify42.0ms

prune224.0ms

localize12.0ms

rewrite60.0ms

series23.0ms

simplify46.0ms

prune169.0ms

localize12.0ms

rewrite71.0ms

series36.0ms

simplify35.0ms

prune142.0ms

regimes98.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample789.0ms

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