Details

sample28.0ms

Algorithm

intervals

Results

17.0ms

301×

body

valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	5167	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: 15.1b

Counts

2 → 2

localize16.0ms

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)))
6.5b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite50.0ms

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

series36.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
6.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
12.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify51.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5018	2682

prune230.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	159	6	165
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	160	7	167

Merged error: 7.3b

Counts

167 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ b a))
0.1b	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
0.2b	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
7.5b	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

196×	`add-exp-log`
112×	`add-cbrt-cube`
95×	`prod-exp`
75×	`add-sqr-sqrt`
70×	`*-un-lft-identity`
65×	`times-frac`
60×	`div-exp`
51×	`cbrt-unprod`
47×	`frac-times`
40×	`add-cube-cbrt`
34×	`associate-r`
32×	`associate-l`
31×	`cbrt-undiv`
29×	`associate-*r/`
23×	`associate-*l/`
21×	`pow1`
11×	`rec-exp` `1-exp`
10×	`pow-prod-down`
9×	`flip3--` `flip--`
8×	`frac-sub` `distribute-lft-out--`
7×	`distribute-lft-out` `difference-of-squares`
6×	`associate-/r/` `div-inv` `unswap-sqr`
4×	`associate-/r*` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `flip3-+` `flip-+`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 254

Calls

4 calls:

5.0ms	(/ 1 (+ b a))
20.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
17.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
30.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1 (+ b a))
9.0ms	(* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a))))
7.0ms	(* (/ 1 (+ b a)) (/ 1.0 (- b a)))
13.0ms	(* (* (/ PI 2.0) (* (/ 1 (+ b a)) (/ 1.0 (- b a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify61.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5280	4087

prune271.0ms

Filtered

149 candidates to 266 candidates (-78.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	263	3	266
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	264	9	273

Merged error: 0.1b

Counts

273 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-exp-log` `add-cbrt-cube`
47×	`*-un-lft-identity`
42×	`add-sqr-sqrt`
36×	`times-frac`
25×	`add-cube-cbrt` `associate-*r/`
21×	`associate-l` `prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp` `associate-r`
11×	`pow1`
10×	`distribute-rgt-in` `distribute-lft-in`
9×	`frac-times`
7×	`flip3--` `flip--` `associate-/l/` `distribute-lft-out`
6×	`sub-neg` `associate-/r/` `frac-sub`
5×	`associate-/r*` `div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `difference-of-squares`
3×	`associate-*l/`
2×	`frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 162

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
28.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
20.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
22.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series42.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
13.0ms	(/ (* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))) (* 2.0 (- b a)))
13.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
11.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify41.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5377	2591

prune220.0ms

Filtered

113 candidates to 174 candidates (-54.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	168	6	174
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Merged error: 0.0b

Counts

183 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
42×	`add-sqr-sqrt` `times-frac`
40×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
16×	`add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
12×	`associate-l`
11×	`associate-/l*`
10×	`distribute-lft-out--`
8×	`associate-/r/` `div-inv` `difference-of-squares`
6×	`pow1` `associate-*l/` `add-log-exp`
5×	`associate-r/` `associate-/r`
4×	`flip3--` `flip--` `associate-/l/` `distribute-lft-out`
3×	`flip3-+` `associate-r` `frac-sub` `flip-+`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 132

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
23.0ms	(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a)) (* 2.0 (- b a)))
21.0ms	(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a))
16.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) PI)

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
15.0ms	(/ (/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a)) (* 2.0 (- b a)))
13.0ms	(/ (* 1.0 (* (- (/ 1.0 a) (/ 1.0 b)) PI)) (+ b a))
6.0ms	(* (- (/ 1.0 a) (/ 1.0 b)) PI)

simplify36.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5332	2270

prune158.0ms

Filtered

98 candidates to 144 candidates (-46.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	4	5	9
Picked	0	1	1
Done	0	0	0
Total	147	7	154

Merged error: 0b

Counts

154 → 7

regimes97.0ms

Accuracy

0% (0.2b 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 (1.0ms)

Iter	Nodes	Cost
0	44	21
1	44	21

end0.0ms

sample815.0ms

Algorithm

intervals

Results

569.0ms

9680×

body

valid

Details

sample28.0ms

simplify14.0ms

prune8.0ms

localize16.0ms

rewrite50.0ms

series36.0ms

simplify51.0ms

prune230.0ms

localize15.0ms

rewrite85.0ms

series33.0ms

simplify61.0ms

prune271.0ms

localize14.0ms

rewrite81.0ms

series42.0ms

simplify41.0ms

prune220.0ms

localize12.0ms

rewrite77.0ms

series38.0ms

simplify36.0ms

prune158.0ms

regimes97.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample815.0ms

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