Details

sample29.0ms

Algorithm

intervals

Results

18.0ms

302×

body

valid

simplify23.0ms

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: 16.8b

Counts

2 → 2

localize13.0ms

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)))
4.5b	(- (* b b) (* a a))
11.4b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite52.0ms

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)))
6.0ms	(- (* b b) (* a a))
23.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

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

simplify53.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5073	2682

prune252.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	154	11	165
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	156	11	167

Merged error: 11.2b

Counts

167 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.1b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
11.4b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

352×	`times-frac`
305×	`*-un-lft-identity`
256×	`add-sqr-sqrt`
149×	`add-cube-cbrt`
108×	`associate-r`
61×	`add-exp-log` `add-cbrt-cube`
42×	`distribute-lft-out--`
41×	`difference-of-squares`
37×	`distribute-lft-out`
28×	`associate-/r/`
22×	`cbrt-undiv` `div-exp`
21×	`associate-/l*`
19×	`prod-exp` `cbrt-unprod`
17×	`div-inv`
14×	`frac-times` `associate-l`
12×	`flip3-+` `flip-+`
11×	`pow1`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/`
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` `clear-num` `*-commutative`
1×	`associate-/l/`

Counts

4 → 358

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
14.0ms	(/ (/ 1.0 (+ b a)) (- b a))
39.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
32.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series34.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
7.0ms	(/ (/ 1.0 (+ b a)) (- b a))
9.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
13.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify71.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4994	6038
1	4994	6038

prune450.0ms

Filtered

234 candidates to 370 candidates (-58.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	366	4	370
Fresh	7	3	10
Picked	0	1	1
Done	0	0	0
Total	373	8	381

Merged error: 0.1b

Counts

381 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* 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)))

rewrite84.0ms

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))
26.0ms	(/ (* 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))))
25.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series40.0ms

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)))
12.0ms	(* PI (* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b))))
10.0ms	(* (/ 1.0 (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify39.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5211	2591

prune226.0ms

Filtered

114 candidates to 174 candidates (-52.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	169	5	174
Fresh	1	5	6
Picked	1	0	1
Done	1	0	1
Total	172	10	182

Merged error: 0.0b

Counts

182 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ b a))
0.2b	(/ (* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b	(* (/ 1.0 (+ b a)) PI)
0.4b	(* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b)))

rewrite67.0ms

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`
21×	`prod-exp` `cbrt-unprod`
19×	`associate-l`
15×	`associate-r`
13×	`cbrt-undiv` `div-exp`
11×	`pow1` `associate-*l/`
8×	`associate-*r/`
7×	`associate-/l/` `distribute-lft-out`
6×	`frac-times` `associate-/r/`
5×	`flip3--` `associate-/r*` `flip--` `div-inv` `distribute-lft-out--`
4×	`pow-prod-down` `frac-sub` `associate-/l*` `add-log-exp` `difference-of-squares`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `*-commutative` `flip-+` `unswap-sqr`

Counts

4 → 148

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
28.0ms	(/ (* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
8.0ms	(* (/ 1.0 (+ b a)) PI)
20.0ms	(* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (+ b a))
12.0ms	(/ (* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
7.0ms	(* (/ 1.0 (+ b a)) PI)
13.0ms	(* (* (/ 1.0 (+ b a)) PI) (- (/ 1.0 a) (/ 1.0 b)))

simplify37.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5227	2106

prune170.0ms

Filtered

104 candidates to 160 candidates (-53.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Merged error: 0.0b

Counts

170 → 8

regimes107.0ms

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

sample835.0ms

Algorithm

intervals

Results

573.0ms

9603×

body

valid

Details

sample29.0ms

simplify23.0ms

prune8.0ms

localize13.0ms

rewrite52.0ms

series33.0ms

simplify53.0ms

prune252.0ms

localize13.0ms

rewrite110.0ms

series34.0ms

simplify71.0ms

prune450.0ms

localize13.0ms

rewrite84.0ms

series40.0ms

simplify39.0ms

prune226.0ms

localize12.0ms

rewrite67.0ms

series37.0ms

simplify37.0ms

prune170.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample835.0ms

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