Details

analyze220.0ms

Algorithm: search

sample23.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	14×	body	80	invalid

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

prune3.0ms

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: 12.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.4b	(/ 1.0 (- (* b b) (* a a)))
3.2b	(- (* b b) (* a a))
8.3b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite51.0ms

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

series34.0ms

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

simplify109.0ms

Algorithm

egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	804	1567
1	4503	1342
2	5001	1342

prune235.0ms

Filtered

119 candidates to 165 candidates (-38.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	157	8	165
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	158	8	166

Merged error: 8.1b

Counts

166 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.3b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite97.0ms

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:

14.0ms	(- (/ 1.0 a) (/ 1.0 b))
30.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
7.0ms	(/ (/ PI 2.0) (+ b a))
30.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series33.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify56.0ms

Algorithm

egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1270	2599
1	5001	2298

prune381.0ms

Filtered

194 candidates to 285 candidates (-46.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	280	5	285
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	285	8	293

Merged error: 0.0b

Counts

293 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite85.0ms

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:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
27.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
8.0ms	(/ (/ PI 2.0) (+ b a))
26.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(- (/ 1.0 a) (/ 1.0 b))
13.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
7.0ms	(/ (/ PI 2.0) (+ b a))
14.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify111.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	931	1844
1	4583	1596
2	5002	1596

prune259.0ms

Filtered

136 candidates to 202 candidates (-48.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	197	5	202
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	201	9	210

Merged error: 0b

Counts

210 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
308×	`add-sqr-sqrt`
288×	`*-un-lft-identity`
114×	`add-cube-cbrt`
85×	`distribute-lft-out--`
73×	`difference-of-squares`
66×	`associate-r`
43×	`add-exp-log` `add-cbrt-cube`
32×	`div-inv`
25×	`associate-/l*`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out`
9×	`pow1` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
4×	`flip3--` `flip--` `associate-/l/`
3×	`pow-prod-down` `associate-*l/`
2×	`frac-2neg` `clear-num` `frac-sub`
1×	`frac-times` `sub-neg` `flip3-+` `diff-log` `div-sub` `associate-r/` `associate-l` `-commutative` `flip-+`

Counts

4 → 299

Calls

4 calls:

12.0ms	(- (/ 1.0 a) (/ 1.0 b))
33.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)))
8.0ms	(/ (/ PI 2.0) (+ b a))
20.0ms	(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series32.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify61.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1245	3083
1	5002	2836

prune410.0ms

Filtered

207 candidates to 311 candidates (-50.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	310	1	311
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	312	8	320

Merged error: 0b

Counts

320 → 8

regimes104.0ms

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 (0.0ms)

Iter	Nodes	Cost
0	16	7
1	16	7

end0.0ms

analyze223.0ms

Algorithm: search

sample621.0ms

Algorithm

intervals

Results

462.0ms	8000×	body	80	valid
22.0ms	386×	body	80	invalid

Details

analyze220.0ms

sample23.0ms

simplify38.0ms

prune3.0ms

localize12.0ms

rewrite51.0ms

series34.0ms

simplify109.0ms

prune235.0ms

localize13.0ms

rewrite97.0ms

series33.0ms

simplify56.0ms

prune381.0ms

localize13.0ms

rewrite85.0ms

series38.0ms

simplify111.0ms

prune259.0ms

localize12.0ms

rewrite95.0ms

series32.0ms

simplify61.0ms

prune410.0ms

regimes104.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze223.0ms

sample621.0ms

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