Details

sample24.0ms

Algorithm

intervals

Results

14.0ms

315×

body

valid

simplify460.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	30	21
2	86	21
3	352	21
4	1426	21
done	5001	21

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.2b

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)))
3.5b	(- (* b b) (* a a))
8.1b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite111.0ms

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:

23.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
72.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
41.0ms	(/ 1.0 (- (* b b) (* a a)))
30.0ms	(- (* b b) (* a a))
86.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.3s

Counts

165 → 165

Iterations

Useful iterations: 2 (288.0ms)

Iter	Nodes	Cost
0	258	3239
1	810	3164
2	4048	2682
done	5000	2682

prune411.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.2b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.2b	(/ (/ PI 2.0) (+ b a))
8.1b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
193×	`*-un-lft-identity`
164×	`add-sqr-sqrt`
117×	`add-cube-cbrt`
61×	`add-exp-log` `add-cbrt-cube`
59×	`associate-l`
33×	`associate-r`
27×	`distribute-lft-out`
22×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
16×	`associate-/l*`
15×	`div-inv`
14×	`frac-times`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-r/` `associate-l/` `associate-/r/`
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` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 288

Calls

4 calls:

5.0ms	(/ 1.0 (- b a))
56.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
9.0ms	(/ (/ PI 2.0) (+ b a))
95.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(/ 1.0 (- b a))
61.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
48.0ms	(/ (/ PI 2.0) (+ b a))
97.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify378.0ms

Counts

300 → 300

Iterations

Useful iterations: 1 (91.0ms)

Iter	Nodes	Cost
0	406	5324
1	1275	5137
done	5000	5137

prune692.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* (* (/ (/ 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)))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

112×	`times-frac`
97×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
57×	`add-cube-cbrt`
42×	`add-exp-log` `add-cbrt-cube`
14×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out` `associate-/l*`
12×	`associate-r`
10×	`associate-*l/`
9×	`associate-/r*` `div-inv`
8×	`pow1` `associate-/l/`
7×	`distribute-lft-out--`
6×	`frac-times` `associate-*r/` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`associate-/r/` `frac-sub`
3×	`pow-prod-down` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+`

Counts

3 → 168

Calls

3 calls:

61.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
9.0ms	(/ (/ PI 2.0) (+ b a))
81.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series242.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
51.0ms	(/ (/ PI 2.0) (+ b a))
100.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.2s

Counts

177 → 177

Iterations

Useful iterations: 2 (307.0ms)

Iter	Nodes	Cost
0	316	3462
1	904	3322
2	4184	2852
done	5001	2852

prune394.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 3 expressions with local error:

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

504×	`times-frac`
405×	`add-sqr-sqrt`
369×	`*-un-lft-identity`
139×	`add-cube-cbrt`
117×	`distribute-lft-out--`
101×	`difference-of-squares`
83×	`associate-/r*`
42×	`add-exp-log` `add-cbrt-cube` `div-inv`
22×	`cbrt-undiv` `div-exp`
19×	`associate-/l*`
14×	`distribute-lft-out`
12×	`associate-/r/`
6×	`prod-exp` `cbrt-unprod`
4×	`flip3--` `flip--` `associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `frac-sub` `add-log-exp`
1×	`flip3-+` `div-sub` `associate-*l/` `flip-+`

Counts

3 → 344

Calls

3 calls:

53.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
9.0ms	(/ (/ PI 2.0) (+ b a))
35.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

series197.0ms

Counts

3 → 9

Calls

3 calls:

95.0ms	(/ (* (/ (/ PI 2.0) (+ b a)) 1.0) (/ (- b a) (- (/ 1.0 a) (/ 1.0 b))))
55.0ms	(/ (/ PI 2.0) (+ b a))
47.0ms	(/ (- b a) (- (/ 1.0 a) (/ 1.0 b)))

simplify437.0ms

Counts

353 → 353

Iterations

Useful iterations: 1 (123.0ms)

Iter	Nodes	Cost
0	532	8164
1	1497	7758
done	5000	7758

prune887.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	18	21
done	18	21

end0.0ms

sample586.0ms

Algorithm

intervals

Results

427.0ms

9578×

body

valid