Details

sample52.0ms

Algorithm

intervals

Results

34.0ms

300×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	90	21
3	384	21
4	1663	21
done	5000	21

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize39.0ms

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)))
5.0b	(- (* b b) (* a a))
7.5b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite405.0ms

Algorithm

rewrite-expression-head

Rules

515×	`times-frac`
419×	`add-sqr-sqrt`
403×	`*-un-lft-identity`
395×	`add-cube-cbrt`
339×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
57×	`div-inv`
36×	`add-exp-log` `add-cbrt-cube`
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×	`distribute-lft-out--`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r*` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`frac-2neg` `fma-neg` `diff-log` `clear-num`

Counts

4 → 501

Calls

4 calls:

79.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
15.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
233.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms	(/ 1.0 (- (* b b) (* a a)))
33.0ms	(- (* b b) (* a a))
101.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts

513 → 513

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	886	27857
1	2290	25797
done	5000	22403

prune1.4s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 7.3b

localize26.0ms

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)))
0.3b	(/ (/ PI 2.0) (+ b a))
7.5b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

702×	`times-frac`
557×	`*-un-lft-identity`
528×	`add-sqr-sqrt`
481×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
67×	`div-inv`
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*`
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×	`expm1-log1p-u` `pow-prod-down` `frac-sub` `log1p-expm1-u` `add-log-exp`
2×	`sub-neg` `frac-2neg` `flip3-+` `clear-num` `*-commutative` `flip-+`
1×	`associate-/l/`

Counts

4 → 634

Calls

4 calls:

11.0ms	(/ 1.0 (- b a))
129.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
32.0ms	(/ (/ PI 2.0) (+ b a))
249.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series376.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- b a))
88.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
73.0ms	(/ (/ PI 2.0) (+ b a))
165.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.2s

Counts

646 → 646

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	1031	29916
1	2733	27749
done	5001	24229

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite607.0ms

Algorithm

rewrite-expression-head

Rules

525×	`times-frac`
437×	`add-sqr-sqrt`
425×	`*-un-lft-identity`
399×	`add-cube-cbrt`
338×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
61×	`add-exp-log` `add-cbrt-cube`
58×	`div-inv`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`associate-/r*`
8×	`frac-sub`
6×	`associate-/r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`sub-neg` `frac-2neg` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 541

Calls

4 calls:

23.0ms	(/ 1.0 (- b a))
236.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
189.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
91.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ 1.0 (- b a))
110.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
123.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
84.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify2.5s

Counts

553 → 553

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	930	25655
1	2439	23543
done	5000	20013

prune1.6s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.2b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.7b	(/ PI (* a b))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`cbrt-undiv` `div-exp`
7×	`times-frac`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`prod-exp` `associate-/r*` `cbrt-unprod`
4×	`associate-/l*`
2×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `associate-/r/` `log1p-expm1-u` `div-inv` `distribute-lft-out` `add-log-exp`
1×	`flip3-+` `associate-*r/` `flip-+` `associate-/l/`

Counts

2 → 55

Calls

2 calls:

54.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
16.0ms	(/ PI (* a b))

series171.0ms

Counts

2 → 6

Calls

2 calls:

127.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
44.0ms	(/ PI (* a b))

simplify933.0ms

Counts

61 → 61

Iterations

Useful iterations: 2 (209.0ms)

Iter	Nodes	Cost
0	111	724
1	289	695
2	1196	563
done	5001	563

prune180.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

regimes62.0ms

Accuracy

0% (0.2b 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	11	13
1	17	13
done	17	13

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

9496×

body

valid