Details

sample25.0ms

Algorithm

intervals

Results

14.0ms

315×

body

valid

simplify486.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	21
1	31	21
2	87	21
3	360	21
4	1477	21
done	5000	21

prune3.0ms

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)))

rewrite184.0ms

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:

22.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
5.0ms	(/ 1.0 (- (* b b) (* a a)))
3.0ms	(- (* b b) (* a a))
104.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series225.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
47.0ms	(/ 1.0 (- (* b b) (* a a)))
31.0ms	(- (* b b) (* a a))
92.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify766.0ms

Counts

513 → 513

Iterations

Useful iterations: done (736.0ms)

Iter	Nodes	Cost
0	886	27857
1	2478	25797
done	5000	25719

prune1.1s

Pruning

6 alts after pruning (6 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)))

rewrite254.0ms

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:

5.0ms	(/ 1.0 (- b a))
56.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
10.0ms	(/ (/ PI 2.0) (+ b a))
124.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (- b a))
62.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
56.0ms	(/ (/ PI 2.0) (+ b a))
98.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify868.0ms

Counts

646 → 646

Iterations

Useful iterations: done (831.0ms)

Iter	Nodes	Cost
0	1031	29916
1	2938	27749
done	5000	27671

prune1.7s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite305.0ms

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:

5.0ms	(/ 1.0 (- b a))
120.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
101.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
27.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ 1.0 (- b a))
96.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
77.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
55.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify784.0ms

Counts

553 → 553

Iterations

Useful iterations: done (751.0ms)

Iter	Nodes	Cost
0	930	25655
1	2637	23543
done	5000	23465

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (/ PI (* a b)))
0.1b	(/ (* 0.5 (/ PI (* a b))) (+ b a))
0.6b	(/ PI (* a b))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-exp-log` `add-cbrt-cube`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `add-cube-cbrt` `times-frac` `div-exp`
9×	`prod-exp` `cbrt-unprod`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `associate-*r/` `clear-num` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `associate-/l/` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

9.0ms	(* 0.5 (/ PI (* a b)))
14.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
3.0ms	(/ PI (* a b))

series131.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* 0.5 (/ PI (* a b)))
73.0ms	(/ (* 0.5 (/ PI (* a b))) (+ b a))
21.0ms	(/ PI (* a b))

simplify580.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	129	1040
1	347	997
2	1645	813
done	5000	813

prune154.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes50.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	11	11
done	11	11

end0.0ms

sample590.0ms

Algorithm

intervals

Results

431.0ms

9578×

body

valid