Details

sample39.0ms

Algorithm

intervals

Results

24.0ms

307×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1569
3	370
2	89
1	31
0	15

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b	(/ 1.0 (- (* b b) (* a a)))
4.5b	(- (* b b) (* a a))
6.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite352.0ms

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-cbrt-cube` `add-exp-log`
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-l/` `associate-r/`
7×	`flip3--` `flip--`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `frac-sub` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg` `associate-/l*`
2×	`*-commutative`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log`

Counts

4 → 501

Calls

4 calls:

73.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
10.0ms	(/ 1.0 (- (* b b) (* a a)))
7.0ms	(- (* b b) (* a a))
189.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
83.0ms	(/ 1.0 (- (* b b) (* a a)))
64.0ms	(- (* b b) (* a a))
152.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.9s

Counts

513 → 513

Iterations

Iter	Nodes
done	5000
1	2893
0	886

prune4.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ a b))
6.2b	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite535.0ms

Algorithm

rewrite-expression-head

Rules

940×	`times-frac`
738×	`*-un-lft-identity`
713×	`add-sqr-sqrt`
662×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
95×	`div-inv`
59×	`add-cbrt-cube` `associate-l` `add-exp-log`
33×	`associate-r`
27×	`distribute-lft-out`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
14×	`frac-times`
13×	`fma-neg` `associate-/l*` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
8×	`associate-l/` `associate-r/`
6×	`flip3--` `associate-/r/` `flip--` `add-log-exp` `unswap-sqr`
5×	`frac-sub`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3-+` `*-commutative` `flip-+`
1×	`clear-num` `frac-2neg` `diff-log` `associate-/l/`

Counts

4 → 801

Calls

4 calls:

43.0ms	(- (/ 1.0 a) (/ 1.0 b))
108.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
22.0ms	(/ (/ PI 2.0) (+ a b))
263.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (/ 1.0 a) (/ 1.0 b))
114.0ms	(* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a)))
87.0ms	(/ (/ PI 2.0) (+ a b))
120.0ms	(* (* (/ (/ PI 2.0) (+ a b)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify3.7s

Counts

813 → 813

Iterations

Iter	Nodes
done	5000
1	3338
0	1025

prune6.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite599.0ms

Algorithm

rewrite-expression-head

Rules

763×	`times-frac`
622×	`add-sqr-sqrt`
606×	`*-un-lft-identity`
580×	`add-cube-cbrt`
507×	`prod-diff`
171×	`distribute-rgt-in` `distribute-lft-in`
86×	`div-inv`
59×	`add-cbrt-cube` `add-exp-log`
33×	`associate-r`
27×	`frac-times`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-l/` `associate-r/` `associate-/l/`
14×	`associate-l`
13×	`fma-neg` `distribute-lft-out--`
11×	`pow1` `difference-of-squares`
10×	`flip3--` `flip--`
9×	`frac-sub`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `pow-prod-down` `associate-/r/` `log1p-expm1-u` `unswap-sqr`
3×	`sub-neg`
2×	`*-commutative` `distribute-lft-out`
1×	`clear-num` `frac-2neg` `flip3-+` `diff-log` `flip-+` `associate-/l*`

Counts

4 → 708

Calls

4 calls:

35.0ms	(- (/ 1.0 a) (/ 1.0 b))
212.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
176.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
66.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (/ 1.0 a) (/ 1.0 b))
132.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ a b))
131.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
74.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify3.6s

Counts

720 → 720

Iterations

Iter	Nodes
done	5002
1	3031
0	924

prune5.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize25.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (/ PI (* a b)))
0.1b	(/ (* 0.5 (/ PI (* a b))) (+ a b))
1.6b	(/ PI (* a b))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-cbrt-cube` `add-exp-log`
14×	`*-un-lft-identity`
12×	`add-sqr-sqrt`
10×	`cbrt-undiv` `times-frac` `div-exp` `add-cube-cbrt`
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×	`clear-num` `frac-2neg` `associate-*r/` `associate-/r/` `distribute-lft-out`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+` `unswap-sqr` `associate-/l/`

Counts

3 → 84

Calls

3 calls:

39.0ms	(* 0.5 (/ PI (* a b)))
41.0ms	(/ (* 0.5 (/ PI (* a b))) (+ a b))
12.0ms	(/ PI (* a b))

series195.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(* 0.5 (/ PI (* a b)))
105.0ms	(/ (* 0.5 (/ PI (* a b))) (+ a b))
38.0ms	(/ PI (* a b))

simplify1.5s

Counts

93 → 93

Iterations

Iter	Nodes
done	5007
2	1266
1	338
0	129

prune387.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

regimes169.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	12
1	12
0	9

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

9527×

body

valid