Details

sample48.0ms

Algorithm

intervals

Results

29.0ms

314×

body

valid

simplify56.0ms

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize33.0ms

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)))
3.7b	(- (* b b) (* a a))
9.0b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite305.0ms

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:

81.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
28.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
178.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series346.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
80.0ms	(/ 1.0 (- (* b b) (* a a)))
42.0ms	(- (* b b) (* a a))
139.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify123.0ms

Counts: 165 → 165

prune678.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (- b a))
0.1b	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
0.3b	(/ (/ PI 2.0) (+ b a))
9.0b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite442.0ms

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:

23.0ms	(/ 1.0 (- b a))
113.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
20.0ms	(/ (/ PI 2.0) (+ b a))
253.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ 1.0 (- b a))
104.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
91.0ms	(/ (/ PI 2.0) (+ b a))
138.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify61.0ms

Counts: 300 → 300

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

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)))

rewrite419.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-sqr-sqrt`
61×	`add-exp-log` `*-un-lft-identity` `add-cbrt-cube`
57×	`times-frac`
35×	`add-cube-cbrt`
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/` `div-inv`
4×	`pow-prod-down` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `*-commutative` `distribute-lft-out`
1×	`flip3-+` `flip-+`

Counts

4 → 195

Calls

4 calls:

22.0ms	(/ 1.0 (- b a))
160.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
179.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
46.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1.0 (- b a))
137.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
94.0ms	(* (* (/ PI 2.0) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))
67.0ms	(* (/ PI 2.0) (/ 1.0 (- b a)))

simplify45.0ms

Counts: 207 → 207

prune730.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ 1.0 2.0) (/ PI (* a b)))
0.1b	(/ (* (/ 1.0 2.0) (/ PI (* a b))) (+ b a))
0.6b	(/ PI (* a b))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log` `add-cbrt-cube`
23×	`cbrt-undiv` `div-exp`
21×	`add-sqr-sqrt`
20×	`*-un-lft-identity` `times-frac`
17×	`prod-exp` `cbrt-unprod`
16×	`add-cube-cbrt`
13×	`associate-l`
7×	`associate-r`
5×	`pow1` `associate-/r*`
4×	`div-inv` `associate-/l*`
3×	`associate-/l/` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-r/` `associate-l/` `clear-num` `associate-/r/` `distribute-lft-out` `unswap-sqr`
1×	`flip3-+` `pow-prod-down` `*-commutative` `flip-+`

Counts

3 → 105

Calls

3 calls:

59.0ms	(* (/ 1.0 2.0) (/ PI (* a b)))
32.0ms	(/ (* (/ 1.0 2.0) (/ PI (* a b))) (+ b a))
13.0ms	(/ PI (* a b))

series172.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* (/ 1.0 2.0) (/ PI (* a b)))
94.0ms	(/ (* (/ 1.0 2.0) (/ PI (* a b))) (+ b a))
38.0ms	(/ PI (* a b))

simplify70.0ms

Counts: 114 → 114

prune243.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify208.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.1s

9575×

body

valid