Details

sample45.0ms

Algorithm

intervals

Results

27.0ms

309×

body

valid

simplify737.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.6b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
1.0b	(/ 1.0 (- (* b b) (* a a)))
2.8b	(- (* b b) (* a a))
9.6b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite281.0ms

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:

68.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
24.0ms	(/ 1.0 (- (* b b) (* a a)))
8.0ms	(- (* b b) (* a a))
174.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series311.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
57.0ms	(/ 1.0 (- (* b b) (* a a)))
53.0ms	(- (* b b) (* a a))
125.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts: 165 → 165

prune645.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.4b

localize28.0ms

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))
9.6b	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite350.0ms

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:

12.0ms	(/ 1.0 (- b a))
125.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
18.0ms	(/ (/ PI 2.0) (+ b a))
174.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series336.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ 1.0 (- b a))
101.0ms	(* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a)))
71.0ms	(/ (/ PI 2.0) (+ b a))
113.0ms	(* (* (/ (/ PI 2.0) (+ b a)) (/ 1.0 (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify724.0ms

Counts: 300 → 300

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite398.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
152.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
36.0ms	(/ (/ PI 2.0) (+ b a))
175.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- (/ 1.0 a) (/ 1.0 b))
143.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
98.0ms	(/ (/ PI 2.0) (+ b a))
152.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts: 202 → 202

prune698.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

247×	`add-exp-log` `add-cbrt-cube`
129×	`times-frac`
108×	`prod-exp` `cbrt-unprod`
105×	`*-un-lft-identity`
88×	`cbrt-undiv` `div-exp`
77×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
19×	`associate-/l*`
16×	`pow1`
14×	`div-inv` `distribute-lft-out`
12×	`associate-*r/`
10×	`associate-/r*`
8×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `associate-*l/`
7×	`associate-/l/`
6×	`distribute-lft-out--` `difference-of-squares`
5×	`flip3--` `flip--`
4×	`frac-times` `sub-neg` `associate-/r/` `add-log-exp`
3×	`frac-2neg` `clear-num`
1×	`flip3-+` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 269

Calls

4 calls:

101.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
20.0ms	(/ (/ PI 2.0) (+ b a))
102.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
127.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

series466.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b)) (- b a))
82.0ms	(/ (/ PI 2.0) (+ b a))
118.0ms	(* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a)))
150.0ms	(/ (* (* (/ (/ PI 2.0) (+ b a)) 1.0) (* 1.0 (- b a))) (* a b))

simplify698.0ms

Counts: 281 → 281

prune702.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes99.0ms

Accuracy

-139.2% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify358.0ms

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

9602×

body

valid