Details

sample30.0ms

Algorithm

intervals

Results

17.0ms

296×

body

valid

simplify33.0ms

Counts: 1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.9b	(/ 1.0 (- (* b b) (* a a)))
3.2b	(- (* b b) (* a a))
12.2b	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite218.0ms

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:

48.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
15.0ms	(/ 1.0 (- (* b b) (* a a)))
9.0ms	(- (* b b) (* a a))
139.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
45.0ms	(/ 1.0 (- (* b b) (* a a)))
38.0ms	(- (* b b) (* a a))
95.0ms	(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify100.0ms

Counts: 165 → 165

prune430.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 12.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ 1.0 a) (/ 1.0 b))
0.1b	(/ (/ 1.0 (+ b a)) (- b a))
0.2b	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
12.2b	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite334.0ms

Algorithm

rewrite-expression-head

Rules

350×	`times-frac`
298×	`*-un-lft-identity`
261×	`add-sqr-sqrt`
142×	`add-cube-cbrt`
108×	`associate-r`
59×	`add-exp-log` `add-cbrt-cube`
47×	`distribute-lft-out--`
45×	`difference-of-squares`
33×	`distribute-lft-out`
26×	`associate-/r/`
21×	`cbrt-undiv` `div-exp`
19×	`prod-exp` `cbrt-unprod`
18×	`div-inv` `associate-/l*`
14×	`frac-times` `associate-l`
11×	`pow1` `flip3-+` `flip-+`
8×	`associate-r/` `associate-l/`
7×	`flip3--` `flip--`
6×	`add-log-exp` `unswap-sqr`
5×	`associate-/r*` `frac-sub`
4×	`pow-prod-down`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l/`

Counts

4 → 347

Calls

4 calls:

29.0ms	(- (/ 1.0 a) (/ 1.0 b))
31.0ms	(/ (/ 1.0 (+ b a)) (- b a))
90.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
161.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(- (/ 1.0 a) (/ 1.0 b))
53.0ms	(/ (/ 1.0 (+ b a)) (- b a))
72.0ms	(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
109.0ms	(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify58.0ms

Counts: 359 → 359

prune865.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

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))) (- 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)))

rewrite290.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
59×	`add-exp-log` `add-cbrt-cube`
52×	`*-un-lft-identity`
50×	`times-frac`
30×	`associate-r`
27×	`frac-times`
26×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
18×	`cbrt-undiv` `div-exp`
15×	`associate-r/` `associate-l/` `associate-/l/`
14×	`associate-l`
12×	`distribute-lft-out--`
11×	`pow1`
10×	`flip3--` `flip--` `difference-of-squares`
9×	`frac-sub`
7×	`div-inv`
6×	`add-log-exp`
5×	`associate-/r*`
4×	`pow-prod-down` `associate-/r/` `unswap-sqr`
3×	`sub-neg` `distribute-lft-out`
2×	`distribute-rgt-in` `distribute-lft-in` `*-commutative`
1×	`frac-2neg` `flip3-+` `diff-log` `clear-num` `flip-+` `associate-/l*`

Counts

4 → 179

Calls

4 calls:

26.0ms	(- (/ 1.0 a) (/ 1.0 b))
95.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
121.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
39.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (/ 1.0 a) (/ 1.0 b))
107.0ms	(/ (* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
113.0ms	(* (* (/ PI 2.0) (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
62.0ms	(* (/ PI 2.0) (/ 1.0 (+ b a)))

simplify38.0ms

Counts: 191 → 191

prune475.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize19.0ms

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

rewrite261.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-exp-log` `add-cbrt-cube`
45×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
33×	`times-frac`
17×	`cbrt-undiv` `div-exp`
15×	`add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
12×	`associate-r` `distribute-lft-out--`
10×	`associate-l` `difference-of-squares`
9×	`associate-/r*`
8×	`associate-/l/`
7×	`div-inv`
6×	`pow1` `frac-times` `flip3--` `associate-*r/` `associate-/r/` `flip--` `add-log-exp`
5×	`frac-sub`
3×	`sub-neg` `associate-*l/` `distribute-lft-out`
2×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `flip-+` `associate-/l*`
1×	`diff-log` `pow-prod-down` `*-commutative` `unswap-sqr`

Counts

4 → 141

Calls

4 calls:

27.0ms	(- (/ 1.0 a) (/ 1.0 b))
74.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
22.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
131.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (/ 1.0 a) (/ 1.0 b))
109.0ms	(/ (* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b))) (- b a))
62.0ms	(/ (* (/ PI 2.0) 1.0) (+ b a))
114.0ms	(* (/ (* (/ PI 2.0) 1.0) (+ b a)) (- (/ 1.0 a) (/ 1.0 b)))

simplify93.0ms

Counts: 153 → 153

prune360.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

regimes54.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

9541×

body

valid