Details

Time bar (total: 17.4s)

sample62.0ms

Algorithm
intervals
Results
36.0ms311×body80valid

simplify731.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b
(/ 1.0 (- (* b b) (* a a)))
4.8b
(- (* b b) (* a a))
7.4b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite267.0ms

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:
55.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
14.0ms
(/ 1.0 (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
184.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series363.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
74.0ms
(/ 1.0 (- (* b b) (* a a)))
59.0ms
(- (* b b) (* a a))
124.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.7s

Counts
165 → 165

prune666.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 7.2b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ 1.0 (+ b a)) (- b a))
0.1b
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
7.4b
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite513.0ms

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:
31.0ms
(- (/ 1.0 a) (/ 1.0 b))
50.0ms
(/ (/ 1.0 (+ b a)) (- b a))
139.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
259.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

series429.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(- (/ 1.0 a) (/ 1.0 b))
99.0ms
(/ (/ 1.0 (+ b a)) (- b a))
98.0ms
(* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a)))
185.0ms
(* (* (/ PI 2.0) (/ (/ 1.0 (+ b a)) (- b a))) (- (/ 1.0 a) (/ 1.0 b)))

simplify827.0ms

Counts
359 → 359

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
0.3b
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
0.4b
(* PI (/ 1.0 (+ b a)))

rewrite453.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log add-cbrt-cube
47×add-sqr-sqrt
40×*-un-lft-identity
34×times-frac
30×associate-*r*
21×prod-exp cbrt-unprod
18×add-cube-cbrt
17×associate-*r/
12×cbrt-undiv div-exp
11×pow1
10×distribute-lft-out--
8×difference-of-squares
7×associate-/l/
6×frac-times flip3-- flip-- div-inv add-log-exp
5×frac-sub
4×associate-*l* pow-prod-down associate-/r/
3×sub-neg distribute-lft-out
2×distribute-rgt-in distribute-lft-in associate-*l/ *-commutative unswap-sqr
1×frac-2neg flip3-+ diff-log clear-num associate-/r* flip-+ associate-/l*
Counts
4 → 137
Calls
4 calls:
49.0ms
(- (/ 1.0 a) (/ 1.0 b))
155.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
170.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
66.0ms
(* PI (/ 1.0 (+ b a)))

series445.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(- (/ 1.0 a) (/ 1.0 b))
146.0ms
(/ (* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b))) (* 2.0 (- b a)))
164.0ms
(* (* PI (/ 1.0 (+ b a))) (- (/ 1.0 a) (/ 1.0 b)))
86.0ms
(* PI (/ 1.0 (+ b a)))

simplify2.0s

Counts
149 → 149

prune583.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
0.2b
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
0.4b
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

rewrite364.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log add-cbrt-cube
42×times-frac
39×add-sqr-sqrt *-un-lft-identity
17×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
15×add-cube-cbrt
12×associate-*r*
11×associate-/l*
10×distribute-lft-out--
9×pow1
8×associate-*r/ associate-/r/ div-inv difference-of-squares
6×add-log-exp
5×associate-/r*
4×flip3-- flip-- associate-/l/ distribute-lft-out
3×sub-neg flip3-+ pow-prod-down frac-sub flip-+
2×distribute-rgt-in frac-2neg distribute-lft-in clear-num
1×diff-log associate-*l* *-commutative
Counts
4 → 136
Calls
4 calls:
27.0ms
(- (/ 1.0 a) (/ 1.0 b))
99.0ms
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
102.0ms
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
124.0ms
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(- (/ 1.0 a) (/ 1.0 b))
163.0ms
(/ (/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a)) (* 2.0 (- b a)))
155.0ms
(/ (* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b))) (+ b a))
80.0ms
(* (* PI 1.0) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.9s

Counts
148 → 148

prune465.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes94.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.8s

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.5s9644×body80valid