Details

Time bar (total: 18.1s)

sample59.0ms

Algorithm
intervals
Results
35.0ms300×body80valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01521
13021
28921
337721
4164421
done500021

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.8b
(/ 1.0 (- (* b b) (* a a)))
5.5b
(- (* b b) (* a a))
9.2b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite302.0ms

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:
80.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
13.0ms
(/ 1.0 (- (* b b) (* a a)))
10.0ms
(- (* b b) (* a a))
192.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series344.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
62.0ms
(/ 1.0 (- (* b b) (* a a)))
64.0ms
(- (* b b) (* a a))
138.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify2.6s

Counts
165 → 165
Iterations

Useful iterations: 2 (788.0ms)

IterNodesCost
02583239
17763164
232672690
done50002690

prune608.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
0.2b
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
0.5b
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

rewrite566.0ms

Algorithm
rewrite-expression-head
Rules
281×add-sqr-sqrt
267×times-frac
239×*-un-lft-identity
87×add-cube-cbrt
80×distribute-lft-out--
79×associate-*l*
69×difference-of-squares
61×add-exp-log add-cbrt-cube
27×div-inv
22×prod-exp cbrt-unprod
19×cbrt-undiv div-exp associate-*r*
15×associate-/l*
11×pow1
9×associate-/r*
8×associate-/r/
7×distribute-lft-out
6×frac-times associate-*r/
4×pow-prod-down associate-*l/ add-log-exp unswap-sqr
3×flip3-- flip-- associate-/l/
2×frac-2neg flip3-+ clear-num *-commutative flip-+
1×div-sub frac-sub
Counts
4 → 287
Calls
4 calls:
11.0ms
(/ 1.0 (+ b a))
175.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
237.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
119.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series371.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (+ b a))
144.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
98.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
53.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify2.7s

Counts
299 → 299
Iterations

Useful iterations: 2 (979.0ms)

IterNodesCost
03886222
111536055
235155355
done50005355

prune1.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(* (/ PI 2.0) (* (/ 1.0 (* a b)) (/ 1.0 (+ b a))))
0.2b
(* (/ 1.0 (* a b)) (/ 1.0 (+ b a)))
0.6b
(/ 1.0 (* a b))

rewrite201.0ms

Algorithm
rewrite-expression-head
Rules
97×add-exp-log add-cbrt-cube
46×*-un-lft-identity
40×times-frac
39×prod-exp cbrt-unprod
37×add-sqr-sqrt
32×add-cube-cbrt
31×cbrt-undiv div-exp
20×associate-*l*
19×associate-*r*
11×pow1
7×distribute-lft-out
6×frac-times associate-*r/ associate-/l*
5×associate-/r* div-inv
4×pow-prod-down associate-*l/ associate-/r/ add-log-exp
2×frac-2neg flip3-+ clear-num *-commutative flip-+ unswap-sqr
Counts
4 → 164
Calls
4 calls:
11.0ms
(/ 1.0 (+ b a))
96.0ms
(* (/ PI 2.0) (* (/ 1.0 (* a b)) (/ 1.0 (+ b a))))
73.0ms
(* (/ 1.0 (* a b)) (/ 1.0 (+ b a)))
13.0ms
(/ 1.0 (* a b))

series293.0ms

Counts
4 → 12
Calls
4 calls:
77.0ms
(/ 1.0 (+ b a))
121.0ms
(* (/ PI 2.0) (* (/ 1.0 (* a b)) (/ 1.0 (+ b a))))
63.0ms
(* (/ 1.0 (* a b)) (/ 1.0 (+ b a)))
31.0ms
(/ 1.0 (* a b))

simplify1.7s

Counts
176 → 176
Iterations

Useful iterations: 2 (735.0ms)

IterNodesCost
02272757
16462621
226911991
done50001991

prune446.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.2b
(/ (* (/ 1.0 (* a b)) 1.0) (+ b a))
0.2b
(* (/ PI 2.0) (/ (* (/ 1.0 (* a b)) 1.0) (+ b a)))
0.6b
(/ 1.0 (* a b))

rewrite217.0ms

Algorithm
rewrite-expression-head
Rules
67×add-exp-log add-cbrt-cube
25×cbrt-undiv div-exp
23×prod-exp cbrt-unprod
22×*-un-lft-identity
21×add-sqr-sqrt times-frac
16×add-cube-cbrt
13×associate-*l*
10×associate-*r*
5×pow1 associate-/r*
4×associate-/r/ div-inv associate-/l*
3×distribute-lft-out add-log-exp
2×frac-2neg flip3-+ associate-*l/ clear-num flip-+ unswap-sqr
1×frac-times associate-*r/ pow-prod-down *-commutative associate-/l/
Counts
3 → 108
Calls
3 calls:
36.0ms
(/ (* (/ 1.0 (* a b)) 1.0) (+ b a))
157.0ms
(* (/ PI 2.0) (/ (* (/ 1.0 (* a b)) 1.0) (+ b a)))
15.0ms
(/ 1.0 (* a b))

series219.0ms

Counts
3 → 9
Calls
3 calls:
93.0ms
(/ (* (/ 1.0 (* a b)) 1.0) (+ b a))
86.0ms
(* (/ PI 2.0) (/ (* (/ 1.0 (* a b)) 1.0) (+ b a)))
41.0ms
(/ 1.0 (* a b))

simplify1.3s

Counts
117 → 117
Iterations

Useful iterations: 2 (428.0ms)

IterNodesCost
01851998
15331920
221791464
done50001464

prune280.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes115.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01215
11615
done1615

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.7s9623×body80valid