Details

Time bar (total: 11.9s)

sample24.0ms

Algorithm
intervals
Results
13.0ms314×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01521
13021
28921
337721
4164421
done500021

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.6b
(/ 1.0 (- (* b b) (* a a)))
3.9b
(- (* b b) (* a a))
9.3b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite181.0ms

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:
43.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
12.0ms
(/ 1.0 (- (* b b) (* a a)))
8.0ms
(- (* b b) (* a a))
112.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series239.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
49.0ms
(/ 1.0 (- (* b b) (* a a)))
32.0ms
(- (* b b) (* a a))
94.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

simplify1.6s

Counts
165 → 165
Iterations

Useful iterations: 2 (493.0ms)

IterNodesCost
02583239
17763164
232672690
done50002690

prune390.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite367.0ms

Algorithm
rewrite-expression-head
Rules
286×add-sqr-sqrt
265×times-frac
232×*-un-lft-identity
85×distribute-lft-out--
80×add-cube-cbrt
79×associate-*l*
73×difference-of-squares
59×add-exp-log add-cbrt-cube
28×div-inv
22×prod-exp cbrt-unprod
19×associate-*r*
18×cbrt-undiv div-exp
12×associate-/l*
11×pow1
6×frac-times associate-*r/ associate-/r/ add-log-exp
5×associate-/r*
4×flip3-- pow-prod-down associate-*l/ flip-- unswap-sqr
3×associate-/l/ distribute-lft-out
2×*-commutative frac-sub
1×sub-neg frac-2neg flip3-+ diff-log div-sub clear-num flip-+
Counts
4 → 276
Calls
4 calls:
24.0ms
(- (/ 1.0 a) (/ 1.0 b))
69.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
117.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
139.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))

series467.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (/ 1.0 a) (/ 1.0 b))
52.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
99.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
282.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))

simplify1.5s

Counts
288 → 288
Iterations

Useful iterations: 2 (682.0ms)

IterNodesCost
03886213
111816052
236265342
done50005342

prune688.0ms

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 a) (/ 1.0 b))
0.1b
(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
0.2b
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
0.3b
(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

rewrite313.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
131×times-frac
120×*-un-lft-identity
48×distribute-lft-out--
47×add-exp-log add-cbrt-cube
41×difference-of-squares
38×add-cube-cbrt
19×prod-exp cbrt-unprod
16×div-inv
13×associate-/l*
12×cbrt-undiv div-exp
9×pow1
6×associate-/r* add-log-exp
4×associate-*r/ associate-/r/ associate-/l/
3×flip3-- associate-*l* pow-prod-down flip--
2×frac-2neg associate-*l/ clear-num frac-sub
1×sub-neg flip3-+ diff-log div-sub associate-*r* *-commutative flip-+
Counts
4 → 170
Calls
4 calls:
24.0ms
(- (/ 1.0 a) (/ 1.0 b))
113.0ms
(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
72.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
95.0ms
(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series265.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (/ 1.0 a) (/ 1.0 b))
103.0ms
(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
49.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
80.0ms
(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.2s

Counts
182 → 182
Iterations

Useful iterations: 2 (479.0ms)

IterNodesCost
02863918
18023790
231163228
done50013228

prune438.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 a) (/ 1.0 b))
0.1b
(/ (/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a)) (* 2.0 (+ b a)))
0.2b
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
0.3b
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

rewrite304.0ms

Algorithm
rewrite-expression-head
Rules
50×add-exp-log add-cbrt-cube
36×times-frac
33×add-sqr-sqrt
29×*-un-lft-identity
17×cbrt-undiv div-exp
16×prod-exp cbrt-unprod
13×add-cube-cbrt
12×associate-/l*
9×pow1 distribute-lft-out--
8×associate-*r/ associate-/r/ difference-of-squares
6×flip3-- associate-*l/ associate-/r* flip-- div-inv add-log-exp
4×associate-/l/
3×associate-*l* pow-prod-down frac-sub
2×frac-2neg clear-num
1×sub-neg flip3-+ diff-log associate-*r* *-commutative flip-+
Counts
4 → 127
Calls
4 calls:
23.0ms
(- (/ 1.0 a) (/ 1.0 b))
88.0ms
(/ (/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a)) (* 2.0 (+ b a)))
97.0ms
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
90.0ms
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

series271.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(- (/ 1.0 a) (/ 1.0 b))
99.0ms
(/ (/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a)) (* 2.0 (+ b a)))
75.0ms
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
64.0ms
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

simplify1.1s

Counts
139 → 139
Iterations

Useful iterations: 2 (432.0ms)

IterNodesCost
02372963
16392881
227032289
done50012289

prune282.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0b

regimes84.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01521
11921
done1921

end0.0ms

sample618.0ms

Algorithm
intervals
Results
407.0ms9629×body80valid