Details

Time bar (total: 11.6s)

sample25.0ms

Algorithm
intervals
Results
14.0ms308×body80valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01521
13021
28921
337721
4164421
done500021

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
0.7b
(/ 1.0 (- (* b b) (* a a)))
3.7b
(- (* b b) (* a a))
8.4b
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

rewrite178.0ms

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))
110.0ms
(* (* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a)))) (- (/ 1.0 a) (/ 1.0 b)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(* (/ PI 2.0) (/ 1.0 (- (* b b) (* a a))))
48.0ms
(/ 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)))

simplify1.5s

Counts
165 → 165
Iterations

Useful iterations: 2 (466.0ms)

IterNodesCost
02583239
17763164
232672690
done50002690

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (+ b a))
0.2b
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 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))

rewrite347.0ms

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))
134.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
114.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
69.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

series502.0ms

Counts
4 → 12
Calls
4 calls:
271.0ms
(/ 1.0 (+ b a))
73.0ms
(* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a)))
101.0ms
(* (/ PI 2.0) (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) (/ 1.0 (+ b a))))
56.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))

simplify1.5s

Counts
299 → 299
Iterations

Useful iterations: 2 (550.0ms)

IterNodesCost
03886222
111536055
235215355
done50005355

prune694.0ms

Pruning

11 alts after pruning (11 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))

rewrite304.0ms

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))
106.0ms
(/ (* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0)) (* 2.0 (+ b a)))
68.0ms
(/ (- (/ 1.0 a) (/ 1.0 b)) (- b a))
95.0ms
(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

series257.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(- (/ 1.0 a) (/ 1.0 b))
97.0ms
(/ (* 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))
77.0ms
(* PI (* (/ (- (/ 1.0 a) (/ 1.0 b)) (- b a)) 1.0))

simplify1.1s

Counts
182 → 182
Iterations

Useful iterations: 2 (452.0ms)

IterNodesCost
02863918
18023790
231163228
done50013228

prune400.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 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)))
0.3b
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
0.3b
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

rewrite290.0ms

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))
87.0ms
(/ (/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a)) (* 2.0 (+ b a)))
93.0ms
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
83.0ms
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

series267.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(- (/ 1.0 a) (/ 1.0 b))
100.0ms
(/ (/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a)) (* 2.0 (+ b a)))
70.0ms
(/ (* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0)) (- b a))
65.0ms
(* PI (* (- (/ 1.0 a) (/ 1.0 b)) 1.0))

simplify993.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (410.0ms)

IterNodesCost
02372963
16392881
227032289
done50012289

prune280.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes65.0ms

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
01419
11719
done1719

end0.0ms

sample655.0ms

Algorithm
intervals
Results
444.0ms9596×body80valid