Details

Time bar (total: 6.6s)

sample50.0ms

Algorithm
intervals
Results
33.0ms452×body80valid

simplify110.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142
done500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.2b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.2b
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0b
(sqrt PI)

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1
33×add-cube-cbrt *-un-lft-identity
22×pow-prod-down
15×associate-*l/
13×sqrt-prod
12×frac-add
9×cbrt-undiv div-exp
6×frac-times flip3-+ associate-*r/ flip-+
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×*-commutative div-inv unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2
Counts
4 → 163
Calls
4 calls:
613.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
58.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.2s
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
1.0ms
(sqrt PI)

series428.0ms

Counts
4 → 10
Calls
4 calls:
56.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
49.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
323.0ms
(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.0ms
(sqrt PI)

simplify61.0ms

Counts
173 → 173
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012244595
150023688
done50023688

prune743.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1.0 5.0) (pow (fabs x) 3))
0.2b
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
64×add-sqr-sqrt
30×add-exp-log
26×add-cube-cbrt *-un-lft-identity times-frac
25×associate-*r* associate-*l*
16×unswap-sqr
14×add-cbrt-cube
12×prod-exp
10×unpow-prod-down cube-prod
6×pow1 div-exp sqrt-prod sqr-pow
4×expm1-log1p-u pow-to-exp pow-exp cbrt-unprod log1p-expm1-u add-log-exp
2×cbrt-undiv cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3 *-commutative div-inv
1×associate-*r/ associate-*l/
Counts
4 → 134
Calls
4 calls:
21.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
20.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series89.0ms

Counts
4 → 8
Calls
4 calls:
42.0ms
(* (/ 1.0 5.0) (pow (fabs x) 3))
47.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify96.0ms

Counts
142 → 142
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0511811
12713766
25002766
done5002766

prune657.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
12×cbrt-prod
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u pow1/3 add-cbrt-cube log1p-expm1-u add-log-exp
Counts
4 → 52
Calls
4 calls:
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify48.0ms

Counts
56 → 56
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
099312
1323300
21495292
35001292
done5001292

prune392.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
1.0ms
(sqrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series0.0ms

Counts
4 → 4
Calls
4 calls:
0.0ms
(sqrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify123.0ms

Counts
58 → 58
Iterations

Useful iterations: 8 (121.0ms)

IterNodesCost
033155
137146
244140
365140
4111140
5223140
6872140
72973139
85001136
done5001136

prune397.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes189.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04235
14235
done4235

end0.0ms

sample1.1s

Algorithm
intervals
Results
908.0ms13844×body80valid