Details

Time bar (total: 18.8s)

sample56.0ms

Algorithm
intervals
Results
37.0ms480×body80valid

simplify114.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
07042
125242
2105942
3471342
4500142
done500142

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite10.5s

Algorithm
rewrite-expression-head
Rules
107×add-exp-log add-cbrt-cube
70×prod-exp cbrt-unprod
51×pow1
48×associate-*l*
42×add-sqr-sqrt
38×times-frac
35×pow-prod-down
33×add-cube-cbrt *-un-lft-identity
15×associate-*l/
13×sqrt-prod
12×frac-add
11×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 → 173
Calls
4 calls:
9.2s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (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)))))
62.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
2.0ms
(sqrt PI)

series434.0ms

Counts
4 → 10
Calls
4 calls:
73.0ms
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
315.0ms
(* (/ 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)))))
47.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify58.0ms

Counts
183 → 183
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013665031
150013864
done50013864

prune708.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.1b
(* (/ 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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
0.1b
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b
(sqrt PI)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
55×associate-*l/
48×associate-*l*
44×prod-exp cbrt-unprod
42×add-sqr-sqrt
38×times-frac
36×pow1 frac-add
33×add-cube-cbrt *-un-lft-identity
22×frac-times associate-*r/ pow-prod-down
14×flip3-+ flip-+
13×sqrt-prod
9×cbrt-undiv div-exp
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 → 179
Calls
4 calls:
622.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
530.0ms
(* (/ 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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
61.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series627.0ms

Counts
4 → 10
Calls
4 calls:
61.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
524.0ms
(* (/ 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)))) (* (/ (sqrt 1.0) (sqrt 21.0)) (* (* (/ (sqrt 1.0) (sqrt 21.0)) (pow (fabs x) 6)) (fabs x)))))
42.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify67.0ms

Counts
189 → 189
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
014686096
150025132
done50025132

prune1.0s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
0.1b
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.3b
(/ (+ (* 1.0 (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* 1.0 (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))) (sqrt PI))
1.0b
(sqrt PI)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
37×times-frac
35×add-cube-cbrt *-un-lft-identity
32×add-exp-log
24×associate-*l*
18×sqrt-prod
16×add-cbrt-cube
15×prod-exp
14×associate-*r*
12×unswap-sqr
10×pow1
9×unpow-prod-down cube-prod
7×distribute-lft-out
6×associate-/r*
5×pow-prod-up cbrt-unprod sqr-pow
4×expm1-log1p-u pow-to-exp div-exp pow-exp log1p-expm1-u associate-/l* add-log-exp
2×cbrt-undiv cube-mult unpow3 *-commutative div-inv associate-/l/
1×pow2 rem-sqrt-square frac-2neg sqrt-pow1 flip3-+ pow-plus pow1/2 associate-*r/ clear-num pow-sqr flip-+
Counts
4 → 156
Calls
4 calls:
23.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
20.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
29.0ms
(/ (+ (* 1.0 (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* 1.0 (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))) (sqrt PI))
1.0ms
(sqrt PI)

series449.0ms

Counts
4 → 10
Calls
4 calls:
43.0ms
(* (pow (fabs x) 3) (* (fabs x) (fabs x)))
42.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
363.0ms
(/ (+ (* 1.0 (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0)))) (* 1.0 (fma (/ 1.0 5.0) (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))))) (sqrt PI))
0.0ms
(sqrt PI)

simplify96.0ms

Counts
166 → 166
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
05933041
126242762
250012653
done50012653

prune818.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1 (* (fabs (cbrt PI)) 1)) (* (/ 1.0 (sqrt (cbrt PI))) (/ (fma (/ 1.0 5.0) (pow (fabs x) 5) (+ (/ (* (* (pow (fabs x) 3) (pow (fabs x) 4)) 1.0) 21.0) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) 1)))
1.0b
(cbrt PI)
1.0b
(cbrt PI)
1.0b
(/ 1 (* (fabs (cbrt PI)) 1))

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
311×add-exp-log
178×prod-exp
118×div-exp
78×add-cbrt-cube
68×1-exp
33×cbrt-unprod
24×cbrt-undiv rec-exp
12×pow1
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×associate-*l*
6×cbrt-prod times-frac
5×frac-times associate-*r/
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×associate-*l/ associate-/l*
2×pow-flip pow1/3 div-inv
1×frac-2neg associate-*r* clear-num associate-/r* *-commutative inv-pow
Counts
4 → 171
Calls
4 calls:
71.0ms
(* (/ 1 (* (fabs (cbrt PI)) 1)) (* (/ 1.0 (sqrt (cbrt PI))) (/ (fma (/ 1.0 5.0) (pow (fabs x) 5) (+ (/ (* (* (pow (fabs x) 3) (pow (fabs x) 4)) 1.0) 21.0) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) 1)))
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)
11.0ms
(/ 1 (* (fabs (cbrt PI)) 1))

series584.0ms

Counts
4 → 6
Calls
4 calls:
584.0ms
(* (/ 1 (* (fabs (cbrt PI)) 1)) (* (/ 1.0 (sqrt (cbrt PI))) (/ (fma (/ 1.0 5.0) (pow (fabs x) 5) (+ (/ (* (* (pow (fabs x) 3) (pow (fabs x) 4)) 1.0) 21.0) (fma (fabs x) 2.0 (* (pow (fabs x) 3) (/ 2.0 3.0))))) 1)))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)
0.0ms
(/ 1 (* (fabs (cbrt PI)) 1))

simplify75.0ms

Counts
177 → 177
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
08084299
126013292
250013200
done50013200

prune460.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes67.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04539
14539
done4539

end0.0ms

sample1.2s

Algorithm
intervals
Results
973.0ms14106×body80valid