Details

Time bar (total: 11.5s)

sample45.0ms

Algorithm
intervals
Results
29.0ms437×body80valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 4 (353.0ms)

IterNodesCost
02867
17066
224247
395735
4331434
done500134

prune18.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (fabs x) (fabs x)) (fabs x))
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)))
1.0b
(sqrt PI)

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
75×add-exp-log add-cbrt-cube
53×pow1
45×prod-exp cbrt-unprod
27×associate-*l*
24×pow-prod-down
22×add-sqr-sqrt
20×add-cube-cbrt *-un-lft-identity
18×times-frac
8×cbrt-undiv div-exp
6×pow-plus pow-prod-up
5×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod *-commutative
2×pow2 associate-*l/ pow-sqr div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 pow3 unswap-sqr
Counts
4 → 135
Calls
4 calls:
7.0ms
(* (* (fabs x) (fabs x)) (fabs x))
312.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
25.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series137.0ms

Counts
4 → 10
Calls
4 calls:
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))
63.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
46.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify961.0ms

Counts
145 → 145
Iterations

Useful iterations: 2 (217.0ms)

IterNodesCost
02242536
16271770
224401220
done50011220

prune464.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
0.3b
(/ 1.0 (/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
0.3b
(/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
1.0b
(sqrt PI)

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
156×times-frac
96×add-sqr-sqrt
95×add-cube-cbrt *-un-lft-identity
51×sqrt-prod
25×associate-/r*
11×add-exp-log add-cbrt-cube
9×associate-/l*
6×div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef
Counts
4 → 174
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
6.0ms
(/ 1.0 (/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
3.0ms
(/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
1.0ms
(sqrt PI)

series724.0ms

Counts
4 → 10
Calls
4 calls:
122.0ms
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
310.0ms
(/ 1.0 (/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
292.0ms
(/ (sqrt PI) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
0.0ms
(sqrt PI)

simplify756.0ms

Counts
184 → 184
Iterations

Useful iterations: 2 (197.0ms)

IterNodesCost
02609026
15588818
221568412
done50008412

prune770.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
0.3b
(/ 1.0 (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
26×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity
18×add-exp-log add-cbrt-cube
10×associate-/r*
7×cbrt-undiv div-exp
6×pow1 sqrt-prod div-inv
4×expm1-log1p-u log1p-expm1-u associate-/l* add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod
1×associate-/r/
Counts
4 → 103
Calls
4 calls:
9.0ms
(/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
12.0ms
(/ 1.0 (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series597.0ms

Counts
4 → 8
Calls
4 calls:
288.0ms
(/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))
308.0ms
(/ 1.0 (/ (* (sqrt (sqrt PI)) (sqrt (sqrt PI))) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify536.0ms

Counts
111 → 111
Iterations

Useful iterations: done (531.0ms)

IterNodesCost
01674426
13773934
214693492
done50003486

prune530.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI))) (/ (cbrt 1.0) (/ (sqrt (cbrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))))
1.0b
(/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI)))
1.0b
(cbrt PI)
1.0b
(cbrt PI)

rewrite109.0ms

Algorithm
rewrite-expression-head
Rules
391×times-frac
251×add-sqr-sqrt
191×associate-*r*
187×add-cube-cbrt *-un-lft-identity
165×cbrt-prod
116×sqrt-prod
45×add-exp-log
31×add-cbrt-cube
18×unswap-sqr
17×cbrt-undiv div-exp
13×prod-exp cbrt-unprod
9×div-inv
7×associate-*l*
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-/r*
2×pow1/3
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num associate-/r/ *-commutative associate-/l*
Counts
4 → 297
Calls
4 calls:
82.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI))) (/ (cbrt 1.0) (/ (sqrt (cbrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))))
4.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI)))
1.0ms
(cbrt PI)
1.0ms
(cbrt PI)

series650.0ms

Counts
4 → 6
Calls
4 calls:
650.0ms
(* (/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI))) (/ (cbrt 1.0) (/ (sqrt (cbrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))))))
0.0ms
(/ (* (cbrt 1.0) (cbrt 1.0)) (fabs (cbrt PI)))
0.0ms
(cbrt PI)
0.0ms
(cbrt PI)

simplify581.0ms

Counts
303 → 303
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
055614182
1183113760
done500013608

prune1.6s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0b

regimes213.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02867
14167
done4167

end0.0ms

sample1.1s

Algorithm
intervals
Results
930.0ms13989×body80valid