Details

Time bar (total: 13.2s)

sample46.0ms

Algorithm
intervals
Results
30.0ms474×body80valid

simplify1.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (337.0ms)

IterNodesCost
02867
17066
224247
395735
4331434
done500134

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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)

rewrite352.0ms

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))
311.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
26.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series131.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (fabs x) (fabs x)) (fabs x))
61.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
44.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify946.0ms

Counts
145 → 145
Iterations

Useful iterations: 2 (209.0ms)

IterNodesCost
02242536
16271770
224401220
done50011220

prune470.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

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))))
0.2b
(/ 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)))))))
0.4b
(/ (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))))
7.0ms
(/ 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)

series700.0ms

Counts
4 → 10
Calls
4 calls:
118.0ms
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
303.0ms
(/ 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)))))))
278.0ms
(/ (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)

simplify739.0ms

Counts
184 → 184
Iterations

Useful iterations: 2 (188.0ms)

IterNodesCost
02609026
15588818
221568412
done50008412

prune930.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
22×associate-*l*
20×times-frac
19×add-cube-cbrt *-un-lft-identity
13×sqrt-prod
9×add-exp-log add-cbrt-cube
7×pow1
4×expm1-log1p-u fma-udef log1p-expm1-u add-log-exp
3×associate-*r* unswap-sqr
2×prod-exp cbrt-unprod
1×cbrt-undiv distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 div-exp pow-prod-down associate-*l/ *-commutative div-inv
Counts
4 → 81
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))
0.0ms
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
14.0ms
(* (/ 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))))))
1.0ms
(sqrt PI)

series467.0ms

Counts
4 → 10
Calls
4 calls:
58.0ms
(fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x)))
118.0ms
(fma (pow (fabs x) 5) (/ 1.0 5.0) (fma (pow (fabs x) 3) (/ 2.0 3.0) (* 2.0 (fabs x))))
291.0ms
(* (/ 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))))))
0.0ms
(sqrt PI)

simplify413.0ms

Counts
91 → 91
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
01452559
13112522
210862262
done50022262

prune390.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (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)

rewrite155.0ms

Algorithm
rewrite-expression-head
Rules
2716×times-frac
1770×sqrt-prod
1246×add-sqr-sqrt
1244×add-cube-cbrt *-un-lft-identity
66×div-inv
40×associate-/l*
34×associate-/r*
18×add-exp-log add-cbrt-cube
9×cbrt-undiv div-exp
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/r/ associate-/l/
Counts
4 → 1128
Calls
4 calls:
4.0ms
(/ (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))))))
36.0ms
(/ (/ 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)

series724.0ms

Counts
4 → 8
Calls
4 calls:
428.0ms
(/ (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))))))
295.0ms
(/ (/ 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)

simplify1.1s

Counts
1136 → 1136
Iterations

Useful iterations: done (1.0s)

IterNodesCost
0118387164
1371583837
done500082849

prune3.2s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes63.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02534
12734
done2734

end0.0ms

sample1.1s

Algorithm
intervals
Results
909.0ms13968×body80valid