Details

Time bar (total: 30.1s)

sample153.0ms

Algorithm
intervals
Results
114.0ms452×body80valid

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 4 (2.3s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune32.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize70.0ms

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)

rewrite1.0s

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:
19.0ms
(* (* (fabs x) (fabs x)) (fabs x))
912.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
67.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
17.0ms
(sqrt PI)

series178.0ms

Counts
4 → 10
Calls
4 calls:
46.0ms
(* (* (fabs x) (fabs x)) (fabs x))
79.0ms
(* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
53.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify1.5s

Counts
145 → 145
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02242536
15421770
219781220
done50001167

prune709.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 3.0 (pow (fabs x) 3))
0.2b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.3b
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
1.0b
(sqrt PI)

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
438×times-frac
235×add-sqr-sqrt
234×add-cube-cbrt *-un-lft-identity
74×associate-/r*
48×unpow-prod-down cube-prod
39×sqrt-prod
24×add-exp-log
16×cube-mult unpow3 add-cbrt-cube sqr-pow
13×div-exp
11×div-inv
9×associate-/l*
7×cbrt-undiv
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-to-exp pow-exp associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 372
Calls
4 calls:
8.0ms
(/ 3.0 (pow (fabs x) 3))
17.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
12.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
1.0ms
(sqrt PI)

series463.0ms

Counts
4 → 10
Calls
4 calls:
43.0ms
(/ 3.0 (pow (fabs x) 3))
58.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
362.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (/ (sqrt PI) 1.0))
0.0ms
(sqrt PI)

simplify2.6s

Counts
382 → 382
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
054410863
110709979
238099589
done50009589

prune2.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0)))
0.3b
(* (/ 1 (sqrt (/ (sqrt PI) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite294.0ms

Algorithm
rewrite-expression-head
Rules
519×times-frac
410×add-sqr-sqrt
392×sqrt-prod
244×*-un-lft-identity
224×add-cube-cbrt
80×associate-*r* associate-*l*
45×unswap-sqr
28×add-exp-log
25×associate-/r*
18×add-cbrt-cube
13×div-inv
9×div-exp
8×pow1 prod-exp
5×cbrt-undiv
4×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
3×sqrt-div associate-/r/ associate-/l*
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp
1×frac-times frac-2neg associate-*r/ pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 379
Calls
4 calls:
14.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0)))
233.0ms
(* (/ 1 (sqrt (/ (sqrt PI) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
1.0ms
(sqrt PI)
2.0ms
(sqrt PI)

series1.4s

Counts
4 → 8
Calls
4 calls:
734.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0)))
636.0ms
(* (/ 1 (sqrt (/ (sqrt PI) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.5s

Counts
387 → 387
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
049320516
1117719776
2333918654
done500118654

prune2.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 (sqrt (/ (expm1 (log1p (sqrt PI))) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
1.0b
(expm1 (log1p (sqrt PI)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite587.0ms

Algorithm
rewrite-expression-head
Rules
286×times-frac
254×add-sqr-sqrt
186×sqrt-prod
130×*-un-lft-identity
115×add-cube-cbrt
80×associate-*r*
53×associate-*l*
35×unswap-sqr
26×add-exp-log
16×add-cbrt-cube
8×pow1 div-exp prod-exp div-inv
4×cbrt-undiv expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 sqrt-div 1-exp associate-/r/
1×frac-times expm1-log1p associate-*r/ pow-prod-down associate-*l/ *-commutative expm1-udef
Counts
4 → 235
Calls
4 calls:
551.0ms
(* (/ 1 (sqrt (/ (expm1 (log1p (sqrt PI))) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
0.0ms
(expm1 (log1p (sqrt PI)))
3.0ms
(sqrt PI)
3.0ms
(sqrt PI)

series1.3s

Counts
4 → 6
Calls
4 calls:
1.3s
(* (/ 1 (sqrt (/ (expm1 (log1p (sqrt PI))) 1.0))) (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (/ 2.0 (/ 3.0 (pow (fabs x) 3))))) (sqrt (/ (sqrt PI) 1.0))))
0.0ms
(expm1 (log1p (sqrt PI)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.1s

Counts
241 → 241
Iterations

Useful iterations: 2 (828.0ms)

IterNodesCost
041811501
1106110528
229649640
done50009640

prune2.1s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes271.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify12.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
02867
14167
done4167

end0.0ms

sample3.7s

Algorithm
intervals
Results
3.3s14083×body80valid