Details

Time bar (total: 14.7s)

sample53.0ms

Algorithm
intervals
Results
36.0ms425×body80valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
02867
17066
225047
3102835
4400134
done500034

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
52×pow1
35×add-exp-log add-cbrt-cube
18×prod-exp cbrt-unprod
17×add-sqr-sqrt
15×associate-*l*
14×add-cube-cbrt *-un-lft-identity
12×pow-plus pow-prod-down pow-prod-up
9×times-frac
7×associate-*r*
4×pow2 expm1-log1p-u pow-sqr log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp sqrt-prod *-commutative
2×pow3 unswap-sqr
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-*l/ div-inv
Counts
4 → 115
Calls
4 calls:
20.0ms
(* (* (fabs x) (fabs x)) (fabs x))
18.0ms
(* (* (fabs x) (fabs x)) (fabs x))
58.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms
(sqrt PI)

series97.0ms

Counts
4 → 10
Calls
4 calls:
25.0ms
(* (* (fabs x) (fabs x)) (fabs x))
29.0ms
(* (* (fabs x) (fabs x)) (fabs x))
42.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify928.0ms

Counts
125 → 125
Iterations

Useful iterations: done (925.0ms)

IterNodesCost
01361427
1308931
21095740
done5001736

prune384.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
78×pow1
46×pow-prod-up
39×add-exp-log add-cbrt-cube
21×sqrt-pow1 pow1/2 prod-exp cbrt-unprod
19×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
15×associate-*l* pow-prod-down
13×associate-*r*
10×sqrt-prod
9×times-frac
6×pow2 pow-plus pow-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp *-commutative
2×unswap-sqr
1×rem-sqrt-square associate-*l/ div-inv
Counts
4 → 130
Calls
4 calls:
67.0ms
(* (* (* (fabs x) (fabs x)) (sqrt (fabs x))) (sqrt (fabs x)))
57.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
23.0ms
(* (* (fabs x) (fabs x)) (sqrt (fabs x)))
1.0ms
(sqrt PI)

series122.0ms

Counts
4 → 10
Calls
4 calls:
26.0ms
(* (* (* (fabs x) (fabs x)) (sqrt (fabs x))) (sqrt (fabs x)))
42.0ms
(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
55.0ms
(* (* (fabs x) (fabs x)) (sqrt (fabs x)))
0.0ms
(sqrt PI)

simplify1.2s

Counts
140 → 140
Iterations

Useful iterations: 2 (216.0ms)

IterNodesCost
01761784
14021112
21490883
done5000883

prune461.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 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))
0.4b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite58.0ms

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))
11.0ms
(/ (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))
18.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)

series367.0ms

Counts
4 → 10
Calls
4 calls:
37.0ms
(/ 3.0 (pow (fabs x) 3))
283.0ms
(/ (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))
47.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify1.7s

Counts
382 → 382
Iterations

Useful iterations: 2 (859.0ms)

IterNodesCost
054410863
110739979
237939589
done50009589

prune1.4s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (/ (/ (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)))))))
0.3b
(/ (/ (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))))))
0.4b
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0b
(sqrt PI)

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
1092×times-frac
529×add-sqr-sqrt
528×add-cube-cbrt *-un-lft-identity
147×sqrt-prod
113×associate-/r*
40×add-exp-log
36×unpow-prod-down cube-prod
28×associate-/l*
27×div-inv
25×div-exp
23×add-cbrt-cube
12×cbrt-undiv cube-mult unpow3 sqr-pow
6×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rec-exp frac-2neg 1-exp clear-num
2×associate-/r/
1×pow-to-exp rem-sqrt-square pow-flip sqrt-pow1 pow1/2 pow-exp associate-/l/ inv-pow
Counts
4 → 615
Calls
4 calls:
25.0ms
(/ 1 (/ (/ (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)))))))
14.0ms
(/ (/ (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))))))
19.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
1.0ms
(sqrt PI)

series654.0ms

Counts
4 → 10
Calls
4 calls:
292.0ms
(/ 1 (/ (/ (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)))))))
312.0ms
(/ (/ (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))))))
50.0ms
(/ 2.0 (/ 3.0 (pow (fabs x) 3)))
0.0ms
(sqrt PI)

simplify1.2s

Counts
625 → 625
Iterations

Useful iterations: done (1.1s)

IterNodesCost
088330489
1190728646
done500027250

prune2.0s

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

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02867
14167
done4167

end0.0ms

sample1.3s

Algorithm
intervals
Results
1.0s13876×body80valid