Details

Time bar (total: 13.6s)

sample49.0ms

Algorithm
intervals
Results
33.0ms472×body80valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 4 (717.0ms)

IterNodesCost
02867
17066
224247
394135
4324434
done500034

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize29.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
34×associate-*l*
33×times-frac
29×add-cube-cbrt *-un-lft-identity
22×add-exp-log
16×associate-*r*
14×add-cbrt-cube
13×sqrt-prod
11×unswap-sqr
8×prod-exp
7×pow1
5×unpow-prod-down cube-prod
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u add-log-exp
3×fma-udef sqr-pow
2×cbrt-undiv pow-to-exp pow-exp *-commutative div-inv
1×distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down associate-*l/
Counts
4 → 123
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
13.0ms
(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
13.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)

series562.0ms

Counts
4 → 10
Calls
4 calls:
195.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
318.0ms
(* (/ 1.0 (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
48.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)

simplify895.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (297.0ms)

IterNodesCost
02133168
15053074
219922788
done50002788

prune638.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
53×times-frac
52×associate-*l*
41×add-cube-cbrt *-un-lft-identity
23×sqrt-prod
22×add-exp-log
20×cbrt-prod
16×associate-*r*
13×add-cbrt-cube unswap-sqr
8×prod-exp
7×pow1
5×unpow-prod-down cube-prod
4×expm1-log1p-u div-exp cbrt-unprod log1p-expm1-u add-log-exp
3×fma-udef sqr-pow
2×cbrt-undiv pow-to-exp pow-exp *-commutative div-inv
1×distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down associate-*l/
Counts
4 → 143
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
18.0ms
(* (/ (cbrt 1.0) (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
12.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
1.0ms
(sqrt PI)

series579.0ms

Counts
4 → 10
Calls
4 calls:
201.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
325.0ms
(* (/ (cbrt 1.0) (sqrt PI)) (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))))
52.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
0.0ms
(sqrt PI)

simplify874.0ms

Counts
153 → 153
Iterations

Useful iterations: 2 (285.0ms)

IterNodesCost
02224004
15203910
220133626
done50003626

prune847.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
49×add-sqr-sqrt
31×times-frac
30×add-cube-cbrt *-un-lft-identity
19×add-exp-log
15×sqrt-prod
13×associate-*r*
12×associate-*l*
11×add-cbrt-cube
8×unswap-sqr
6×prod-exp associate-/r*
5×pow1 unpow-prod-down cube-prod
4×expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×associate-/l* sqr-pow
2×cbrt-undiv pow-to-exp pow-exp cbrt-unprod div-inv
1×cube-mult rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ clear-num *-commutative fma-udef
Counts
4 → 118
Calls
4 calls:
0.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
12.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
3.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt PI))
4.0ms
(sqrt PI)

series519.0ms

Counts
4 → 10
Calls
4 calls:
199.0ms
(fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0))))
46.0ms
(* (pow (fabs x) 3) (/ 2.0 3.0))
273.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt PI))
0.0ms
(sqrt PI)

simplify815.0ms

Counts
128 → 128
Iterations

Useful iterations: 2 (222.0ms)

IterNodesCost
02003351
14313235
215633019
done50003019

prune679.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize38.0ms

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) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI)))
0.4b
(/ (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI))) (sqrt (sqrt PI)))
1.0b
(sqrt PI)
1.0b
(sqrt PI)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
600×sqrt-prod
576×times-frac
316×add-sqr-sqrt
314×add-cube-cbrt *-un-lft-identity
34×associate-/l*
18×associate-/r*
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 419
Calls
4 calls:
4.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI)))
17.0ms
(/ (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI))) (sqrt (sqrt PI)))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series892.0ms

Counts
4 → 8
Calls
4 calls:
424.0ms
(/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI)))
467.0ms
(/ (/ (fma (pow (fabs x) 7) (/ 1.0 21.0) (fma (fabs x) (fma (pow (fabs x) 4) (/ 1.0 5.0) 2.0) (* (pow (fabs x) 3) (/ 2.0 3.0)))) (sqrt (sqrt PI))) (sqrt (sqrt PI)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify1.7s

Counts
427 → 427
Iterations

Useful iterations: done (1.6s)

IterNodesCost
041927165
192626165
2211525199
done500025085

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes74.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 1 (1.0ms)

IterNodesCost
03043
13541
done3541

end0.0ms

sample1.2s

Algorithm
intervals
Results
1.0s14200×body80valid