Details

Time bar (total: 10.2s)

sample398.0ms

Algorithm
intervals
Results
317.0ms4008×body80valid

simplify66.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (64.0ms)

IterNodesCost
09061
140658
2226736
3500135
done500135

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)
1.2b
(pow (/ 1.0 (fabs x)) 6)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×unpow-prod-down
37×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
13×add-exp-log cube-prod
9×pow-unpow
8×pow1
7×add-cbrt-cube
6×pow-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×pow-to-exp pow-pow div-exp sqrt-prod sqr-pow
2×rem-cube-cbrt
1×cbrt-undiv cube-div cube-mult rem-sqrt-square sqrt-pow1 pow1/2 unpow3
Counts
4 → 123
Calls
4 calls:
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)
6.0ms
(pow (/ 1.0 (fabs x)) 6)

series119.0ms

Counts
4 → 10
Calls
4 calls:
36.0ms
(pow (/ 1.0 (fabs x)) 3)
33.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)
50.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify73.0ms

Counts
133 → 133
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
0545752
12496663
25001647
done5001647

prune640.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.9b
(pow (/ 1.0 (fabs x)) 4)
1.0b
(sqrt PI)

rewrite89.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
38×*-un-lft-identity
37×times-frac
36×add-cube-cbrt
26×unpow-prod-down
15×add-exp-log
13×cube-prod associate-*l*
12×add-cbrt-cube
9×pow1
6×pow-unpow
4×expm1-log1p-u associate-*r* pow-exp log1p-expm1-u div-inv add-log-exp
3×div-exp sqrt-prod
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ associate-*r/ prod-exp cbrt-unprod flip-+ rem-cube-cbrt unswap-sqr sqr-pow
1×cube-div distribute-rgt-in cube-mult rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 unpow3 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 134
Calls
4 calls:
71.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
6.0ms
(pow (/ 1.0 (fabs x)) 4)
1.0ms
(sqrt PI)

series236.0ms

Counts
4 → 10
Calls
4 calls:
170.0ms
(* (/ 1.0 (fabs x)) (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
34.0ms
(pow (/ 1.0 (fabs x)) 4)
0.0ms
(sqrt PI)

simplify107.0ms

Counts
144 → 144
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
07221344
136371199
250021192
done50021192

prune757.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.3b
(/ 1 (pow (fabs x) 6))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
66×times-frac
54×*-un-lft-identity
51×add-cube-cbrt
36×add-exp-log unpow-prod-down
25×associate-*r*
14×add-cbrt-cube
13×cube-prod div-exp
10×prod-exp sqr-pow
8×pow1 pow-exp
7×pow-to-exp associate-/r* unswap-sqr
6×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv pow-unpow associate-*l* sqrt-prod associate-/l*
2×cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-flip pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 178
Calls
4 calls:
22.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
8.0ms
(/ 1 (pow (fabs x) 6))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series127.0ms

Counts
4 → 10
Calls
4 calls:
41.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
48.0ms
(/ 1 (pow (fabs x) 6))
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify75.0ms

Counts
188 → 188
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07101089
13321875
25001849
done5001849

prune767.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 6))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 4)))
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
67×add-sqr-sqrt
66×times-frac
54×*-un-lft-identity
51×add-cube-cbrt
36×add-exp-log unpow-prod-down
25×associate-*r*
14×add-cbrt-cube
13×cube-prod div-exp
10×prod-exp sqr-pow
8×pow1 pow-exp
7×pow-to-exp associate-/r* unswap-sqr
6×rec-exp 1-exp
4×expm1-log1p-u log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv pow-unpow associate-*l* sqrt-prod associate-/l*
2×cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult rem-sqrt-square pow-flip pow-pow frac-2neg sqrt-pow1 pow1/2 unpow3 associate-*r/ pow-prod-down clear-num un-div-inv *-commutative inv-pow
Counts
4 → 178
Calls
4 calls:
8.0ms
(/ 1 (pow (fabs x) 6))
22.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
6.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series128.0ms

Counts
4 → 10
Calls
4 calls:
53.0ms
(/ 1 (pow (fabs x) 6))
38.0ms
(* 0.75 (/ 1 (pow (fabs x) 4)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify76.0ms

Counts
188 → 188
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07081088
13308875
25002849
done5002849

prune692.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.1b

regimes330.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04132
14132
done4132

end0.0ms

sample5.2s

Algorithm
intervals
Results
4.3s55664×body80valid