Details

Time bar (total: 12.7s)

sample299.0ms

Algorithm
intervals
Results
245.0ms3272×body80valid

simplify883.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (177.0ms)

IterNodesCost
031103
190103
236466
3180354
done500054

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)
1.3b
(pow (/ 1.0 (fabs x)) 6)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
69×add-sqr-sqrt
67×times-frac
56×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down
22×add-exp-log
19×add-cbrt-cube
14×pow1
13×cube-prod swap-sqr associate-*r* associate-*l*
7×div-inv
6×pow-unpow div-exp
5×cbrt-undiv
4×pow-exp prod-exp cbrt-unprod add-log-exp unswap-sqr
3×sqrt-prod
2×pow-to-exp pow-pow rem-cube-cbrt sqr-pow
1×cube-div pow2 cube-mult frac-times rem-sqrt-square sqrt-pow1 pow-plus pow1/2 unpow3 associate-*r/ pow-prod-down associate-*l/ pow-sqr *-commutative pow-prod-up
Counts
4 → 154
Calls
4 calls:
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)
4.0ms
(pow (/ 1.0 (fabs x)) 6)

series108.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)
53.0ms
(pow (/ 1.0 (fabs x)) 6)

simplify1.5s

Counts
164 → 164
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02302063
16701701
232501503
done50001483

prune662.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) 1) (/ 1.0 (fabs x)))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
74×add-sqr-sqrt
68×times-frac
56×add-cube-cbrt *-un-lft-identity
26×associate-*r*
24×add-exp-log add-cbrt-cube
16×associate-*l*
15×pow1
13×unpow-prod-down cube-prod swap-sqr
7×div-inv
6×cbrt-undiv div-exp prod-exp cbrt-unprod unswap-sqr
4×add-log-exp
3×frac-times pow-unpow associate-*l/ sqrt-prod
2×flip3-+ associate-*r/ pow-prod-down pow-exp *-commutative flip-+ rem-cube-cbrt
1×cube-div pow2 cube-mult pow-to-exp rem-sqrt-square pow-pow sqrt-pow1 pow-plus pow1/2 unpow3 pow-sqr pow-prod-up sqr-pow
Counts
4 → 162
Calls
4 calls:
31.0ms
(* (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) 1) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series164.0ms

Counts
4 → 10
Calls
4 calls:
103.0ms
(* (+ (* (/ 15.0 8.0) (/ 1.0 (pow (fabs x) 6))) 1) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.9s

Counts
172 → 172
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02302598
17062250
235001952
done50011931

prune790.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) 1) 1.0) (fabs x)) (* (pow (/ 1.0 (fabs x)) 3) (+ (* (/ 3.0 4.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (/ 1.0 2.0)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
0.6b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.8b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
84×add-sqr-sqrt
71×add-cube-cbrt *-un-lft-identity
33×frac-add
28×add-cbrt-cube
27×add-exp-log
21×associate-/l/
20×frac-times associate-*r/
15×sqrt-prod
13×pow1 unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
11×cube-div div-inv
10×cbrt-undiv div-exp associate-/r*
8×associate-*l/
5×prod-exp cbrt-unprod
4×add-log-exp unswap-sqr
3×pow-unpow flip3-+ flip-+ associate-/l*
2×pow-exp rem-cube-cbrt
1×pow2 cube-mult pow-to-exp rem-sqrt-square pow-pow frac-2neg sqrt-pow1 pow-plus pow1/2 unpow3 pow-prod-down clear-num associate-/r/ pow-sqr *-commutative pow-prod-up sqr-pow
Counts
4 → 207
Calls
4 calls:
88.0ms
(/ (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) 1) 1.0) (fabs x)) (* (pow (/ 1.0 (fabs x)) 3) (+ (* (/ 3.0 4.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (/ 1.0 2.0)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
14.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series507.0ms

Counts
4 → 10
Calls
4 calls:
446.0ms
(/ (+ (/ (* (+ (/ 1.875 (pow (fabs x) 6)) 1) 1.0) (fabs x)) (* (pow (/ 1.0 (fabs x)) 3) (+ (* (/ 3.0 4.0) (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))) (/ 1.0 2.0)))) (/ (sqrt PI) (* 1.0 (exp (* (fabs x) (fabs x))))))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
37.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify503.0ms

Counts
217 → 217
Iterations

Useful iterations: done (492.0ms)

IterNodesCost
03767408
111636886
done50006450

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow (fabs x) 7))
0.3b
(/ 1 (pow (fabs x) 5))
0.3b
(* (+ (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x)))) (sqrt (/ 1 PI)))
0.3b
(* 0.75 (/ 1 (pow (fabs x) 5)))

rewrite259.0ms

Algorithm
rewrite-expression-head
Rules
104×frac-add
84×add-sqr-sqrt
80×times-frac
66×*-un-lft-identity
60×add-cube-cbrt
46×associate-*r/
45×un-div-inv
44×add-exp-log
41×associate-*r*
35×unpow-prod-down
27×sqrt-div
26×frac-times associate-*l/
22×flip3-+ flip-+
18×div-exp
16×sqrt-prod
15×add-cbrt-cube
14×associate-/r*
13×sqr-pow
11×prod-exp unswap-sqr
9×pow-to-exp rec-exp 1-exp pow-exp
8×pow1
7×associate-*l*
6×associate-/l*
4×div-inv add-log-exp
3×cbrt-undiv cbrt-unprod
2×pow-flip frac-2neg pow-prod-down clear-num *-commutative inv-pow
1×distribute-lft-out
Counts
4 → 252
Calls
4 calls:
4.0ms
(/ 1 (pow (fabs x) 7))
4.0ms
(/ 1 (pow (fabs x) 5))
224.0ms
(* (+ (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x)))) (sqrt (/ 1 PI)))
14.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))

series510.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(/ 1 (pow (fabs x) 7))
55.0ms
(/ 1 (pow (fabs x) 5))
329.0ms
(* (+ (+ (* 0.5 (/ 1 (pow (fabs x) 3))) (* 0.75 (/ 1 (pow (fabs x) 5)))) (+ (* 1.875 (/ 1 (pow (fabs x) 7))) (/ 1.0 (fabs x)))) (sqrt (/ 1 PI)))
57.0ms
(* 0.75 (/ 1 (pow (fabs x) 5)))

simplify1.4s

Counts
264 → 264
Iterations

Useful iterations: done (1.4s)

IterNodesCost
04588744
111926977
236906653
done50016577

prune923.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes157.0ms

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03039
13839
done3839

end0.0ms

sample660.0ms

Algorithm
intervals
Results
562.0ms7530×body80valid