Details

Time bar (total: 19.6s)

sample334.0ms

Algorithm
intervals
Results
275.0ms3513×body80valid

simplify720.0ms

Counts
1 → 1
Iterations

Useful iterations: 3 (148.0ms)

IterNodesCost
031103
190103
238365
3198351
done500151

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.5b
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0b
(sqrt PI)

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
126×add-sqr-sqrt
120×times-frac
89×add-cube-cbrt *-un-lft-identity
40×add-exp-log add-cbrt-cube
39×swap-sqr associate-*r* associate-*l*
26×pow1
12×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow2 frac-times pow-plus associate-*r/ pow-prod-down associate-*l/ sqrt-prod pow-sqr *-commutative pow-prod-up
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 222
Calls
4 calls:
17.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
13.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
1.0ms
(sqrt PI)

series69.0ms

Counts
4 → 10
Calls
4 calls:
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
23.0ms
(* (/ 1.0 (fabs x)) (/ 1.0 (fabs x)))
0.0ms
(sqrt PI)

simplify1.2s

Counts
232 → 232
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01503287
14272964
219962446
done50002437

prune1.1s

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
52×times-frac
44×unpow-prod-down
43×add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
38×cube-prod
24×add-exp-log
16×add-cbrt-cube
13×pow-exp
9×pow-unpow
8×pow1 div-exp
7×rem-cube-cbrt
6×div-inv
5×pow-to-exp sqr-pow
4×cbrt-undiv expm1-log1p-u log1p-expm1-u add-log-exp
3×cube-div cube-mult pow-pow unpow3 prod-exp sqrt-prod
2×unpow2
1×rem-sqrt-square sqrt-pow1 pow1/2 cbrt-unprod
Counts
4 → 163
Calls
4 calls:
7.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series129.0ms

Counts
4 → 10
Calls
4 calls:
57.0ms
(pow (/ (* 1.0 1.0) (pow (fabs x) 2)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
39.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.7s

Counts
173 → 173
Iterations

Useful iterations: 2 (236.0ms)

IterNodesCost
01932107
15831869
228111505
done50011505

prune684.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 0.3b

localize34.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (* (pow 1.0 6) (/ 1 (pow (fabs x) 6))) (/ 15.0 8.0))))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
129×associate-*r/
115×frac-times
70×frac-add
59×associate-*l/
49×add-sqr-sqrt
46×times-frac
43×add-cube-cbrt *-un-lft-identity
42×cube-div
28×un-div-inv
26×unpow-prod-down cube-prod
15×add-exp-log add-cbrt-cube
13×associate-*l*
9×pow1
6×pow-unpow
5×div-inv
4×expm1-log1p-u pow-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×cbrt-undiv div-exp associate-*r* sqrt-prod
2×cube-mult pow-to-exp pow-pow flip3-+ unpow3 prod-exp cbrt-unprod flip-+ unswap-sqr sqr-pow
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down *-commutative
Counts
4 → 221
Calls
4 calls:
112.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (* (pow 1.0 6) (/ 1 (pow (fabs x) 6))) (/ 15.0 8.0))))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series232.0ms

Counts
4 → 10
Calls
4 calls:
168.0ms
(* (/ 1.0 (fabs x)) (+ (* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) (/ 1.0 (fabs x)))) (* (* (pow 1.0 6) (/ 1 (pow (fabs x) 6))) (/ 15.0 8.0))))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
32.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify553.0ms

Counts
231 → 231
Iterations

Useful iterations: done (545.0ms)

IterNodesCost
04216123
117445132
done50015103

prune1.2s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 0.2b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) 1.0))
0.7b
(pow (/ 1.0 (fabs x)) 3)
0.7b
(pow (/ 1.0 (fabs x)) 3)
1.0b
(sqrt PI)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
43×add-exp-log add-sqr-sqrt
42×add-cube-cbrt *-un-lft-identity
26×unpow-prod-down cube-prod
22×add-cbrt-cube
18×prod-exp
13×associate-*l*
9×pow1 div-exp
8×pow-exp
6×pow-unpow cbrt-unprod
5×div-inv
4×cbrt-undiv cube-div expm1-log1p-u pow-to-exp log1p-expm1-u add-log-exp rem-cube-cbrt
3×associate-*l/ sqrt-prod
2×cube-mult pow-pow unpow3 sqr-pow
1×frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ associate-*r* pow-prod-down *-commutative
Counts
4 → 153
Calls
4 calls:
23.0ms
(* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) 1.0))
4.0ms
(pow (/ 1.0 (fabs x)) 3)
4.0ms
(pow (/ 1.0 (fabs x)) 3)
1.0ms
(sqrt PI)

series152.0ms

Counts
4 → 10
Calls
4 calls:
82.0ms
(* (/ 3.0 4.0) (* (pow (/ 1.0 (fabs x)) 3) 1.0))
32.0ms
(pow (/ 1.0 (fabs x)) 3)
38.0ms
(pow (/ 1.0 (fabs x)) 3)
0.0ms
(sqrt PI)

simplify1.1s

Counts
163 → 163
Iterations

Useful iterations: 2 (212.0ms)

IterNodesCost
02022021
15861825
224621577
done50011577

prune716.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 0.2b

regimes229.0ms

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03668
14668
done4668

end0.0ms

sample9.2s

Algorithm
intervals
Results
7.9s103451×body80valid