Details

Time bar (total: 14.8s)

sample20.0ms

Algorithm
intervals
Results
10.0ms293×body80valid

simplify3.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
297
done97

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ (fabs (- x y)) (fabs y))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt add-cube-cbrt *-un-lft-identity times-frac
3×add-exp-log associate-/r* add-cbrt-cube associate-/l*
1×pow1 cbrt-undiv frac-2neg div-exp clear-num div-inv add-log-exp
Counts
1 → 27
Calls
1 calls:
5.0ms
(/ (fabs (- x y)) (fabs y))

series21.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(/ (fabs (- x y)) (fabs y))

simplify3.3s

Counts
30 → 30
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
052369
186360
2179332
3330332
4551332
5867332
62008332
done5000332

prune134.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fabs (- x y)) (fabs y))
0.1b
(sqrt (/ (fabs (- x y)) (fabs y)))
0.1b
(sqrt (/ (fabs (- x y)) (fabs y)))
0.2b
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
92×add-sqr-sqrt sqrt-prod
71×times-frac
58×add-cube-cbrt *-un-lft-identity
21×pow1
18×swap-sqr
16×associate-*r* associate-*l*
10×sqrt-pow1 pow1/2
9×unswap-sqr
8×add-exp-log add-cbrt-cube
7×div-inv
6×sqrt-div
5×pow-prod-up
4×rem-sqrt-square add-log-exp
3×pow-prod-down associate-/r* pow-sqr associate-/l*
1×cbrt-undiv pow2 frac-times frac-2neg pow-plus sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 164
Calls
4 calls:
9.0ms
(/ (fabs (- x y)) (fabs y))
8.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
4.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
44.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))))

series86.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(/ (fabs (- x y)) (fabs y))
32.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
24.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
17.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))))

simplify2.4s

Counts
176 → 176
Iterations

Useful iterations: done (2.4s)

IterNodesCost
01543207
12312397
27412235
327052187
done50012147

prune737.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (fabs (- x y)) (fabs y))
0.1b
(sqrt (/ (fabs (- x y)) (fabs y)))
0.1b
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y))))
0.2b
(/ (* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y)))) (sqrt (fabs y)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
42×sqrt-prod
36×times-frac
33×add-cube-cbrt *-un-lft-identity
16×associate-*l*
13×add-exp-log add-cbrt-cube
9×pow1 associate-/r*
6×associate-*r* unswap-sqr
4×div-inv associate-/l* add-log-exp
3×cbrt-undiv sqrt-pow1 pow1/2 sqrt-div div-exp pow-prod-down
2×rem-sqrt-square frac-2neg sqrt-unprod associate-*l/ prod-exp clear-num cbrt-unprod
1×sqrt-undiv *-commutative associate-/l/
Counts
4 → 124
Calls
4 calls:
5.0ms
(/ (fabs (- x y)) (fabs y))
4.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
40.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y))))
36.0ms
(/ (* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y)))) (sqrt (fabs y)))

series90.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ (fabs (- x y)) (fabs y))
32.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
29.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y))))
20.0ms
(/ (* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (fabs (- x y)))) (sqrt (fabs y)))

simplify3.8s

Counts
136 → 136
Iterations

Useful iterations: 3 (1.8s)

IterNodesCost
01572268
12812101
28841971
341931960
done50001960

prune657.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (fabs (- x y)) (fabs y)))
0.1b
(sqrt (/ (fabs (- x y)) (fabs y)))
0.2b
(* (pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3) (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))))
0.3b
(pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3)

rewrite126.0ms

Algorithm
rewrite-expression-head
Rules
261×sqrt-prod
165×add-sqr-sqrt
83×times-frac
65×add-cube-cbrt *-un-lft-identity
54×unpow-prod-down cube-prod
44×associate-*l*
40×unswap-sqr
19×associate-*r*
12×sqrt-div
10×pow1 add-exp-log
7×add-cbrt-cube div-inv
6×sqrt-pow1 sqr-pow
5×pow-pow
4×rem-sqrt-square pow1/2 add-log-exp
3×cube-div pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 pow-exp
1×frac-times pow-plus associate-*r/ associate-*l/ *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 231
Calls
4 calls:
4.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
4.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
87.0ms
(* (pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3) (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))))
10.0ms
(pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3)

series218.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
38.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
20.0ms
(* (pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3) (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))))
117.0ms
(pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3)

simplify1.9s

Counts
243 → 243
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02085759
14814644
217374252
done50014178

prune1.0s

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes3.0ms