Details

Time bar (total: 14.3s)

sample16.0ms

Algorithm
intervals
Results
8.0ms293×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

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite12.0ms

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 expm1-log1p-u frac-2neg div-exp clear-num log1p-expm1-u div-inv add-log-exp
Counts
1 → 29
Calls
1 calls:
10.0ms
(/ (fabs (- x y)) (fabs y))

series18.0ms

Counts
1 → 3
Calls
1 calls:
18.0ms
(/ (fabs (- x y)) (fabs y))

simplify3.2s

Counts
32 → 32
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
054385
188376
2178348
3328348
4549348
5864348
62003348
done5000348

prune115.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize19.0ms

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))))

rewrite79.0ms

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×expm1-log1p-u rem-sqrt-square log1p-expm1-u 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 → 172
Calls
4 calls:
5.0ms
(/ (fabs (- x y)) (fabs y))
9.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
9.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
44.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(/ (fabs (- x y)) (fabs y))
23.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
29.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
10.0ms
(* (sqrt (/ (fabs (- x y)) (fabs y))) (sqrt (/ (fabs (- x y)) (fabs y))))

simplify2.7s

Counts
184 → 184
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01603295
12372465
27422303
326922255
done50002215

prune702.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize13.0ms

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

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
42×sqrt-prod
36×times-frac
33×add-cube-cbrt *-un-lft-identity
16×associate-*r*
13×add-exp-log add-cbrt-cube
9×pow1 associate-/r*
6×associate-*l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u 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-*r/ prod-exp clear-num cbrt-unprod
1×sqrt-undiv *-commutative associate-/l/
Counts
4 → 132
Calls
4 calls:
5.0ms
(/ (fabs (- x y)) (fabs y))
12.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
22.0ms
(* (sqrt (fabs (- x y))) (sqrt (/ (fabs (- x y)) (fabs y))))
18.0ms
(/ (* (sqrt (fabs (- x y))) (sqrt (/ (fabs (- x y)) (fabs y)))) (sqrt (fabs y)))

series83.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(/ (fabs (- x y)) (fabs y))
27.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
36.0ms
(* (sqrt (fabs (- x y))) (sqrt (/ (fabs (- x y)) (fabs y))))
11.0ms
(/ (* (sqrt (fabs (- x y))) (sqrt (/ (fabs (- x y)) (fabs y)))) (sqrt (fabs y)))

simplify3.8s

Counts
144 → 144
Iterations

Useful iterations: 3 (1.9s)

IterNodesCost
01642391
12882211
29482059
342622048
done50012048

prune626.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

localize35.0ms

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

rewrite158.0ms

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-*r*
40×unswap-sqr
19×associate-*l*
12×sqrt-div
10×pow1 add-exp-log
7×add-cbrt-cube div-inv
6×sqrt-pow1 sqr-pow
5×pow-pow
4×expm1-log1p-u rem-sqrt-square pow1/2 log1p-expm1-u add-log-exp
3×cube-div pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 pow-exp
1×frac-times associate-*r/ associate-*l/ *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 238
Calls
4 calls:
8.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
8.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
95.0ms
(* (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) (pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3))
21.0ms
(pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3)

series213.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
21.0ms
(sqrt (/ (fabs (- x y)) (fabs y)))
17.0ms
(* (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) (pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3))
135.0ms
(pow (sqrt (sqrt (/ (fabs (- x y)) (fabs y)))) 3)

simplify1.5s

Counts
250 → 250
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02165890
14785373
217104354
done50004268

prune883.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 0b

regimes2.0ms