Details

Time bar (total: 12.0s)

sample16.0ms

Algorithm
intervals
Results
7.0ms242×body80valid
1.0ms6×body640valid
0.0ms3×body2560valid
0.0ms3×body1280valid
0.0ms2×body320valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
1108
2118
done118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(+ x (/ (fabs (- y x)) 2.0))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
3×*-un-lft-identity add-log-exp
1×pow1 add-exp-log +-commutative add-sqr-sqrt add-cube-cbrt flip3-+ sum-log add-cbrt-cube flip-+ distribute-lft-out
Counts
1 → 12
Calls
1 calls:
10.0ms
(+ x (/ (fabs (- y x)) 2.0))

series29.0ms

Counts
1 → 3
Calls
1 calls:
29.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify3.1s

Counts
15 → 15
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
031195
184187
2209171
3459171
41200171
52875171
done5001171

prune76.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
0.5b
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite143.0ms

Algorithm
rewrite-expression-head
Rules
36×cbrt-prod
35×*-un-lft-identity
23×add-sqr-sqrt
18×cbrt-div
15×add-cube-cbrt
11×pow1
9×flip3-+ pow1/3 swap-sqr flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 95
Calls
4 calls:
10.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
9.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
108.0ms
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))

series839.0ms

Counts
4 → 12
Calls
4 calls:
537.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
107.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
85.0ms
(cbrt (+ x (/ (fabs (- y x)) 2.0)))
110.0ms
(* (cbrt (+ x (/ (fabs (- y x)) 2.0))) (cbrt (+ x (/ (fabs (- y x)) 2.0))))

simplify2.1s

Counts
107 → 107
Iterations

Useful iterations: done (2.1s)

IterNodesCost
01602656
13672458
29402303
326232056
done50001984

prune404.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ x (/ (fabs (- y x)) 2.0))
0.1b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.1b
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
0.4b
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
34×*-un-lft-identity sqrt-prod
28×add-sqr-sqrt
21×pow1
16×sqrt-div
14×add-cube-cbrt
11×swap-sqr
10×sqrt-pow1 pow1/2
9×flip3-+ flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log add-cbrt-cube add-log-exp
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 106
Calls
4 calls:
21.0ms
(+ x (/ (fabs (- y x)) 2.0))
34.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
21.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
118.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ x (/ (fabs (- y x)) 2.0))
57.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
67.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
34.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.8s

Counts
118 → 118
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01292569
12681841
27461711
323141658
done50001574

prune390.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.1b
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
0.3b
(* (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
0.6b
(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

rewrite368.0ms

Algorithm
rewrite-expression-head
Rules
121×sqrt-prod
74×add-sqr-sqrt
39×*-un-lft-identity
36×sqrt-div
29×unpow-prod-down cube-prod
26×associate-*l*
25×add-cube-cbrt
24×unswap-sqr
12×pow1 sqrt-pow1
10×add-exp-log associate-*r*
9×flip3-+ flip-+
8×cube-div
7×add-cbrt-cube distribute-lft-out
6×pow1/2
5×pow-pow sqr-pow
4×frac-times rem-sqrt-square add-log-exp
3×pow-unpow prod-exp
2×cube-mult pow-to-exp unpow3 associate-*r/ associate-*l/ pow-exp
1×pow-plus *-commutative pow-prod-up sqrt-pow2 cbrt-unprod rem-cube-cbrt
Counts
4 → 170
Calls
4 calls:
38.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
33.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
247.0ms
(* (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
36.0ms
(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

series327.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
81.0ms
(sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0))))
32.0ms
(* (pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3) (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))))
133.0ms
(pow (sqrt (sqrt (+ x (/ (fabs (- y x)) 2.0)))) 3)

simplify1.4s

Counts
182 → 182
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02294891
15863610
219303335
done50013163

prune580.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes2.0ms