Details

Time bar (total: 8.1s)

sample13.0ms

Algorithm
intervals
Results
5.0ms248×body80valid
0.0ms5×body1280valid
0.0ms1×body2560valid
0.0ms2×body320valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
078
1108
2118
done118

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×*-un-lft-identity
3×fma-def add-log-exp
2×add-sqr-sqrt add-cube-cbrt
1×pow1 add-exp-log +-commutative expm1-log1p-u flip3-+ sum-log add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
Counts
1 → 17
Calls
1 calls:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))

series17.0ms

Counts
1 → 3
Calls
1 calls:
17.0ms
(+ x (/ (fabs (- y x)) 2.0))

simplify1.5s

Counts
20 → 20
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
033213
189204
2199185
3456185
41181185
53439185
done5000185

prune48.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

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

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×*-un-lft-identity
34×sqrt-prod
21×pow1
16×sqrt-div
15×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×expm1-log1p-u frac-times hypot-def log1p-expm1-u unswap-sqr
3×fma-def pow-prod-down pow-sqr
2×rem-sqrt-square times-frac associate-*r/ associate-*l/
1×+-commutative pow2 pow-plus sqrt-unprod prod-exp sum-log rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 121
Calls
4 calls:
6.0ms
(+ x (/ (fabs (- y x)) 2.0))
11.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
11.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
49.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

series133.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ x (/ (fabs (- y x)) 2.0))
49.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
47.0ms
(sqrt (+ x (/ (fabs (- y x)) 2.0)))
21.0ms
(* (sqrt (+ x (/ (fabs (- y x)) 2.0))) (sqrt (+ x (/ (fabs (- y x)) 2.0))))

simplify1.0s

Counts
133 → 133
Iterations

Useful iterations: 3 (299.0ms)

IterNodesCost
01352667
12871913
28571765
329011708
done50001708

prune271.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt x) (cbrt x))
0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
6.0ms
(* (cbrt x) (cbrt x))
0.0ms
(cbrt x)
0.0ms
(cbrt x)
1.0ms
(cbrt x)

series697.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(* (cbrt x) (cbrt x))
167.0ms
(cbrt x)
169.0ms
(cbrt x)
173.0ms
(cbrt x)

simplify3.8s

Counts
93 → 93
Iterations

Useful iterations: 4 (745.0ms)

IterNodesCost
065554
1122495
2367423
31231405
44187400
done5000400

prune262.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.1b
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
0.0ms
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

series101.0ms

Counts
1 → 3
Calls
1 calls:
101.0ms
(fma (sqrt x) (sqrt x) (/ (fabs (- y x)) 2.0))

simplify66.0ms

Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
040216
189171
2238145