Details

Time bar (total: 8.2s)

sample32.0ms

Algorithm
intervals
Results
16.0ms323×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (4.0ms)

IterNodesCost
067
1147
2236
3286
done286

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.1b

localize8.0ms

Local error

Found 1 expressions with local error:

4.8b
(* x (+ 1.0 (* y y)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt
3×pow1 add-exp-log add-cube-cbrt *-un-lft-identity associate-*r* associate-*l* add-cbrt-cube
2×associate-*r/
1×distribute-rgt-in expm1-log1p-u distribute-lft-in flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ log1p-expm1-u add-log-exp unswap-sqr
Counts
1 → 24
Calls
1 calls:
16.0ms
(* x (+ 1.0 (* y y)))

series82.0ms

Counts
1 → 3
Calls
1 calls:
81.0ms
(* x (+ 1.0 (* y y)))

simplify649.0ms

Counts
27 → 27
Iterations

Useful iterations: done (647.0ms)

IterNodesCost
052263
1165258
2820201
done5001199

prune89.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 4.9b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (fma y y 1.0)) x)
0.1b
(* (* (sqrt (fma y y 1.0)) x) (sqrt (+ 1.0 (* y y))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (fma y y 1.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
13×pow1 sqrt-prod
11×add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r*
7×associate-*l*
4×expm1-log1p-u sqrt-div pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r/ *-commutative flip-+ unswap-sqr
1×hypot-def
Counts
4 → 82
Calls
4 calls:
14.0ms
(* (sqrt (fma y y 1.0)) x)
53.0ms
(* (* (sqrt (fma y y 1.0)) x) (sqrt (+ 1.0 (* y y))))
8.0ms
(sqrt (+ 1.0 (* y y)))
3.0ms
(sqrt (fma y y 1.0))

series432.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(* (sqrt (fma y y 1.0)) x)
180.0ms
(* (* (sqrt (fma y y 1.0)) x) (sqrt (+ 1.0 (* y y))))
56.0ms
(sqrt (+ 1.0 (* y y)))
56.0ms
(sqrt (fma y y 1.0))

simplify1.1s

Counts
94 → 94
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01401186
13481077
21827939
done5000822

prune397.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0))))
4.7b
(sqrt (+ 1.0 (* y y)))
4.7b
(sqrt (fma y y 1.0))
4.7b
(sqrt (fma y y 1.0))

rewrite76.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
14×add-sqr-sqrt
12×pow1
10×add-cube-cbrt *-un-lft-identity
9×add-exp-log associate-*l* add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 pow-prod-down prod-exp cbrt-unprod
2×sqrt-div
1×flip3-+ associate-*r* *-commutative flip-+ hypot-def
Counts
4 → 74
Calls
4 calls:
59.0ms
(* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0))))
10.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (fma y y 1.0))
2.0ms
(sqrt (fma y y 1.0))

series574.0ms

Counts
4 → 12
Calls
4 calls:
357.0ms
(* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0))))
77.0ms
(sqrt (+ 1.0 (* y y)))
64.0ms
(sqrt (fma y y 1.0))
76.0ms
(sqrt (fma y y 1.0))

simplify873.0ms

Counts
86 → 86
Iterations

Useful iterations: done (869.0ms)

IterNodesCost
01431106
13441007
21435834
done5000816

prune516.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 4.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (sqrt (fma y y 1.0))) x)
4.7b
(sqrt (fma y y 1.0))
4.7b
(sqrt (fma y y 1.0))
4.7b
(sqrt (+ 1.0 (* y y)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt sqrt-prod
11×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
6×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2 associate-*r* unswap-sqr
2×sqrt-div
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ hypot-def
Counts
4 → 76
Calls
4 calls:
24.0ms
(* (sqrt (sqrt (fma y y 1.0))) x)
2.0ms
(sqrt (fma y y 1.0))
3.0ms
(sqrt (fma y y 1.0))
8.0ms
(sqrt (+ 1.0 (* y y)))

series591.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(* (sqrt (sqrt (fma y y 1.0))) x)
90.0ms
(sqrt (fma y y 1.0))
75.0ms
(sqrt (fma y y 1.0))
72.0ms
(sqrt (+ 1.0 (* y y)))

simplify1.3s

Counts
88 → 88
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0141950
1318874
21410792
done5001788

prune435.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 4.9b

regimes173.0ms

Accuracy

0% (0.2b remaining)

Error of 5.8b against oracle of 5.6b and baseline of 5.8b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
187
done87

end0.0ms

sample661.0ms

Algorithm
intervals
Results
292.0ms10557×body80valid