Details

Time bar (total: 10.5s)

sample32.0ms

Algorithm
intervals
Results
14.0ms351×body80valid

simplify16.0ms

Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
067
1147
2236
3286
done286

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.3b

localize10.0ms

Local error

Found 1 expressions with local error:

6.0b
(* x (+ 1.0 (* y y)))

rewrite23.0ms

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:
22.0ms
(* x (+ 1.0 (* y y)))

series86.0ms

Counts
1 → 3
Calls
1 calls:
85.0ms
(* x (+ 1.0 (* y y)))

simplify753.0ms

Counts
27 → 27
Iterations

Useful iterations: done (752.0ms)

IterNodesCost
052263
1165258
2820201
done5001199

prune138.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.1b

localize24.0ms

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))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (fma y y 1.0))

rewrite89.0ms

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)
61.0ms
(* (* (sqrt (fma y y 1.0)) x) (sqrt (+ 1.0 (* y y))))
8.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (fma y y 1.0))

series540.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(* (sqrt (fma y y 1.0)) x)
242.0ms
(* (* (sqrt (fma y y 1.0)) x) (sqrt (+ 1.0 (* y y))))
67.0ms
(sqrt (+ 1.0 (* y y)))
82.0ms
(sqrt (fma y y 1.0))

simplify1.3s

Counts
94 → 94
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01401186
13481077
21827939
done5000822

prune522.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0)))) (sqrt (sqrt (+ 1.0 (* y y)))))
5.9b
(sqrt (+ 1.0 (* y y)))
5.9b
(sqrt (fma y y 1.0))
5.9b
(sqrt (fma y y 1.0))

rewrite160.0ms

Algorithm
rewrite-expression-head
Rules
18×sqrt-prod
16×pow1
14×add-sqr-sqrt
13×add-exp-log add-cbrt-cube
10×add-cube-cbrt *-un-lft-identity
9×associate-*r*
6×sqrt-div pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
2×flip3-+ associate-*r/ flip-+
1×associate-*l* *-commutative hypot-def
Counts
4 → 79
Calls
4 calls:
137.0ms
(* (* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0)))) (sqrt (sqrt (+ 1.0 (* y y)))))
15.0ms
(sqrt (+ 1.0 (* y y)))
2.0ms
(sqrt (fma y y 1.0))
2.0ms
(sqrt (fma y y 1.0))

series769.0ms

Counts
4 → 12
Calls
4 calls:
547.0ms
(* (* (sqrt (sqrt (fma y y 1.0))) (* x (sqrt (fma y y 1.0)))) (sqrt (sqrt (+ 1.0 (* y y)))))
64.0ms
(sqrt (+ 1.0 (* y y)))
72.0ms
(sqrt (fma y y 1.0))
85.0ms
(sqrt (fma y y 1.0))

simplify1.7s

Counts
91 → 91
Iterations

Useful iterations: done (1.7s)

IterNodesCost
01421494
13651331
222001028
done5001793

prune555.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 6.1b

localize54.0ms

Local error

Found 4 expressions with local error:

5.9b
(sqrt (fma y y 1.0))
5.9b
(sqrt (+ 1.0 (* y y)))
6.2b
(cbrt (fma y y 1.0))
6.2b
(cbrt (fma y y 1.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3 sqrt-div
1×flip3-+ flip-+ hypot-def
Counts
4 → 59
Calls
4 calls:
2.0ms
(sqrt (fma y y 1.0))
8.0ms
(sqrt (+ 1.0 (* y y)))
1.0ms
(cbrt (fma y y 1.0))
1.0ms
(cbrt (fma y y 1.0))

series721.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(sqrt (fma y y 1.0))
64.0ms
(sqrt (+ 1.0 (* y y)))
296.0ms
(cbrt (fma y y 1.0))
282.0ms
(cbrt (fma y y 1.0))

simplify961.0ms

Counts
71 → 71
Iterations

Useful iterations: done (958.0ms)

IterNodesCost
0120784
1269721
21090652
done5001633

prune662.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 6.1b

regimes375.0ms

Accuracy

0% (0.2b remaining)

Error of 5.3b against oracle of 5.1b and baseline of 5.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01014
11314
done1314

end0.0ms

sample911.0ms

Algorithm
intervals
Results
498.0ms10768×body80valid