Details

Time bar (total: 16.8s)

sample69.0ms

Algorithm
intervals
Results
17.0ms482×body80nan
16.0ms218×body160nan
12.0ms256×body80valid

simplify10.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
079
1119
2129
done129

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(log (+ x (sqrt (- (* x x) 1.0))))
0.0b
(- (* x x) 1.0)
30.6b
(sqrt (- (* x x) 1.0))

rewrite112.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod sqrt-prod
3×expm1-log1p-u prod-diff add-cbrt-cube log1p-expm1-u
2×log-div flip3-- sqrt-div flip-- difference-of-squares
1×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 fma-neg diff-log rem-log-exp log-pow flip-+ distribute-lft-out
Counts
3 → 54
Calls
3 calls:
36.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
19.0ms
(- (* x x) 1.0)
55.0ms
(sqrt (- (* x x) 1.0))

series401.0ms

Counts
3 → 9
Calls
3 calls:
259.0ms
(log (+ x (sqrt (- (* x x) 1.0))))
43.0ms
(- (* x x) 1.0)
99.0ms
(sqrt (- (* x x) 1.0))

simplify902.0ms

Counts
63 → 63
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
0155803
1355704
21490638
done5001599

prune246.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x (sqrt 1.0)))
0.0b
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.5b
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite124.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
20×sqrt-prod
15×*-un-lft-identity
14×sqrt-div
9×pow1 add-cube-cbrt associate-*r*
7×associate-*l*
6×add-exp-log
5×flip3-+ add-cbrt-cube flip-+
4×frac-times unswap-sqr
3×expm1-log1p-u log-prod flip3-- sqrt-pow1 pow1/2 pow-prod-down flip-- log1p-expm1-u add-log-exp
2×log-div associate-*r/ associate-*l/ hypot-def distribute-lft-out difference-of-squares
1×rem-sqrt-square sqrt-unprod rem-log-exp prod-exp log-pow *-commutative cbrt-unprod distribute-lft-out--
Counts
3 → 80
Calls
3 calls:
19.0ms
(sqrt (+ x (sqrt 1.0)))
6.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
94.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series728.0ms

Counts
3 → 9
Calls
3 calls:
85.0ms
(sqrt (+ x (sqrt 1.0)))
399.0ms
(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
243.0ms
(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify1.1s

Counts
89 → 89
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02071595
14811377
217381268
done50001254

prune358.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.0b
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity 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 fma-udef
Counts
4 → 50
Calls
4 calls:
2.0ms
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
2.0ms
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)

series1.8s

Counts
4 → 12
Calls
4 calls:
561.0ms
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
636.0ms
(sqrt (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
318.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
323.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)

simplify1.0s

Counts
62 → 62
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01471572
13781464
214821354
done50001308

prune286.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.1b
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
0.5b
(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
0.7b
(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
14×cbrt-prod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
10×pow1
8×unpow-prod-down cube-prod
6×add-exp-log
5×log-pow add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow log-prod
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 rem-log-exp pow-exp rem-cbrt-cube fma-udef rem-cube-cbrt
Counts
4 → 76
Calls
4 calls:
2.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
0.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
3.0ms
(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
3.0ms
(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

series2.5s

Counts
4 → 12
Calls
4 calls:
582.0ms
(log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x))
293.0ms
(fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)
525.0ms
(cbrt (pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3))
1.1s
(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)

simplify2.8s

Counts
88 → 88
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02952775
19252516
248462230
done50002227

prune459.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes18.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01129
11229
done1229

end0.0ms

sample3.7s

Algorithm
intervals
Results
1.1s8000×body80valid
985.0ms16242×body80nan
834.0ms7633×body160nan