Details

Time bar (total: 5.4s)

sample31.0ms

Algorithm
intervals
Results
8.0ms256×body80valid
7.0ms230×body80nan

simplify9.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
056
176
2116
3136
done136

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(sqrt (- 1.0 (* x x)))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt sqrt-prod
2×pow1 add-cube-cbrt *-un-lft-identity sqrt-div
1×add-exp-log expm1-log1p-u rem-sqrt-square flip3-- sqrt-pow1 pow1/2 add-cbrt-cube flip-- log1p-expm1-u add-log-exp difference-of-squares
Counts
1 → 18
Calls
1 calls:
11.0ms
(sqrt (- 1.0 (* x x)))

series86.0ms

Counts
1 → 3
Calls
1 calls:
86.0ms
(sqrt (- 1.0 (* x x)))

simplify596.0ms

Counts
21 → 21
Iterations

Useful iterations: done (595.0ms)

IterNodesCost
069260
1172230
2756214
done5000212

prune62.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
0.0b
(sqrt (- 1.0 (* x x)))
1.0b
(expm1 (sqrt (- 1.0 (* x x))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
4×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod log1p-expm1-u
3×add-exp-log expm1-log1p-u add-cbrt-cube add-log-exp
2×sqrt-div
1×rem-sqrt-square log1p-udef expm1-log1p flip3-- sqrt-pow1 pow1/2 log1p-expm1 flip-- expm1-udef difference-of-squares
Counts
3 → 40
Calls
3 calls:
0.0ms
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
9.0ms
(sqrt (- 1.0 (* x x)))
1.0ms
(expm1 (sqrt (- 1.0 (* x x))))

series373.0ms

Counts
3 → 9
Calls
3 calls:
220.0ms
(log1p (expm1 (sqrt (- 1.0 (* x x)))))
61.0ms
(sqrt (- 1.0 (* x x)))
92.0ms
(expm1 (sqrt (- 1.0 (* x x))))

simplify1.2s

Counts
49 → 49
Iterations

Useful iterations: 2 (540.0ms)

IterNodesCost
0106580
1252509
21112471
done5000471

prune166.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0b
(fma 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3)) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
54×add-sqr-sqrt
52×associate-*r*
32×add-cube-cbrt *-un-lft-identity
28×sqrt-prod
20×unpow-prod-down
12×add-exp-log
9×unswap-sqr
8×unpow2 sqr-pow
7×add-cbrt-cube
4×pow1 prod-exp
3×div-exp associate-*l*
2×expm1-log1p-u cbrt-unprod log1p-expm1-u add-log-exp
1×cbrt-undiv pow-to-exp associate-*r/ pow-prod-down pow-exp *-commutative fma-udef div-inv
Counts
2 → 92
Calls
2 calls:
37.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
0.0ms
(fma 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3)) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

series451.0ms

Counts
2 → 6
Calls
2 calls:
83.0ms
(* 1/2 (/ (pow x 2) (sqrt 1.0)))
368.0ms
(fma 1/8 (/ (pow x 4) (pow (sqrt 1.0) 3)) (* 1/2 (/ (pow x 2) (sqrt 1.0))))

simplify909.0ms

Counts
98 → 98
Iterations

Useful iterations: done (904.0ms)

IterNodesCost
01721307
14401157
218881023
done50001020

prune333.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes72.0ms

Accuracy

0% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 0.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
078
done78

end0.0ms

sample1.0s

Algorithm
intervals
Results
349.0ms8000×body80valid
308.0ms8027×body80nan