Details

Time bar (total: 24.1s)

sample83.0ms

Algorithm
intervals
Results
27.0ms273×body160nan
26.0ms593×body80nan
14.0ms256×body80valid

simplify10.2s

Counts
1 → 1
Iterations
IterNodes
94832
81321
7464
6246
5119
468
337
221
117
07

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize31.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ x (sqrt (fma x x -1)))
26.4b
(sqrt (fma x x -1))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×add-cube-cbrt add-log-exp
3×pow1 fma-def sqrt-prod
2×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 flip3-+ pow1/2 flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
10.0ms
(+ x (sqrt (fma x x -1)))
2.0ms
(sqrt (fma x x -1))

series164.0ms

Counts
2 → 6
Calls
2 calls:
102.0ms
(+ x (sqrt (fma x x -1)))
61.0ms
(sqrt (fma x x -1))

simplify2.3s

Counts
40 → 40
Iterations
IterNodes
42761
31025
2410
1172
073

prune370.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))
0.0b
(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x))))
0.1b
(/ (/ 1/8 x) (* x x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
103×times-frac
74×add-sqr-sqrt
64×*-un-lft-identity
60×add-cube-cbrt
51×prod-diff
16×add-exp-log
15×add-cbrt-cube
13×associate-/l*
9×div-inv
7×log-prod
6×cbrt-undiv div-exp difference-of-squares
5×add-log-exp
4×pow1
3×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
2×log-div flip3-- prod-exp cbrt-unprod flip-- distribute-lft-out--
1×clear-num associate-/r* sub-neg frac-2neg diff-log rem-log-exp associate--l+ log-pow fma-udef associate-/l/
Counts
3 → 144
Calls
3 calls:
13.0ms
(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))
12.0ms
(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x))))
14.0ms
(/ (/ 1/8 x) (* x x))

series180.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x)))
91.0ms
(log (- (fma 2 x (/ -1/2 x)) (/ (/ 1/8 x) (* x x))))
45.0ms
(/ (/ 1/8 x) (* x x))

simplify765.0ms

Counts
153 → 153
Iterations
IterNodes
22264
1785
0319

prune1.7s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (cbrt (fma x x -1)))
0.3b
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
27.5b
(cbrt (fma x x -1))
27.5b
(cbrt (fma x x -1))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt
14×cbrt-prod sqrt-prod
12×*-un-lft-identity add-cube-cbrt
9×associate-*r*
7×pow1
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 associate-*l* unswap-sqr
2×rem-sqrt-square sqrt-pow1
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 78
Calls
4 calls:
3.0ms
(sqrt (cbrt (fma x x -1)))
15.0ms
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))

series688.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(sqrt (cbrt (fma x x -1)))
178.0ms
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
171.0ms
(cbrt (fma x x -1))
143.0ms
(cbrt (fma x x -1))

simplify2.1s

Counts
90 → 90
Iterations
IterNodes
33475
21075
1370
0157

prune1.1s

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
111
011

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s7679×body160nan
1.2s16393×body80nan
771.0ms8000×body80valid