Details

Time bar (total: 16.1s)

sample142.0ms

Algorithm
intervals
Results
49.0ms500×body80nan
44.0ms244×body160nan
24.0ms256×body80valid

simplify183.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
183.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize12.0ms

Local error

Found 2 expressions with local error:

27.8b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite10.0ms

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:
Slowest
8.0ms
(+ x (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))

series156.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
99.0ms
(+ x (sqrt (fma x x -1)))
57.0ms
(sqrt (fma x x -1))

simplify3.5s

Counts
39 → 40
Calls
39 calls:
Slowest
453.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
324.0ms
(+ (* x x) (- (* (sqrt (fma x x -1)) (sqrt (fma x x -1))) (* x (sqrt (fma x x -1)))))
289.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
268.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
237.0ms
(- (* x x) (* (sqrt (fma x x -1)) (sqrt (fma x x -1))))

prune318.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b
(/ (/ -1/8 x) (* x x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
15×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log associate-/l*
6×cbrt-undiv div-exp
3×div-inv
2×prod-exp cbrt-unprod
1×expm1-log1p-u pow1 clear-num associate-/r* frac-2neg insert-posit16 log1p-expm1-u add-log-exp associate-/l/
Counts
1 → 49
Calls
1 calls:
Slowest
21.0ms
(/ (/ -1/8 x) (* x x))

series71.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
71.0ms
(/ (/ -1/8 x) (* x x))

simplify2.8s

Counts
66 → 52
Calls
66 calls:
Slowest
372.0ms
(* (* (/ (/ -1/8 x) (* x x)) (/ (/ -1/8 x) (* x x))) (/ (/ -1/8 x) (* x x)))
162.0ms
(/ (* (* (/ -1/8 x) (/ -1/8 x)) (/ -1/8 x)) (* (* (* x x) x) (* (* x x) x)))
159.0ms
(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) x) (* (* x x) x)))
150.0ms
(/ (/ (* (* -1/8 -1/8) -1/8) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))
138.0ms
(/ (/ (* (cbrt -1/8) (cbrt -1/8)) (* (cbrt x) (cbrt x))) x)

prune505.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

27.8b
(sqrt (fma x x -1))
0.5b
(cbrt x)
0.5b
(cbrt x)
0.5b
(cbrt x)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
5×pow1
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
3.0ms
(sqrt (fma x x -1))
2.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)

series848.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
280.0ms
(cbrt x)
260.0ms
(cbrt x)
247.0ms
(cbrt x)
60.0ms
(sqrt (fma x x -1))

simplify2.2s

Counts
77 → 70
Calls
77 calls:
Slowest
478.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
286.0ms
(+ (* 1/8 (/ (pow x 4) (sqrt -1))) (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)))
243.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
177.0ms
(* (pow (* x -1) 1/3) (cbrt -1))
168.0ms
(* (* (sqrt (fma x x -1)) (sqrt (fma x x -1))) (sqrt (fma x x -1)))

prune658.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes23.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch3.0ms

end0.0ms

sample4.5s

Algorithm
intervals
Results
1.8s16657×body80nan
1.5s7775×body160nan
794.0ms8000×body80valid