Details

Time bar (total: 51.6s)

sample86.0ms

Algorithm
intervals
Results
34.0ms769×body80nan
24.0ms256×body80valid

simplify30.0ms

Counts
1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
0.0b
(/ (sqrt (- 1.0 (* x x))) x)
0.0b
(sqrt (- 1.0 (* x x)))
0.2b
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

rewrite150.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
33×times-frac
32×add-sqr-sqrt
26×add-cube-cbrt
20×sqrt-prod
8×log-prod distribute-lft-out
7×add-exp-log associate-/l*
6×pow1 add-cbrt-cube add-log-exp
5×div-inv difference-of-squares
4×sqrt-div
3×log-div associate-/r*
2×distribute-rgt-out flip3-- flip3-+ frac-add flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp rem-log-exp clear-num sum-log log-pow
Counts
4 → 98
Calls
4 calls:
55.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
16.0ms
(/ (sqrt (- 1.0 (* x x))) x)
26.0ms
(sqrt (- 1.0 (* x x)))
50.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

series1.2s

Counts
4 → 12
Calls
4 calls:
140.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
211.0ms
(/ (sqrt (- 1.0 (* x x))) x)
406.0ms
(sqrt (- 1.0 (* x x)))
449.0ms
(log (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x)))

simplify791.0ms

Counts
110 → 110

prune471.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
0.3b
(/ 1 (sqrt x))
0.3b
(/ 1.0 (sqrt x))
0.3b
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
104×*-un-lft-identity
93×add-sqr-sqrt sqrt-prod
82×add-cube-cbrt
35×log-prod
22×associate-+l+
18×associate-/r*
13×associate-+r+ distribute-lft-out associate-/l*
12×add-exp-log
10×pow1 add-cbrt-cube
7×difference-of-squares
6×div-inv
4×log-div div-exp log-pow add-log-exp
3×cbrt-undiv associate-+r- pow-flip frac-2neg clear-num
2×flip3-+ sqrt-div flip-+ associate-/l/
1×+-commutative associate-+l- rec-exp sqrt-undiv distribute-rgt-out flip3-- sqrt-pow1 pow1/2 1-exp frac-add sum-log flip-- inv-pow
Counts
4 → 208
Calls
4 calls:
124.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
8.0ms
(/ 1 (sqrt x))
7.0ms
(/ 1.0 (sqrt x))
34.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

series754.0ms

Counts
4 → 12
Calls
4 calls:
548.0ms
(+ (log (/ 1 (sqrt x))) (log (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x)))))
37.0ms
(/ 1 (sqrt x))
71.0ms
(/ 1.0 (sqrt x))
98.0ms
(/ (sqrt (- 1.0 (* x x))) (sqrt x))

simplify1.2s

Counts
220 → 220

prune805.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes81.0ms

Accuracy

0.2% (0.2b remaining)

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

bsearch0.0ms

simplify42.3s

end0.0ms

sample3.6s

Algorithm
intervals
Results
2.2s23497×body80nan
686.0ms8000×body80valid