Details

Time bar (total: 20.6s)

sample133.0ms

Algorithm
intervals
Results
45.0ms247×body160nan
42.0ms548×body80nan
25.0ms256×body80valid

simplify181.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
181.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.9b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
7×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×log-prod add-exp-log
3×expm1-log1p-u fma-def add-cbrt-cube sqrt-prod insert-posit16 log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-sqrt-square sum-log sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
3 → 52
Calls
3 calls:
Slowest
5.0ms
(+ x (sqrt (fma x x -1)))
4.0ms
(log (+ x (sqrt (fma x x -1))))
1.0ms
(sqrt (fma x x -1))

series332.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
199.0ms
(log (+ x (sqrt (fma x x -1))))
71.0ms
(+ x (sqrt (fma x x -1)))
61.0ms
(sqrt (fma x x -1))

simplify3.4s

Counts
25 → 61
Calls
25 calls:
Slowest
529.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
446.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
357.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
278.0ms
(+ (* 1/16 (/ 1 (pow x 5))) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
266.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune519.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
24×*-un-lft-identity
20×add-sqr-sqrt add-cube-cbrt
17×add-exp-log
16×add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×pow1
4×expm1-log1p-u log-prod insert-posit16 log1p-expm1-u
3×fma-def div-inv
2×log-div flip3-+ prod-exp cbrt-unprod flip-+ fma-udef distribute-lft-out
1×+-commutative associate-+l+ clear-num associate-/r* sum-log frac-2neg rem-log-exp log-pow associate-/l/
Counts
4 → 97
Calls
4 calls:
Slowest
17.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))
14.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
13.0ms
(/ (/ -1/8 x) (* x x))
0.0ms
(fma 2 x (/ -1/2 x))

series278.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))
62.0ms
(fma 2 x (/ -1/2 x))
54.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
42.0ms
(/ (/ -1/8 x) (* x x))

simplify4.9s

Counts
69 → 109
Calls
69 calls:
Slowest
407.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
367.0ms
(log (- (* (fma 2 x (/ -1/2 x)) (fma 2 x (/ -1/2 x))) (* (/ (/ -1/8 x) (* x x)) (/ (/ -1/8 x) (* x x)))))
290.0ms
(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
269.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
265.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune945.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
9×*-un-lft-identity add-cube-cbrt
7×pow1
6×cbrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
1×pow1/3
Counts
4 → 65
Calls
4 calls:
Slowest
1.0ms
(sqrt (fma x x -1))
1.0ms
(cbrt (sqrt (fma x x -1)))
1.0ms
(sqrt (fma x x -1))
1.0ms
(sqrt (fma x x -1))

series316.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
146.0ms
(cbrt (sqrt (fma x x -1)))
59.0ms
(sqrt (fma x x -1))
59.0ms
(sqrt (fma x x -1))
52.0ms
(sqrt (fma x x -1))

simplify4.6s

Counts
33 → 77
Calls
33 calls:
Slowest
556.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
541.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
523.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
418.0ms
(- (pow -1 1/6) (+ (* 1/6 (* (pow x 2) (pow -1 1/6))) (* 5/72 (* (pow x 4) (pow -1 1/6)))))
337.0ms
(- (pow (/ -1 x) -1/3) (+ (* 5/72 (pow (/ -1 (pow x 11)) 1/3)) (* 1/6 (pow (/ -1 (pow x 5)) 1/3))))

prune752.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.7s16673×body80nan
1.3s7701×body160nan
678.0ms8000×body80valid