Details

Time bar (total: 17.7s)

sample158.0ms

Algorithm
intervals
Results
57.0ms601×body80nan
54.0ms306×body160nan
23.0ms256×body80valid

simplify149.0ms

Calls
1 calls:
Slowest
149.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize16.0ms

Local error

Found 3 expressions with local error:

29.9b
(sqrt (fma x x -1))
0.0b
(+ x (sqrt (fma x x -1)))
0.0b
(log (+ x (sqrt (fma x x -1))))

rewrite4.0ms

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

series143.0ms

Calls
3 calls:
Slowest
85.0ms
(log (+ x (sqrt (fma x x -1))))
31.0ms
(sqrt (fma x x -1))
28.0ms
(+ x (sqrt (fma x x -1)))

simplify2.7s

Calls
19 calls:
Slowest
365.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
328.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
323.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
262.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
240.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))

prune500.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ -1/8 (* x x))
0.1b
(/ (/ -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)) (/ (/ -1/8 (* x x)) x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
7×add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×pow1 add-exp-log
4×expm1-log1p-u log-prod add-cbrt-cube insert-posit16 log1p-expm1-u associate-/l*
3×fma-def div-inv
2×log-div clear-num frac-2neg flip3-+ flip-+ distribute-lft-out
1×+-commutative associate-+l+ associate-/r* sum-log rem-log-exp log-pow fma-udef associate-/l/
Calls
4 calls:
Slowest
9.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
6.0ms
(/ (/ -1/8 (* x x)) x)
4.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x)))
1.0ms
(/ -1/8 (* x x))

series166.0ms

Calls
4 calls:
Slowest
111.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x)))
27.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
17.0ms
(/ (/ -1/8 (* x x)) x)
11.0ms
(/ -1/8 (* x x))

simplify3.1s

Calls
26 calls:
Slowest
504.0ms
(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
401.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
380.0ms
(log (+ (pow (fma 2 x (/ -1/2 x)) 3) (pow (/ (/ -1/8 (* x x)) x) 3)))
358.0ms
(log (- (* (fma 2 x (/ -1/2 x)) (fma 2 x (/ -1/2 x))) (* (/ (/ -1/8 (* x x)) x) (/ (/ -1/8 (* x x)) x))))
263.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune697.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

30.9b
(cbrt (fma x x -1))
30.9b
(cbrt (fma x x -1))
0.2b
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
0.2b
(sqrt (cbrt (fma x x -1)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×cbrt-prod
12×*-un-lft-identity add-cube-cbrt sqrt-prod
9×associate-*r*
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
2×rem-sqrt-square pow1/3
1×pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
16.0ms
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
3.0ms
(sqrt (cbrt (fma x x -1)))
1.0ms
(cbrt (fma x x -1))
1.0ms
(cbrt (fma x x -1))

series531.0ms

Calls
4 calls:
Slowest
158.0ms
(sqrt (cbrt (fma x x -1)))
135.0ms
(* (fabs (cbrt (fma x x -1))) (sqrt (cbrt (fma x x -1))))
131.0ms
(cbrt (fma x x -1))
107.0ms
(cbrt (fma x x -1))

simplify4.3s

Calls
40 calls:
Slowest
431.0ms
(- (* (pow (* x -1) 1/3) (fabs (pow (fma x x -1) 1/3))) (+ (* 5/72 (* (pow (/ -1 (pow x 11)) 1/3) (fabs (pow (fma x x -1) 1/3)))) (* 1/6 (* (pow (/ -1 (pow x 5)) 1/3) (fabs (pow (fma x x -1) 1/3))))))
400.0ms
(- (* (pow x 1/3) (fabs (pow (fma x x -1) 1/3))) (+ (* 5/72 (* (pow (/ 1 (pow x 11)) 1/3) (fabs (pow (fma x x -1) 1/3)))) (* 1/6 (* (pow (/ 1 (pow x 5)) 1/3) (fabs (pow (fma x x -1) 1/3))))))
396.0ms
(- (* (fabs (pow (fma x x -1) 1/3)) (pow -1 1/6)) (+ (* 5/72 (* (* (pow x 4) (fabs (pow (fma x x -1) 1/3))) (pow -1 1/6))) (* 1/6 (* (* (pow x 2) (fabs (pow (fma x x -1) 1/3))) (pow -1 1/6)))))
339.0ms
(- (pow -1 1/6) (+ (* 1/6 (* (pow x 2) (pow -1 1/6))) (* 5/72 (* (pow x 4) (pow -1 1/6)))))
321.0ms
(- (pow -1 1/3) (+ (* 1/3 (* (pow x 2) (pow -1 1/3))) (* 1/9 (* (pow x 4) (pow -1 1/3)))))

prune874.0ms

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

bsearch3.0ms

end0.0ms

sample4.2s

Algorithm
intervals
Results
1.7s7755×body160nan
1.3s16298×body80nan
719.0ms8000×body80valid