Details

Time bar (total: 41.0s)

sample115.0ms

Algorithm
intervals
Results
39.0ms250×body160nan
34.0ms511×body80nan
21.0ms256×body80valid

simplify161.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
161.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize24.0ms

Local error

Found 3 expressions with local error:

29.6b
(sqrt (fma x x -1))
0.2b
(log (+ x (sqrt (fma x x -1))))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite20.0ms

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
10.0ms
(+ x (sqrt (fma x x -1)))
7.0ms
(log (+ x (sqrt (fma x x -1))))
3.0ms
(sqrt (fma x x -1))

series367.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
194.0ms
(log (+ x (sqrt (fma x x -1))))
96.0ms
(+ x (sqrt (fma x x -1)))
77.0ms
(sqrt (fma x x -1))

simplify3.1s

Counts
25 → 61
Calls
25 calls:
Slowest
429.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
412.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
344.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
272.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
246.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune574.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize57.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ -1 (* x x))
0.5b
(/ 3/32 (* (* x x) (* x x)))
0.2b
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
0.1b
(* (* x x) (* x x))

rewrite387.0ms

Algorithm
rewrite-expression-head
Rules
139×pow1
59×*-un-lft-identity
56×prod-diff
54×add-sqr-sqrt
39×add-cbrt-cube add-exp-log
36×pow-prod-up add-cube-cbrt
30×associate--r+
24×log-pow
23×pow-prod-down
22×times-frac pow-sqr
18×pow-plus distribute-lft-out--
17×prod-exp cbrt-unprod
13×pow2
9×difference-of-squares
7×cbrt-undiv div-exp
6×div-inv associate-/l* add-log-exp
4×expm1-log1p-u fma-neg insert-posit16 log1p-expm1-u
3×log-prod diff-log associate--l+
2×clear-num associate-/r* sub-neg frac-2neg
1×flip3-- swap-sqr associate-*r* associate-*l* *-commutative flip-- associate--r- unswap-sqr
Counts
4 → 209
Calls
4 calls:
Slowest
277.0ms
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
47.0ms
(* (* x x) (* x x))
42.0ms
(/ 3/32 (* (* x x) (* x x)))
14.0ms
(/ -1 (* x x))

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
2.2s
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
71.0ms
(* (* x x) (* x x))
66.0ms
(/ 3/32 (* (* x x) (* x x)))
30.0ms
(/ -1 (* x x))

simplify21.8s

Counts
212 → 221
Calls
212 calls:
Slowest
712.0ms
(fma (- (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x)))) (* (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x))) (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x)))) (* (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x))) (* (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x))) (cbrt (- (/ 3/32 (* (* x x) (* x x))) (log x))))))
478.0ms
(fma (sqrt (log 2)) (sqrt (log 2)) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))
473.0ms
(fma 1 (log 2) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))
472.0ms
(fma (* (cbrt (log 2)) (cbrt (log 2))) (cbrt (log 2)) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))
462.0ms
(* (* (* (* x x) x) (* (* x x) x)) (* (* (* x x) (* x x)) (* x x)))

prune2.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 3 expressions with local error:

0.2b
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))
0.1b
(/ (/ -1/8 x) (* x x))
0.0b
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
23×*-un-lft-identity
19×add-sqr-sqrt add-cube-cbrt
16×add-exp-log
15×add-cbrt-cube
13×associate-/l*
6×cbrt-undiv div-exp
5×add-log-exp
4×pow1 log-prod
3×expm1-log1p-u fma-def insert-posit16 log1p-expm1-u div-inv
2×log-div flip3-+ prod-exp cbrt-unprod flip-+ distribute-lft-out
1×+-commutative associate-+l+ clear-num associate-/r* sum-log frac-2neg rem-log-exp log-pow fma-udef associate-/l/
Counts
3 → 86
Calls
3 calls:
Slowest
22.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
17.0ms
(/ (/ -1/8 x) (* x x))
10.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))

series241.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
129.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x))))
58.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 x) (* x x)))
54.0ms
(/ (/ -1/8 x) (* x x))

simplify4.4s

Counts
66 → 95
Calls
66 calls:
Slowest
408.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
323.0ms
(log (- (* (fma 2 x (/ -1/2 x)) (fma 2 x (/ -1/2 x))) (* (/ (/ -1/8 x) (* x x)) (/ (/ -1/8 x) (* x x)))))
271.0ms
(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
242.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
228.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune887.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes38.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch2.0ms

end0.0ms

sample4.0s

Algorithm
intervals
Results
1.5s7461×body160nan
1.3s16101×body80nan
739.0ms8000×body80valid