Details

Time bar (total: 1.5m)

sample143.0ms

Algorithm
intervals
Results
56.0ms542×body80nan
43.0ms262×body160nan
23.0ms256×body80valid

simplify139.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
138.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.5b

localize29.0ms

Local error

Found 2 expressions with local error:

26.3b
(sqrt (fma x x -1))
0.2b
(log (+ x (sqrt (fma x x -1))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
6×*-un-lft-identity
5×add-sqr-sqrt
4×pow1 log-prod add-cube-cbrt
3×add-exp-log sqrt-prod
2×expm1-log1p-u log-div add-cbrt-cube insert-posit16 log1p-expm1-u add-log-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 rem-log-exp log-pow flip-+ distribute-lft-out
Counts
2 → 34
Calls
2 calls:
Slowest
7.0ms
(log (+ x (sqrt (fma x x -1))))
3.0ms
(sqrt (fma x x -1))

series237.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
184.0ms
(log (+ x (sqrt (fma x x -1))))
53.0ms
(sqrt (fma x x -1))

simplify2.8s

Counts
18 → 40
Calls
18 calls:
Slowest
507.0ms
(- (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))) x)
489.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
421.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
258.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))
240.0ms
(log (+ (pow x 3) (pow (sqrt (fma x x -1)) 3)))

prune405.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

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

rewrite705.0ms

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
604.0ms
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
47.0ms
(* (* x x) (* x x))
38.0ms
(/ 3/32 (* (* x x) (* x x)))
7.0ms
(/ -1 (* x x))

series2.4s

Counts
4 → 12
Calls
4 calls:
Slowest
2.2s
(- (log 2) (- (/ 3/32 (* (* x x) (* x x))) (log x)))
70.0ms
(/ 3/32 (* (* x x) (* x x)))
48.0ms
(/ -1 (* x x))
38.0ms
(* (* x x) (* x x))

simplify21.9s

Counts
212 → 221
Calls
212 calls:
Slowest
454.0ms
(fma 1 (log 2) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))
454.0ms
(- (+ (log 2) (log -1)) (+ (log (/ -1 x)) (* 3/32 (/ 1 (pow x 4)))))
419.0ms
(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))))))
418.0ms
(fma 1 (log 2) (- (* (- (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))) (+ (sqrt (/ 3/32 (* (* x x) (* x x)))) (sqrt (log x))))))
411.0ms
(fma (sqrt (log 2)) (sqrt (log 2)) (- (* (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)))))))

prune2.9s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize47.0ms

Local error

Found 3 expressions with local error:

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

rewrite239.0ms

Algorithm
rewrite-expression-head
Rules
232×times-frac
217×add-sqr-sqrt
173×*-un-lft-identity
141×prod-diff
125×add-cube-cbrt
41×associate--r+
37×difference-of-squares
23×distribute-lft-out--
20×div-inv
17×fma-neg
16×add-exp-log
15×add-cbrt-cube
13×associate-/l*
8×add-log-exp
6×cbrt-undiv log-prod div-exp
4×pow1
3×expm1-log1p-u diff-log insert-posit16 log1p-expm1-u distribute-lft-out
2×log-div sub-neg flip3-- prod-exp frac-sub cbrt-unprod flip--
1×clear-num associate-/r* frac-2neg flip3-+ rem-log-exp log-pow flip-+ associate--r- associate-/l/
Counts
3 → 253
Calls
3 calls:
Slowest
133.0ms
(log (+ x (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))))
80.0ms
(- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))
17.0ms
(/ (/ -1/8 x) (* x x))

series251.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
126.0ms
(log (+ x (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))))
72.0ms
(/ (/ -1/8 x) (* x x))
52.0ms
(- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x))

simplify52.8s

Counts
338 → 262
Calls
338 calls:
Slowest
937.0ms
(log (+ (pow x 3) (pow (- (/ (/ -1/8 x) (* x x)) (- (/ 1/2 x) x)) 3)))
587.0ms
(fma (/ (/ 1 (sqrt x)) x) (/ (/ -1/8 (sqrt x)) x) (- (* (- (/ 1/2 x) x) 1)))
569.0ms
(fma (/ (/ 1 (* (cbrt x) (cbrt x))) x) (/ (/ -1/8 (cbrt x)) x) (- (* (cbrt (- (/ 1/2 x) x)) (* (cbrt (- (/ 1/2 x) x)) (cbrt (- (/ 1/2 x) x))))))
508.0ms
(fma (/ (/ (* (cbrt -1/8) (cbrt -1/8)) 1) x) (/ (/ (cbrt -1/8) x) x) (- (* (- (/ 1/2 x) x) 1)))
497.0ms
(- (* (/ -1/8 x) (+ (/ 1/2 x) x)) (* (* x x) (- (* (/ 1/2 x) (/ 1/2 x)) (* x x))))

prune2.4s

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes33.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch4.0ms

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.6s7896×body160nan
1.2s8000×body80valid
1.2s16517×body80nan