Details

Time bar (total: 9.1m)

sample91.0ms

Algorithm
intervals
Results
30.0ms218×body160nan
25.0ms430×body80nan
21.0ms256×body80valid

simplify107.0ms

Calls
1 calls:
Slowest
107.0ms
(log (+ x (sqrt (- (* x x) 1))))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize21.0ms

Local error

Found 3 expressions with local error:

30.0b
(sqrt (fma x x -1))
0.5b
(log (+ x (sqrt (fma x x -1))))
0.0b
(+ x (sqrt (fma x x -1)))

rewrite7.0ms

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
2.0ms
(log (+ x (sqrt (fma x x -1))))
2.0ms
(sqrt (fma x x -1))
2.0ms
(+ x (sqrt (fma x x -1)))

series184.0ms

Calls
3 calls:
Slowest
110.0ms
(log (+ x (sqrt (fma x x -1))))
46.0ms
(+ x (sqrt (fma x x -1)))
28.0ms
(sqrt (fma x x -1))

simplify2.5s

Calls
19 calls:
Slowest
373.0ms
(+ (log -1/2) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
344.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
259.0ms
(- (+ (* 1/2 (/ (pow x 2) (sqrt -1))) (sqrt -1)) (* 1/8 (/ (pow x 4) (pow (sqrt -1) 3))))
222.0ms
(- (+ (log (sqrt -1)) (/ x (sqrt -1))) (* 1/6 (/ (pow x 3) (pow (sqrt -1) 3))))
204.0ms
(- x (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune437.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(+ (log x) (log 2))
0.1b
(/ (/ -1/4 x) x)
0.1b
(/ 3/32 (pow x 4))
0.0b
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
40×*-un-lft-identity
19×associate-+l+
18×add-sqr-sqrt
16×prod-diff add-cube-cbrt
11×add-log-exp
10×distribute-lft-out
9×fma-def
7×div-inv
5×sum-log
4×expm1-log1p-u pow1 add-cbrt-cube frac-add add-exp-log insert-posit16 log1p-expm1-u associate-/l* distribute-lft-out--
3×associate-/r* flip3-+ flip-+
2×+-commutative clear-num frac-2neg diff-log frac-sub
1×sub-neg flip3-- associate--l+ associate-+l- flip-- difference-of-squares associate-/l/
Calls
4 calls:
Slowest
112.0ms
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))
6.0ms
(+ (log x) (log 2))
3.0ms
(/ (/ -1/4 x) x)
1.0ms
(/ 3/32 (pow x 4))

series418.0ms

Calls
4 calls:
Slowest
296.0ms
(+ (log x) (log 2))
88.0ms
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))
22.0ms
(/ 3/32 (pow x 4))
12.0ms
(/ (/ -1/4 x) x)

simplify6.4s

Calls
58 calls:
Slowest
438.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
423.0ms
(+ (* (- (* (- (* (log x) (log x)) (* (log 2) (log 2))) (pow x 4)) (* (- (log x) (log 2)) 3/32)) x) (* (* (- (log x) (log 2)) (pow x 4)) (/ -1/4 x)))
352.0ms
(- (+ (log 2) (log -1)) (+ (log (/ -1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
289.0ms
(+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))
285.0ms
(* (/ (exp (+ (log x) (log 2))) (exp (/ 3/32 (pow x 4)))) (exp (/ (/ -1/4 x) x)))

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.5b
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x)))
0.4b
(/ -1/8 (* x x))
0.1b
(/ (/ -1/8 (* x x)) x)
0.0b
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))

rewrite15.0ms

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
6.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
5.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x)))
3.0ms
(/ (/ -1/8 (* x x)) x)
0.0ms
(/ -1/8 (* x x))

series161.0ms

Calls
4 calls:
Slowest
103.0ms
(log (+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x)))
21.0ms
(/ (/ -1/8 (* x x)) x)
19.0ms
(+ (fma 2 x (/ -1/2 x)) (/ (/ -1/8 (* x x)) x))
17.0ms
(/ -1/8 (* x x))

simplify2.9s

Calls
26 calls:
Slowest
421.0ms
(- (+ (log -1/8) (* 4 (pow x 2))) (+ (* 24 (pow x 4)) (* 3 (log x))))
347.0ms
(log (- (* (fma 2 x (/ -1/2 x)) (fma 2 x (/ -1/2 x))) (* (/ (/ -1/8 (* x x)) x) (/ (/ -1/8 (* x x)) x))))
334.0ms
(log (+ (pow (fma 2 x (/ -1/2 x)) 3) (pow (/ (/ -1/8 (* x x)) x) 3)))
326.0ms
(- (log 2) (+ (log (/ 1 x)) (+ (* 3/32 (/ 1 (pow x 4))) (* 1/4 (/ 1 (pow x 2))))))
312.0ms
(- (* 2 x) (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 x))))

prune792.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))
0.5b
(* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
0.3b
(* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
0.2b
(+ (log x) (log 2))

rewrite1.9s

Algorithm
rewrite-expression-head
Rules
1232×frac-add
1116×frac-times
617×flip3-+ flip-+
616×frac-sub
342×cbrt-div
308×flip3-- flip--
186×associate-*l/
102×associate-*r/
37×*-un-lft-identity
23×pow1
13×distribute-lft-out
12×associate-*r*
11×add-cbrt-cube add-exp-log
8×add-sqr-sqrt add-cube-cbrt
7×associate-*l*
6×pow-plus pow-prod-up distribute-lft-out--
4×expm1-log1p-u pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×pow2 fma-def
2×distribute-rgt-in distribute-lft-in pow3 *-commutative
1×cbrt-prod +-commutative sum-log pow1/3 rem-cbrt-cube
Calls
4 calls:
Slowest
926.0ms
(* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
505.0ms
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))
390.0ms
(* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
8.0ms
(+ (log x) (log 2))

series762.0ms

Calls
4 calls:
Slowest
393.0ms
(+ (log x) (log 2))
154.0ms
(* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
115.0ms
(* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)))
99.0ms
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))

simplify8.5m

Calls
1115 calls:
Slowest
2.2s
(cbrt (* (* (- (* (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (- (+ (log x) (log 2)) (/ 3/32 (pow x 4)))) (* (/ (/ -1/4 x) x) (/ (/ -1/4 x) x))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))))
2.2s
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (* (- (pow (+ (log x) (log 2)) 3) (pow (/ 3/32 (pow x 4)) 3)) x) (* (+ (* (+ (log x) (log 2)) (+ (log x) (log 2))) (+ (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4))) (* (+ (log x) (log 2)) (/ 3/32 (pow x 4))))) (/ -1/4 x)))) (+ (* (- (pow (+ (log x) (log 2)) 3) (pow (/ 3/32 (pow x 4)) 3)) x) (* (+ (* (+ (log x) (log 2)) (+ (log x) (log 2))) (+ (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4))) (* (+ (log x) (log 2)) (/ 3/32 (pow x 4))))) (/ -1/4 x)))))
1.9s
(cbrt (* (* (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3)) (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))))
1.8s
(cbrt (* (* (+ (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ (/ -1/4 x) x)) (+ (* (- (* (- (* (log x) (log x)) (* (log 2) (log 2))) (pow x 4)) (* (- (log x) (log 2)) 3/32)) x) (* (* (- (log x) (log 2)) (pow x 4)) (/ -1/4 x)))) (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3))))
1.7s
(cbrt (* (* (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x))) (+ (pow (- (+ (log x) (log 2)) (/ 3/32 (pow x 4))) 3) (pow (/ (/ -1/4 x) x) 3))) (+ (* (- (* (+ (log x) (log 2)) (+ (log x) (log 2))) (* (/ 3/32 (pow x 4)) (/ 3/32 (pow x 4)))) x) (* (+ (+ (log x) (log 2)) (/ 3/32 (pow x 4))) (/ -1/4 x)))))

prune14.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes20.0ms

Accuracy

0% (0.3b remaining)

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

bsearch1.0ms

end0.0ms

sample2.8s

Algorithm
intervals
Results
939.0ms7770×body160nan
830.0ms8000×body80valid
754.0ms16329×body80nan