Details

Time bar (total: 28.1s)

sample177.0ms

Algorithm
intervals
Results
111.0ms861×body80nan
30.0ms295×body80valid

simplify200.0ms

Calls
1 calls:
Slowest
200.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.3b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×associate-*r*
9×associate-*r/
8×sqrt-prod
6×add-cbrt-cube sqrt-div add-exp-log
5×flip3-- flip--
4×pow1 associate-/r* associate-/r/ insert-posit16 add-log-exp
3×associate-/l*
2×distribute-rgt-in sub-neg distribute-lft-in *-commutative div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-sub div-exp
Calls
4 calls:
Slowest
7.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
6.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
3.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series298.0ms

Calls
4 calls:
Slowest
113.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
72.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
70.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
43.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify6.2s

Calls
80 calls:
Slowest
436.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
297.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
225.0ms
(- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))
208.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
202.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
0.3b
(/ (sqrt (- a (/ 1.0 3.0))) 3)
0.0b
(sqrt (- a (/ 1.0 3.0)))
0.0b
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×sqrt-prod associate-/l* add-log-exp
4×pow1 add-cbrt-cube sqrt-div add-exp-log insert-posit16
3×flip3-- associate-*l/ associate-*r/ flip--
2×associate-+r+ frac-add associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-+r- sum-log sub-neg frac-2neg flip3-+ pow1/2 associate-*r* *-commutative flip-+ div-inv
Calls
4 calls:
Slowest
10.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
7.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
6.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series334.0ms

Calls
4 calls:
Slowest
122.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
83.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
81.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
48.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify3.3s

Calls
33 calls:
Slowest
408.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
361.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
358.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
341.0ms
(+ (* (* rand (* (sqrt (- a (/ 1.0 3.0))) 1)) (+ a (/ 1.0 3.0))) (* 3 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
301.0ms
(* 3 (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune689.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* rand (* (/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0))))) 1))
0.2b
(/ 3 (sqrt (- a (/ 1.0 3.0))))
0.2b
(/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0)))))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-/r*
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×sqrt-div sqrt-prod
5×pow1 add-exp-log associate-/r/
4×add-cbrt-cube insert-posit16 add-log-exp
3×flip3-- div-inv flip--
2×clear-num frac-2neg
1×rem-sqrt-square rec-exp pow1/2 associate-*r* associate-*l/ associate-*r/ *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
3.0ms
(* rand (* (/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0))))) 1))
1.0ms
(/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0)))))
1.0ms
(/ 3 (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series352.0ms

Calls
4 calls:
Slowest
110.0ms
(* rand (* (/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0))))) 1))
105.0ms
(/ 1 (/ 3 (sqrt (- a (/ 1.0 3.0)))))
90.0ms
(/ 3 (sqrt (- a (/ 1.0 3.0))))
47.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify2.4s

Calls
35 calls:
Slowest
396.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
370.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
258.0ms
(- (* 3 (sqrt -3.0)) (+ (* 13.5 (/ a (sqrt -3.0))) (+ (* 40.5 (/ (pow a 2) (sqrt -3.0))) (* 30.375 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
232.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
203.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))

prune789.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ 3 (sqrt (- a (/ 1.0 3.0))))
0.0b
(+ (/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-/r*
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt
8×sqrt-div associate-/r/
6×times-frac add-cbrt-cube add-exp-log sqrt-prod add-log-exp
5×flip3-- flip--
4×pow1 insert-posit16 div-inv
2×associate-+r+ clear-num frac-2neg frac-add
1×cbrt-undiv +-commutative rem-sqrt-square associate-+r- sum-log sub-neg flip3-+ distribute-rgt-out pow1/2 div-exp flip-+ distribute-lft-out associate-/l*
Calls
4 calls:
Slowest
18.0ms
(+ (/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
11.0ms
(/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0)))))
2.0ms
(/ 3 (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series357.0ms

Calls
4 calls:
Slowest
109.0ms
(/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0)))))
106.0ms
(/ 3 (sqrt (- a (/ 1.0 3.0))))
94.0ms
(+ (/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
47.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify4.9s

Calls
58 calls:
Slowest
418.0ms
(+ (* (* rand (* 1 1)) (+ a (/ 1.0 3.0))) (* (/ 3 (sqrt (- a (/ 1.0 3.0)))) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
410.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
404.0ms
(/ rand (/ 3 (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))))
339.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
269.0ms
(* (exp (/ (* rand (* 1 1)) (/ 3 (sqrt (- a (/ 1.0 3.0)))))) (exp (- a (/ 1.0 3.0))))

prune849.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch3.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
3.9s27528×body80nan
1.2s9173×body80valid