Details

Time bar (total: 35.9s)

sample156.0ms

Algorithm
intervals
Results
99.0ms957×body80nan
29.0ms286×body80valid

simplify604.0ms

Calls
1 calls:
Slowest
604.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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))))))
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite18.0ms

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
6.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
5.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
4.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series129.0ms

Calls
4 calls:
Slowest
47.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
35.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
24.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
23.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify6.4s

Calls
80 calls:
Slowest
394.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
290.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
218.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
207.0ms
(- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))
196.0ms
(- (pow a 3) (pow (/ 1.0 3.0) 3))

prune940.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9)))
0.3b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9))))
0.1b
(sqrt (* (- a (/ 1.0 3.0)) 9))
0.0b
(* (- a (/ 1.0 3.0)) 9)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-*r*
8×associate-*l/ 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* associate-/l*
2×*-commutative div-inv associate-/l/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-sub div-exp associate-*r/
Calls
4 calls:
Slowest
4.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9)))
4.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9))))
3.0ms
(* (- a (/ 1.0 3.0)) 9)
1.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))

series155.0ms

Calls
4 calls:
Slowest
56.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9))))
38.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (- a (/ 1.0 3.0)) 9)))
34.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
26.0ms
(* (- a (/ 1.0 3.0)) 9)

simplify6.6s

Calls
75 calls:
Slowest
441.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
365.0ms
(sqrt (* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9))
231.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
231.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9)
210.0ms
(- (pow a 3) (pow (/ 1.0 3.0) 3))

prune1.0s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

8.8b
(* (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (/ (- a (/ 1.0 3.0)) 3))
0.2b
(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.2b
(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
0.0b
(/ (- a (/ 1.0 3.0)) 3)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r*
9×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1 add-exp-log
6×associate-/r* add-cbrt-cube
4×sqrt-div associate-*r/ associate-/r/ insert-posit16 div-inv add-log-exp
3×flip3-- un-div-inv sqrt-prod flip-- associate-/l*
2×frac-times clear-num frac-2neg associate-*l/ *-commutative pow-flip associate-/l/
1×rec-exp pow1/2 div-sub associate-*l* pow-prod-down prod-exp cbrt-unprod inv-pow
Calls
4 calls:
Slowest
13.0ms
(* (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (/ (- a (/ 1.0 3.0)) 3))
5.0ms
(/ (- a (/ 1.0 3.0)) 3)
3.0ms
(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
3.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))

series166.0ms

Calls
4 calls:
Slowest
55.0ms
(* (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (/ (- a (/ 1.0 3.0)) 3))
45.0ms
(* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))
38.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
28.0ms
(/ (- a (/ 1.0 3.0)) 3)

simplify3.5s

Calls
48 calls:
Slowest
464.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
344.0ms
(+ (log (* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))) (log (/ (- a (/ 1.0 3.0)) 3)))
244.0ms
(* (* (* (* rand (/ 1 (sqrt (- a (/ 1.0 3.0))))) (* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))) (* rand (/ 1 (sqrt (- a (/ 1.0 3.0)))))) (* (* (/ (- a (/ 1.0 3.0)) 3) (/ (- a (/ 1.0 3.0)) 3)) (/ (- a (/ 1.0 3.0)) 3)))
225.0ms
(- (sqrt -3.0) (+ (* 4.5 (/ a (sqrt -3.0))) (+ (* 13.5 (/ (pow a 2) (sqrt -3.0))) (* 10.125 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
208.0ms
(- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))

prune876.0ms

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
(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0))))
0.3b
(* rand (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))))
0.3b
(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))
0.1b
(sqrt (* (- a (/ 1.0 3.0)) 9))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
22×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
21×associate-/r*
9×add-exp-log
8×sqrt-prod
6×add-cbrt-cube associate-/r/
5×pow1 associate-*r*
4×flip3-- sqrt-div associate-*l/ insert-posit16 div-inv flip-- associate-/l* add-log-exp
2×rec-exp clear-num frac-2neg div-exp associate-/l/
1×cbrt-undiv pow1/2 associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Calls
4 calls:
Slowest
10.0ms
(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))
4.0ms
(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0))))
2.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))
2.0ms
(* rand (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))))

series141.0ms

Calls
4 calls:
Slowest
43.0ms
(* rand (/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))))
34.0ms
(/ 1 (/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0))))
33.0ms
(/ (sqrt (* (- a (/ 1.0 3.0)) 9)) (- a (/ 1.0 3.0)))
30.0ms
(sqrt (* (- a (/ 1.0 3.0)) 9))

simplify7.2s

Calls
78 calls:
Slowest
530.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
521.0ms
(/ (* (* (sqrt (* (- a (/ 1.0 3.0)) 9)) (sqrt (* (- a (/ 1.0 3.0)) 9))) (sqrt (* (- a (/ 1.0 3.0)) 9))) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
318.0ms
(sqrt (* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9))
277.0ms
(sqrt (* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) 9))
242.0ms
(- (* 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))))))

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes136.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample6.5s

Algorithm
intervals
Results
4.4s27369×body80nan
1.4s9161×body80valid