Details

Time bar (total: 36.4s)

sample204.0ms

Algorithm
intervals
Results
135.0ms922×body80nan
35.0ms291×body80valid

simplify673.0ms

Calls
1 calls:
Slowest
673.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* 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)))

rewrite11.0ms

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
4.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
3.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
2.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series136.0ms

Calls
4 calls:
Slowest
50.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
37.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
28.0ms
(* 9 (- a (/ 1.0 3.0)))
21.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify5.9s

Calls
80 calls:
Slowest
435.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
283.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
186.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
181.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
181.0ms
(- (pow a 3) (pow (/ 1.0 3.0) 3))

prune1.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite18.0ms

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
7.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
5.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
4.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series132.0ms

Calls
4 calls:
Slowest
55.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
35.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
26.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
15.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify3.6s

Calls
33 calls:
Slowest
433.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
416.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
406.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))
378.0ms
(+ (* (* rand (* (sqrt (- a (/ 1.0 3.0))) 1)) (+ a (/ 1.0 3.0))) (* 3 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
291.0ms
(* 3 (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune679.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize25.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
15×associate-*r*
10×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×associate-*r/
6×times-frac add-cbrt-cube sqrt-div add-exp-log add-log-exp
5×flip3-- flip--
4×pow1 associate-/r/ insert-posit16
3×sqrt-prod associate-/l*
2×associate-+r+ frac-add *-commutative div-inv associate-/l/
1×cbrt-undiv +-commutative clear-num associate-+r- associate-/r* sum-log sub-neg frac-2neg flip3-+ div-sub div-exp flip-+
Calls
4 calls:
Slowest
10.0ms
(+ (* rand (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
9.0ms
(/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))
7.0ms
(* rand (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0))))))
5.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))

series205.0ms

Calls
4 calls:
Slowest
73.0ms
(* rand (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0))))))
70.0ms
(+ (* rand (/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
35.0ms
(/ (- a (/ 1.0 3.0)) (* 3 (sqrt (- a (/ 1.0 3.0)))))
26.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))

simplify4.1s

Calls
54 calls:
Slowest
427.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
359.0ms
(* (* 3 (sqrt (- a (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
254.0ms
(+ (* (* rand (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (* 3 (sqrt (- a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
213.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
206.0ms
(- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))

prune764.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))
0.4b
(* rand (/ 1 3))
0.3b
(* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
0.0b
(+ (* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
33×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
28×associate-*r*
21×sqrt-prod
11×add-cbrt-cube add-exp-log
10×frac-add associate-*r/
8×flip3-- flip--
7×pow1 un-div-inv
6×frac-times associate-/r* associate-*l/ add-log-exp
4×sqrt-div associate-/r/ insert-posit16
3×div-inv associate-/l*
2×cbrt-undiv associate-+r+ div-exp prod-exp *-commutative cbrt-unprod associate-/l/
1×+-commutative clear-num associate-+r- sum-log sub-neg frac-2neg flip3-+ pow1/2 div-sub associate-*l* pow-prod-down flip-+ pow-div
Calls
4 calls:
Slowest
8.0ms
(+ (* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
8.0ms
(* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
4.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))
1.0ms
(* rand (/ 1 3))

series174.0ms

Calls
4 calls:
Slowest
74.0ms
(* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0)))))
53.0ms
(+ (* (* rand (/ 1 3)) (/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
34.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (- a (/ 1.0 3.0))))
13.0ms
(* rand (/ 1 3))

simplify10.8s

Calls
129 calls:
Slowest
461.0ms
(* (* (* (* rand (/ 1 3)) (* rand (/ 1 3))) (* rand (/ 1 3))) (/ (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
441.0ms
(/ (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
422.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
395.0ms
(+ (* (* (* rand (/ 1 3)) (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (sqrt (- a (/ 1.0 3.0))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
362.0ms
(* (sqrt (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune1.3s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes156.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
3.6s26886×body80nan
1.6s9160×body80valid