Details

Time bar (total: 1.4m)

sample179.0ms

Algorithm
intervals
Results
95.0ms851×body80nan
52.0ms285×body80valid

simplify250.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
250.0ms
(* (- 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: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite187.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
59×times-frac
50×*-un-lft-identity
36×associate-*r*
30×add-cube-cbrt
20×difference-of-squares
14×sqrt-prod
13×add-cbrt-cube add-exp-log
11×pow1
10×distribute-lft-out--
9×associate-*r/
6×sqrt-div associate-*l* associate-/l*
5×flip3-- flip--
4×associate-/r* associate-/r/ insert-posit16 add-log-exp
3×pow-prod-down prod-exp cbrt-unprod unswap-sqr
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in sqrt-pow1 div-exp *-commutative div-inv associate-/l/
1×clear-num frac-2neg pow1/2 div-sub
Counts
4 → 144
Calls
4 calls:
Slowest
84.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
53.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
34.0ms
(* 9 (- a (/ 1.0 3.0)))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series384.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
137.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
107.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
77.0ms
(* 9 (- a (/ 1.0 3.0)))
63.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.6s

Counts
141 → 156
Calls
141 calls:
Slowest
486.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
369.0ms
(* (* (* rand rand) rand) (/ (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))) (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt (* 9 (- a (/ 1.0 3.0)))))))
365.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
351.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
313.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))
0.2b
(* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))
0.0b
(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
0.0b
(* (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
496×add-sqr-sqrt
369×sqrt-prod
321×times-frac
281×*-un-lft-identity
160×difference-of-squares
139×associate-*r*
107×add-cube-cbrt
61×distribute-lft-out--
34×add-cbrt-cube add-exp-log
26×distribute-lft-out
16×associate-/l*
15×associate-/r*
12×prod-exp cbrt-unprod
11×pow1
8×cbrt-undiv div-exp
4×sqrt-div associate-*l* pow-prod-down associate-*r/ associate-/r/ insert-posit16 div-inv add-log-exp associate-/l/
3×flip3-- flip-- unswap-sqr
2×clear-num frac-2neg *-commutative
1×frac-times flip3-+ div-sub associate-*l/ flip-+
Counts
4 → 380
Calls
4 calls:
Slowest
85.0ms
(* (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))
54.0ms
(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
53.0ms
(/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))
31.0ms
(* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
728.0ms
(* (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))))
303.0ms
(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))
141.0ms
(* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))
101.0ms
(/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))

simplify26.3s

Counts
479 → 392
Calls
479 calls:
Slowest
745.0ms
(* (* (* (* rand rand) rand) (/ (* (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (* (* (sqrt 9) (sqrt 9)) (sqrt 9)))) (/ (* (* (- (sqrt a) (sqrt (/ 1.0 3.0))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
615.0ms
(* (* (* (* rand rand) rand) (* (* (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)) (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))) (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))) (/ (* (* (- (sqrt a) (sqrt (/ 1.0 3.0))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
586.0ms
(+ (log (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))) (- (log (- (sqrt a) (sqrt (/ 1.0 3.0)))) (log (sqrt (- a (/ 1.0 3.0))))))
582.0ms
(* (* (* (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9))) (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))) (* rand (/ (+ (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt 9)))) (/ (* (* (- (sqrt a) (sqrt (/ 1.0 3.0))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))
550.0ms
(* (* (* (* rand rand) rand) (/ (* (* (+ (sqrt a) (sqrt (/ 1.0 3.0))) (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (* (* (sqrt 9) (sqrt 9)) (sqrt 9)))) (* (* (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))) (/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0))))))

prune6.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite144.0ms

Algorithm
rewrite-expression-head
Rules
87×add-sqr-sqrt
59×times-frac
50×*-un-lft-identity
33×associate-*l*
30×add-cube-cbrt
20×difference-of-squares
14×sqrt-prod
13×add-cbrt-cube add-exp-log
11×pow1
10×distribute-lft-out--
9×associate-*r*
8×associate-*r/
6×sqrt-div associate-/l*
5×flip3-- flip--
4×associate-/r* associate-/r/ insert-posit16 add-log-exp
3×pow-prod-down prod-exp cbrt-unprod unswap-sqr
2×distribute-rgt-in cbrt-undiv sub-neg distribute-lft-in sqrt-pow1 div-exp *-commutative div-inv associate-/l/
1×clear-num frac-2neg pow1/2 div-sub associate-*l/
Counts
4 → 144
Calls
4 calls:
Slowest
57.0ms
(* (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
37.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
33.0ms
(* 9 (- a (/ 1.0 3.0)))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series445.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
182.0ms
(* (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
92.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
85.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
85.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify12.4s

Counts
140 → 156
Calls
140 calls:
Slowest
512.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
424.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3)))))
403.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
340.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
334.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

8.2b
(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))
0.3b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)

rewrite335.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt
32×add-exp-log
27×times-frac
26×*-un-lft-identity
24×associate-*l*
23×add-cube-cbrt
20×add-cbrt-cube
18×pow1
13×prod-exp
8×sqrt-prod
7×associate-*r/ cbrt-unprod
6×sqrt-div div-exp pow-prod-down associate-*l/
5×flip3-- flip--
4×associate-/r* sqrt-pow1 associate-*r* associate-/r/ insert-posit16 pow-flip add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×frac-times pow1/2 *-commutative div-inv difference-of-squares
1×clear-num frac-2neg distribute-lft-out-- inv-pow
Counts
4 → 127
Calls
4 calls:
Slowest
205.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))
105.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
17.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
6.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series598.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
222.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
194.0ms
(* (- a (/ 1.0 3.0)) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))
103.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
79.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify14.0s

Counts
109 → 139
Calls
109 calls:
Slowest
724.0ms
(* (* (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (* rand rand) rand))
514.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
478.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))
407.0ms
(- (* 1/3 (sqrt -3.0)) (+ (* 1.5 (/ a (sqrt -3.0))) (+ (* 4.5 (/ (pow a 2) (sqrt -3.0))) (* 3.375 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
384.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.4s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes129.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.3s

Algorithm
intervals
Results
4.1s27227×body80nan
1.3s9123×body80valid