Details

Time bar (total: 1.5m)

sample231.0ms

Algorithm
intervals
Results
115.0ms902×body80nan
77.0ms294×body80valid

simplify197.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
197.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite153.0ms

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
48.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
47.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
39.0ms
(* 9 (- a (/ 1.0 3.0)))
15.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series373.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
140.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
96.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
75.0ms
(* 9 (- a (/ 1.0 3.0)))
62.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.4s

Counts
141 → 156
Calls
141 calls:
Slowest
518.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
406.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
378.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
334.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
317.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune1.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))
0.3b
(* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0))))
0.3b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))))
0.2b
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))))

rewrite469.0ms

Algorithm
rewrite-expression-head
Rules
97×add-sqr-sqrt
60×times-frac
57×*-un-lft-identity
52×associate-*r*
31×add-cube-cbrt
27×associate-*r/
24×sqrt-prod difference-of-squares
18×add-cbrt-cube add-exp-log
16×sqrt-div associate-/r/
13×pow1
12×frac-times
11×distribute-lft-out--
10×flip3-+ flip3-- flip-+ flip--
7×associate-*l*
6×associate-*l/ prod-exp cbrt-unprod associate-/l*
5×pow-prod-down
4×associate-/r* insert-posit16 add-log-exp
3×distribute-rgt-in distribute-lft-in *-commutative unswap-sqr
2×cbrt-undiv sub-neg div-exp div-inv distribute-lft-out associate-/l/
1×clear-num frac-2neg div-sub
Counts
4 → 178
Calls
4 calls:
Slowest
257.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))))
83.0ms
(* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))
74.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))))
52.0ms
(* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0))))

series9.7s

Counts
4 → 12
Calls
4 calls:
Slowest
4.8s
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))))
4.5s
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))))
331.0ms
(* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))
78.0ms
(* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0))))

simplify30.2s

Counts
178 → 190
Calls
178 calls:
Slowest
705.0ms
(/ (- a (/ 1.0 3.0)) (cbrt (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))))
657.0ms
(* (* 9 (+ (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3))) (- (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)))
559.0ms
(* (* 9 (- (* (sqrt a) (sqrt a)) (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0))))) (- (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3)))
476.0ms
(* (* (* rand rand) rand) (/ (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))) (* (* (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))))))
427.0ms
(* (* 9 (+ (pow (sqrt a) 3) (pow (sqrt (/ 1.0 3.0)) 3))) (- (sqrt a) (sqrt (/ 1.0 3.0))))

prune2.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (- a (/ 1.0 3.0))) 3)
0.3b
(* 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)))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
50×add-sqr-sqrt
34×*-un-lft-identity
32×times-frac
30×sqrt-prod
24×add-cube-cbrt
20×add-exp-log
15×add-cbrt-cube
10×pow1 difference-of-squares
9×prod-exp associate-/l* add-log-exp
5×cbrt-unprod distribute-lft-out--
4×sqrt-div insert-posit16
3×associate-/r* flip3-- div-exp associate-*l* pow-prod-down associate-*l/ associate-*r/ flip--
2×cbrt-undiv associate-+r+ sum-log 1-exp frac-add associate-/l/
1×+-commutative rem-sqrt-square clear-num associate-+r- sub-neg frac-2neg sqrt-pow1 flip3-+ pow1/2 diff-log associate-*r* *-commutative flip-+ div-inv
Counts
4 → 115
Calls
4 calls:
Slowest
56.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
36.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
25.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
9.0ms
(sqrt (- a (/ 1.0 3.0)))

series293.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
118.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
72.0ms
(+ (* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (- a (/ 1.0 3.0)))
60.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
43.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify7.4s

Counts
111 → 127
Calls
111 calls:
Slowest
458.0ms
(* (* (* rand rand) rand) (* (/ (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))) (* (* 3 3) 3)) (* (* 1 1) 1)))
388.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
364.0ms
(* 3 (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
334.0ms
(+ (* (* rand (* (sqrt (- a (/ 1.0 3.0))) 1)) (+ a (/ 1.0 3.0))) (* 3 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
329.0ms
(* (* (* rand rand) rand) (* (* (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1) (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)) (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1)))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

rewrite219.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
27×*-un-lft-identity times-frac
24×associate-*l* add-cube-cbrt
19×add-exp-log
15×pow1
13×add-cbrt-cube
8×associate-*r/ sqrt-prod
6×flip3-- sqrt-div associate-*r* flip--
5×prod-exp
4×frac-times associate-/r* sqrt-pow1 div-exp pow-prod-down associate-/r/ insert-posit16 pow-flip add-log-exp unswap-sqr
3×flip3-+ associate-*l/ cbrt-unprod flip-+ associate-/l*
2×cbrt-undiv rec-exp pow1/2 1-exp *-commutative div-inv difference-of-squares
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in distribute-lft-out-- inv-pow
Counts
4 → 128
Calls
4 calls:
Slowest
116.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
53.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
33.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series549.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
126.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
99.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
91.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify13.0s

Counts
114 → 140
Calls
114 calls:
Slowest
681.0ms
(* (* (* (/ 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))
419.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (+ (pow 1 3) (pow (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand) 3)))
412.0ms
(* (+ a (/ 1.0 3.0)) (- 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
411.0ms
(- (* 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))))))
357.0ms
(* (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))) (- 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes310.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
3.6s26867×body80nan
1.6s9092×body80valid