Details

Time bar (total: 36.3s)

sample203.0ms

Algorithm
intervals
Results
110.0ms855×body80nan
37.0ms291×body80valid

simplify212.0ms

Calls
1 calls:
Slowest
212.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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)))

rewrite151.0ms

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
Calls
4 calls:
Slowest
68.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
49.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
26.0ms
(* 9 (- a (/ 1.0 3.0)))
6.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series369.0ms

Calls
4 calls:
Slowest
147.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
78.0ms
(* 9 (- a (/ 1.0 3.0)))
73.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
71.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.3s

Calls
141 calls:
Slowest
459.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
436.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
383.0ms
(* (* (* 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)))))))
329.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
282.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

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
(- a (/ 1.0 3.0))
0.0b
(- a (/ 1.0 3.0))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
35×*-un-lft-identity
33×times-frac
24×sqrt-prod
23×add-cube-cbrt
20×add-exp-log
15×add-cbrt-cube
12×difference-of-squares
9×pow1 prod-exp associate-/l*
8×add-log-exp
6×distribute-lft-out--
5×cbrt-unprod
4×insert-posit16
3×associate-/r* flip3-- div-exp associate-*l* pow-prod-down flip--
2×cbrt-undiv sub-neg sqrt-div diff-log 1-exp associate-/l/
1×clear-num frac-2neg associate-*r* associate-*l/ associate-*r/ *-commutative div-inv
Calls
4 calls:
Slowest
34.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
31.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
11.0ms
(- a (/ 1.0 3.0))
5.0ms
(- a (/ 1.0 3.0))

series264.0ms

Calls
4 calls:
Slowest
127.0ms
(* rand (* (/ (sqrt (- a (/ 1.0 3.0))) 3) 1))
80.0ms
(/ (sqrt (- a (/ 1.0 3.0))) 3)
32.0ms
(- a (/ 1.0 3.0))
25.0ms
(- a (/ 1.0 3.0))

simplify5.5s

Calls
104 calls:
Slowest
414.0ms
(* (* (* 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)))
407.0ms
(/ (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (* (cbrt 3) (cbrt 3)))
341.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
274.0ms
(* (* (* rand rand) rand) (* (* (* (/ (sqrt (- a (/ 1.0 3.0))) 3) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (/ (sqrt (- a (/ 1.0 3.0))) 3)) (* (* 1 1) 1)))
254.0ms
(* (* (* 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

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
23×add-exp-log
18×add-cbrt-cube
17×add-sqr-sqrt
11×*-un-lft-identity
10×prod-exp
9×pow1
8×add-log-exp
7×add-cube-cbrt
6×cbrt-unprod
5×times-frac
4×flip3-- sqrt-div div-exp associate-*l/ associate-*r/ insert-posit16 flip-- difference-of-squares
3×cbrt-undiv associate-/r* associate-*l* pow-prod-down
2×sub-neg diff-log 1-exp distribute-lft-out-- associate-/l/
1×clear-num frac-2neg associate-*r* *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
53.0ms
(* rand (* (sqrt (- a (/ 1.0 3.0))) 1))
37.0ms
(/ (* rand (* (sqrt (- a (/ 1.0 3.0))) 1)) 3)
6.0ms
(- a (/ 1.0 3.0))
5.0ms
(- a (/ 1.0 3.0))

series312.0ms

Calls
4 calls:
Slowest
149.0ms
(/ (* rand (* (sqrt (- a (/ 1.0 3.0))) 1)) 3)
80.0ms
(* rand (* (sqrt (- a (/ 1.0 3.0))) 1))
41.0ms
(- a (/ 1.0 3.0))
41.0ms
(- a (/ 1.0 3.0))

simplify3.1s

Calls
52 calls:
Slowest
249.0ms
(* rand (* (sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3))) 1))
221.0ms
(* rand (* (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))) 1))
208.0ms
(* (* (* rand rand) rand) (* (* (* (sqrt (- a (/ 1.0 3.0))) 1) (* (sqrt (- a (/ 1.0 3.0))) 1)) (* (sqrt (- a (/ 1.0 3.0))) 1)))
206.0ms
(* (* (* rand rand) rand) (* (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))) (* (* 1 1) 1)))
163.0ms
(/ (* (* (* rand rand) rand) (* (* (* (sqrt (- a (/ 1.0 3.0))) 1) (* (sqrt (- a (/ 1.0 3.0))) 1)) (* (sqrt (- a (/ 1.0 3.0))) 1))) (* (* 3 3) 3))

prune876.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
14×*-un-lft-identity
11×pow1 add-cbrt-cube add-exp-log
10×associate-*r*
8×add-cube-cbrt add-log-exp
7×sqrt-prod
6×associate-*l* associate-*r/ difference-of-squares
4×flip3-- sqrt-div pow-prod-down prod-exp cbrt-unprod insert-posit16 flip--
3×times-frac distribute-lft-out--
2×sub-neg diff-log *-commutative unswap-sqr
Calls
4 calls:
Slowest
53.0ms
(* rand (* 1/3 (sqrt (- a (/ 1.0 3.0)))))
45.0ms
(* 1/3 (sqrt (- a (/ 1.0 3.0))))
11.0ms
(- a (/ 1.0 3.0))
11.0ms
(- a (/ 1.0 3.0))

series279.0ms

Calls
4 calls:
Slowest
111.0ms
(* rand (* 1/3 (sqrt (- a (/ 1.0 3.0)))))
82.0ms
(* 1/3 (sqrt (- a (/ 1.0 3.0))))
45.0ms
(- a (/ 1.0 3.0))
40.0ms
(- a (/ 1.0 3.0))

simplify2.6s

Calls
55 calls:
Slowest
577.0ms
(* (* (* rand rand) rand) (* (* (* 1/3 (sqrt (- a (/ 1.0 3.0)))) (* 1/3 (sqrt (- a (/ 1.0 3.0))))) (* 1/3 (sqrt (- a (/ 1.0 3.0))))))
278.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
243.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
145.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
125.0ms
(* (* (* rand rand) rand) (* (* (* 1/3 1/3) 1/3) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))))

prune838.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
4.1s27427×body80nan
1.2s9054×body80valid