Details

Time bar (total: 1.2m)

sample222.0ms

Algorithm
intervals
Results
140.0ms866×body80nan
39.0ms284×body80valid

simplify222.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
222.0ms
(* (- 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

localize39.0ms

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)))

rewrite145.0ms

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
64.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
36.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
29.0ms
(* 9 (- a (/ 1.0 3.0)))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series299.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
73.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
58.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
48.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify12.0s

Counts
141 → 156
Calls
141 calls:
Slowest
504.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
386.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
317.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
301.0ms
(* (* (* 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)))))))
294.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite275.0ms

Algorithm
rewrite-expression-head
Rules
80×add-sqr-sqrt
58×times-frac
48×*-un-lft-identity
31×associate-*r*
30×add-cube-cbrt
18×difference-of-squares
17×pow1 associate-*r/ sqrt-prod
16×add-cbrt-cube add-exp-log
9×associate-*l* distribute-lft-out--
8×distribute-rgt-in distribute-lft-in
7×pow-prod-down
6×sqrt-div associate-/l*
5×flip3-- prod-exp cbrt-unprod flip--
4×associate-/r* sub-neg associate-/r/ insert-posit16 add-log-exp
3×sqrt-pow1
2×cbrt-undiv div-exp *-commutative div-inv unswap-sqr associate-/l/
1×clear-num frac-2neg pow1/2 div-sub
Counts
4 → 149
Calls
4 calls:
Slowest
140.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))))
55.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
53.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
24.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
119.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))))
108.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
78.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
70.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

simplify19.3s

Counts
145 → 161
Calls
145 calls:
Slowest
804.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- (pow a 3) (pow (/ 1.0 3.0) 3)))))
343.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
323.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
274.0ms
(* (* (* (sqrt 9) (sqrt 9)) (sqrt 9)) (* (* (* (sqrt 9) (- a (/ 1.0 3.0))) (* (sqrt 9) (- a (/ 1.0 3.0)))) (* (sqrt 9) (- a (/ 1.0 3.0)))))
269.0ms
(/ (- (sqrt a) (/ (sqrt 1.0) (sqrt 3.0))) (sqrt (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))))

prune1.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize26.0ms

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)))

rewrite189.0ms

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
101.0ms
(* (/ 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)))
20.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
12.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
220.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
106.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
105.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
65.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify13.6s

Counts
114 → 140
Calls
114 calls:
Slowest
800.0ms
(* (* (* (/ 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))
495.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (+ (pow 1 3) (pow (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand) 3)))
451.0ms
(* (+ a (/ 1.0 3.0)) (- 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
403.0ms
(- (* 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))))))
397.0ms
(+ (* 1 1) (- (* (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand) (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)) (* 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))

prune1.4s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)
0.1b
(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite120.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
19×add-exp-log
15×*-un-lft-identity
14×associate-*l*
12×associate-*r*
11×pow1 add-cube-cbrt
10×add-cbrt-cube
8×prod-exp
4×frac-times flip3-- pow-exp associate-*r/ insert-posit16 flip-- add-log-exp difference-of-squares unswap-sqr
3×distribute-rgt-in pow-unpow distribute-lft-in flip3-+ pow-prod-down *-commutative cbrt-unprod flip-+ sqr-pow
2×pow-to-exp sub-neg unpow-prod-down pow-pow times-frac associate-*l/ distribute-lft-out--
Counts
4 → 102
Calls
4 calls:
Slowest
55.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
27.0ms
(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)
19.0ms
(* 9 (- a (/ 1.0 3.0)))
17.0ms
(pow (* 9 (- a (/ 1.0 3.0))) -1/2)

series542.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
230.0ms
(* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)
128.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)))
124.0ms
(pow (* 9 (- a (/ 1.0 3.0))) -1/2)
60.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify13.4s

Counts
79 → 114
Calls
79 calls:
Slowest
1.1s
(+ (* 1 1) (- (* (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand) (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand)) (* 1 (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) rand))))
635.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
515.0ms
(+ (* 0.041666666666666664 (/ (exp (* -1/2 (- (log 9) (log (/ 1 a))))) (pow a 2))) (+ (exp (* -1/2 (- (log 9) (log (/ 1 a))))) (* 0.16666666666666666 (/ (exp (* -1/2 (- (log 9) (log (/ 1 a))))) a))))
463.0ms
(+ (exp (* -1/2 (- (log -9) (log (/ -1 a))))) (+ (* 0.041666666666666664 (/ (exp (* -1/2 (- (log -9) (log (/ -1 a))))) (pow a 2))) (* 0.16666666666666666 (/ (exp (* -1/2 (- (log -9) (log (/ -1 a))))) a))))
437.0ms
(* (* (* (pow (* 9 (- a (/ 1.0 3.0))) -1/2) (pow (* 9 (- a (/ 1.0 3.0))) -1/2)) (pow (* 9 (- a (/ 1.0 3.0))) -1/2)) (* (* rand rand) rand))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes110.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.4s27374×body80nan
1.4s9125×body80valid