Details

Time bar (total: 1.1m)

sample194.0ms

Algorithm
intervals
Results
117.0ms888×body80nan
40.0ms301×body80valid

simplify194.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
194.0ms
(* (- 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

localize44.0ms

Local error

Found 4 expressions with local error:

0.6b
(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)
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

rewrite185.0ms

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
88.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
52.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
28.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
14.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)
110.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
106.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
105.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.9s

Counts
114 → 140
Calls
114 calls:
Slowest
663.0ms
(* (* (* (/ 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))
404.0ms
(* (+ a (/ 1.0 3.0)) (- 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))
386.0ms
(- (* 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
(+ (* 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))))
375.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ (pow 1 3) (pow (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand) 3)))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.2b
(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))

rewrite158.0ms

Algorithm
rewrite-expression-head
Rules
96×add-sqr-sqrt
66×times-frac
60×*-un-lft-identity
44×sqrt-prod
42×add-cube-cbrt
39×associate-*r*
34×add-exp-log
22×add-cbrt-cube
16×difference-of-squares
15×pow1
14×prod-exp
10×associate-*l*
9×associate-/r*
8×cbrt-unprod distribute-lft-out--
6×div-exp unswap-sqr
5×flip3-- pow-prod-down flip--
4×frac-times sqrt-div associate-*l/ associate-*r/ associate-/r/ insert-posit16 add-log-exp
3×cbrt-undiv rec-exp flip3-+ 1-exp *-commutative flip-+ pow-flip associate-/l*
2×un-div-inv div-inv
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in sqrt-pow1 pow1/2 inv-pow
Counts
4 → 176
Calls
4 calls:
Slowest
66.0ms
(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
40.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
25.0ms
(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))
24.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))

series531.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
254.0ms
(* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)
99.0ms
(* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))
91.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
87.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))

simplify13.7s

Counts
179 → 188
Calls
179 calls:
Slowest
771.0ms
(* (* (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))) (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0)))))) (* (* rand rand) rand))
466.0ms
(* (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))) (- 1 (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand)))
435.0ms
(- (* 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))))))
424.0ms
(/ (* (cbrt 1) (cbrt 1)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0)))))
385.0ms
(* (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))) (+ (pow 1 3) (pow (* (* 1/3 (/ 1 (sqrt (- a (/ 1.0 3.0))))) rand) 3)))

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.1b
(* (- a (/ 1.0 3.0)) (+ 1 (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
27×*-un-lft-identity times-frac
24×add-cube-cbrt
21×associate-*r*
19×add-exp-log
15×pow1
13×add-cbrt-cube
9×associate-*l* associate-*r/
8×sqrt-prod
6×flip3-- sqrt-div 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-+ cbrt-unprod flip-+ associate-/l*
2×cbrt-undiv rec-exp pow1/2 1-exp associate-*l/ *-commutative div-inv difference-of-squares
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in un-div-inv distribute-lft-out-- inv-pow
Counts
4 → 129
Calls
4 calls:
Slowest
61.0ms
(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
46.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))))
33.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
13.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
115.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
111.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))))
74.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify12.9s

Counts
117 → 141
Calls
117 calls:
Slowest
533.0ms
(* (* (* rand rand) rand) (* (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))
423.0ms
(* (+ a (/ 1.0 3.0)) (- 1 (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))))
416.0ms
(- (* 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))))))
379.0ms
(+ (* 1 1) (- (* (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))) (* 1 (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))))
343.0ms
(* (- (pow a 3) (pow (/ 1.0 3.0) 3)) (+ (pow 1 3) (pow (* rand (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) 3)))

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.6b
(sqrt (* 9 (- a (/ 1.0 3.0))))
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))))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite140.0ms

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
60.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
39.0ms
(* 9 (- a (/ 1.0 3.0)))
30.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
6.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series433.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
162.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
110.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
89.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
71.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify12.7s

Counts
141 → 156
Calls
141 calls:
Slowest
541.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
500.0ms
(/ (- (sqrt a) (sqrt (/ 1.0 3.0))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
358.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
342.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))
327.0ms
(* (* (* 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)))))))

prune1.7s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes144.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample6.4s

Algorithm
intervals
Results
4.1s27717×body80nan
1.3s9149×body80valid