Details

Time bar (total: 1.6m)

sample146.0ms

Algorithm
intervals
Results
72.0ms874×body80nan
27.0ms289×body80valid

simplify221.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
90×add-sqr-sqrt
85×*-un-lft-identity
83×add-cube-cbrt
78×prod-diff
67×times-frac
41×distribute-rgt-in distribute-lft-in
9×pow1
8×add-cbrt-cube add-exp-log
7×div-inv
6×associate-*r* associate-*r/
5×sqrt-prod
4×expm1-log1p-u associate-/r* sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*l* flip-- associate-/l*
2×sub-neg sqrt-pow1 pow-prod-down associate-/r/ difference-of-squares
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp prod-exp *-commutative cbrt-unprod fma-udef distribute-lft-out-- unswap-sqr
Counts
4 → 171
Calls
4 calls:
Slowest
25.0ms
(* 9 (- a (/ 1.0 3.0)))
14.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
11.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series441.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
123.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
82.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
72.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.5s

Counts
148 → 183
Calls
148 calls:
Slowest
589.0ms
(* 9 (fma (- (/ (cbrt 1.0) (cbrt 3.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 1.0) (cbrt 3.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 3.0) (cbrt 3.0))))))
579.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
410.0ms
(* 9 (fma (- (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))) (* (cbrt (/ 1.0 3.0)) (* (cbrt (/ 1.0 3.0)) (cbrt (/ 1.0 3.0))))))
398.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
396.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))

prune2.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ rand (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
64×times-frac
56×*-un-lft-identity
49×sqrt-prod
40×add-cube-cbrt
33×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×associate-/r*
8×distribute-lft-out--
7×pow1
6×sqrt-div
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*l* flip-- associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative fma-udef
Counts
4 → 144
Calls
4 calls:
Slowest
29.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
18.0ms
(sqrt (- a (/ 1.0 3.0)))
13.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
0.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series413.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
155.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
102.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
99.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
57.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify6.3s

Counts
138 → 156
Calls
138 calls:
Slowest
356.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
329.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (/ rand (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt (- a (/ 1.0 3.0))))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
276.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
271.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
256.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))

prune1.6s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
0.2b
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.1b
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
62×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
19×associate-/r*
17×add-exp-log sqrt-prod
11×add-cbrt-cube
8×pow1 div-exp
7×associate-/l*
6×div-inv
4×expm1-log1p-u cbrt-undiv sqrt-div associate-*r/ insert-posit16 log1p-expm1-u add-log-exp
2×rec-exp clear-num frac-2neg sqrt-pow1 flip3-- 1-exp flip-- associate-/l/
1×pow1/2 pow-prod-down associate-/r/ fma-udef pow-flip inv-pow
Counts
4 → 154
Calls
4 calls:
Slowest
21.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
17.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
14.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series592.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
232.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
146.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
141.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
72.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify19.3s

Counts
171 → 166
Calls
171 calls:
Slowest
609.0ms
(/ (* (* 1 1) 1) (* (* (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand) (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)))
579.0ms
(/ 1 (/ (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (sqrt rand)))
428.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (cbrt rand) (cbrt rand))))
427.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
422.0ms
(/ (sqrt 1) (/ (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (cbrt rand) (cbrt rand))))

prune1.7s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

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

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
112×add-sqr-sqrt
106×times-frac
86×sqrt-prod
71×*-un-lft-identity
65×add-cube-cbrt
32×add-exp-log
27×associate-*r* associate-*l*
20×add-cbrt-cube sqrt-div
15×pow1 unswap-sqr
14×associate-/r*
12×sqrt-pow1
11×div-exp associate-*r/
8×prod-exp associate-/r/
6×cbrt-undiv pow-flip associate-/l*
5×flip3-- flip--
4×expm1-log1p-u pow1/2 cbrt-unprod insert-posit16 log1p-expm1-u div-inv add-log-exp
3×rec-exp 1-exp pow-prod-down
2×clear-num frac-2neg
1×frac-times rem-sqrt-square associate-*l/ *-commutative inv-pow
Counts
4 → 223
Calls
4 calls:
Slowest
102.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))
35.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
22.0ms
(/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
16.0ms
(sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
Slowest
317.0ms
(/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
290.0ms
(* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))))
257.0ms
(/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))
180.0ms
(sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))

simplify27.8s

Counts
239 → 235
Calls
239 calls:
Slowest
524.0ms
(* (* (* (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (/ 1 (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (* (* (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))) (/ rand (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))))))
510.0ms
(- (/ (* (sqrt -3.0) rand) (pow (sqrt 3) 2)) (+ (* 10.125 (/ (* (pow a 2) rand) (* (pow (sqrt -3.0) 3) (pow (sqrt 3) 2)))) (+ (* 4.5 (/ (* a rand) (* (sqrt -3.0) (pow (sqrt 3) 2)))) (* 13.5 (/ (* (pow a 2) rand) (* (sqrt -3.0) (pow (sqrt 3) 2)))))))
502.0ms
(/ 1 (sqrt (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))))
417.0ms
(- (+ (* (/ rand (sqrt 3)) (pow -3.0 1/4)) (+ (* 2.53125 (* (/ (* (pow a 2) rand) (sqrt 3)) (pow -3.0 1/4))) (* 0.75 (* (/ (* a rand) (sqrt 3)) (pow -3.0 1/4))))) (* 10.125 (* (/ (* (pow a 2) rand) (sqrt 3)) (pow (/ 1 (pow -3.0 7)) 1/4))))
378.0ms
(- (+ (* (pow -3.0 1/4) (/ 1 (sqrt 3))) (+ (* 0.75 (* (/ a (sqrt 3)) (pow -3.0 1/4))) (* 2.53125 (* (/ (pow a 2) (sqrt 3)) (pow -3.0 1/4))))) (* 10.125 (* (/ (pow a 2) (sqrt 3)) (pow (/ 1 (pow -3.0 7)) 1/4))))

prune3.0s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes131.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.3s27096×body80nan
1.7s9129×body80valid