Details

Time bar (total: 3.0m)

sample170.0ms

Algorithm
intervals
Results
108.0ms925×body80nan
35.0ms301×body80valid

simplify284.0ms

Calls
1 calls:
Slowest
284.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite133.0ms

Algorithm
rewrite-expression-head
Rules
157×add-sqr-sqrt
124×*-un-lft-identity
114×times-frac
112×add-cube-cbrt
78×prod-diff
75×sqrt-prod
41×distribute-rgt-in distribute-lft-in
36×associate-*r*
18×associate-/r* associate-*l*
12×difference-of-squares
9×pow1
8×add-cbrt-cube add-exp-log
7×div-inv unswap-sqr
6×associate-*r/ *-commutative distribute-lft-out--
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- flip-- associate-/l*
2×rem-sqrt-square sub-neg sqrt-pow1 pow-prod-down associate-/r/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp prod-exp cbrt-unprod fma-udef
Calls
4 calls:
Slowest
49.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
44.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
30.0ms
(* 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)))

series420.0ms

Calls
4 calls:
Slowest
156.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
108.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
102.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
54.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify28.7s

Calls
262 calls:
Slowest
770.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
535.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
411.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
406.0ms
(* (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))))) 9)
391.0ms
(* (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))) 9)

prune2.8s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 3 expressions with local error:

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

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
402×times-frac
304×add-sqr-sqrt
237×sqrt-prod
231×*-un-lft-identity
183×add-cube-cbrt
48×difference-of-squares
25×associate-/l*
24×distribute-lft-out--
15×associate-/r*
12×associate-/l/
11×div-inv
8×add-cbrt-cube add-exp-log
4×pow1 sqrt-div
3×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg flip3-- associate-/r/ flip--
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Calls
3 calls:
Slowest
25.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
19.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series363.0ms

Calls
3 calls:
Slowest
171.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
120.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
72.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify25.2s

Calls
459 calls:
Slowest
476.0ms
(/ (* (* (/ rand (sqrt 9)) (/ rand (sqrt 9))) (/ rand (sqrt 9))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
455.0ms
(/ (/ (* (* rand rand) rand) (* (* (sqrt 9) (sqrt 9)) (sqrt 9))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
449.0ms
(/ (/ (* (cbrt rand) (cbrt rand)) (* (cbrt (sqrt 9)) (cbrt (sqrt 9)))) (* (cbrt (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt (- a (/ 1.0 3.0))))))
417.0ms
(/ (/ (sqrt rand) (* (cbrt (sqrt 9)) (cbrt (sqrt 9)))) (sqrt (* (cbrt (- a (/ 1.0 3.0))) (cbrt (- a (/ 1.0 3.0))))))
275.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune3.7s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
252×times-frac
215×add-sqr-sqrt
160×*-un-lft-identity
124×add-cube-cbrt
108×sqrt-prod
39×associate-/l*
36×difference-of-squares
21×associate-/r*
18×distribute-lft-out--
15×associate-/l/
12×sqrt-div
11×add-cbrt-cube add-exp-log
10×associate-/r/
6×flip3-- div-inv flip--
5×pow1
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Calls
4 calls:
Slowest
47.0ms
(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3)
23.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
20.0ms
(sqrt (- a (/ 1.0 3.0)))
1.0ms
(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series445.0ms

Calls
4 calls:
Slowest
156.0ms
(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3)
134.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
101.0ms
(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
53.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify18.8s

Calls
338 calls:
Slowest
482.0ms
(/ (/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))) (* (* 3 3) 3))
462.0ms
(/ (/ (* (cbrt rand) (cbrt rand)) (* (cbrt (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt (- a (/ 1.0 3.0)))))) (* (cbrt 3) (cbrt 3)))
387.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
320.0ms
(/ (/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))) (* (cbrt 3) (cbrt 3)))
309.0ms
(/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune3.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite416.0ms

Algorithm
rewrite-expression-head
Rules
331×add-sqr-sqrt
253×*-un-lft-identity
232×times-frac
227×add-cube-cbrt
167×sqrt-prod
156×prod-diff
96×associate-*l*
82×distribute-rgt-in distribute-lft-in
78×associate-*r*
72×associate-/r*
48×frac-times
29×flip3-- flip--
26×difference-of-squares
24×associate-*l/
18×unswap-sqr
14×div-inv
13×add-cbrt-cube add-exp-log *-commutative distribute-lft-out--
12×associate-/l*
11×pow1
10×associate-*r/
6×sqrt-div
4×expm1-log1p-u clear-num sub-neg frac-2neg associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×cbrt-undiv rem-sqrt-square sqrt-pow1 div-exp
1×pow1/2
Calls
4 calls:
Slowest
227.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
66.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
54.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
43.0ms
(* 9 (- a (/ 1.0 3.0)))

series479.0ms

Calls
4 calls:
Slowest
164.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
157.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
97.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
61.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify1.4m

Calls
543 calls:
Slowest
640.0ms
(* (- (sqrt (* 9 (- a (/ 1.0 3.0))))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
593.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
589.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (fma (- (/ (cbrt 1.0) (sqrt 3.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 3.0)) (* (/ (cbrt 1.0) (sqrt 3.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 3.0)))))
512.0ms
(* (/ rand (sqrt (* 9 1))) (- (pow a 3) (pow (/ 1.0 3.0) 3)))
507.0ms
(* (/ rand (sqrt (* 9 (* (cbrt (- a (/ 1.0 3.0))) (cbrt (- a (/ 1.0 3.0))))))) (- (pow a 3) (pow (/ 1.0 3.0) 3)))

prune5.9s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes159.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
4.1s27460×body80nan
1.3s9161×body80valid