Details

Time bar (total: 4.3m)

sample217.0ms

Algorithm
intervals
Results
123.0ms920×body80nan
38.0ms292×body80valid

simplify268.0ms

Calls
1 calls:
Slowest
267.0ms
(* (- 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

localize21.0ms

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)))

rewrite130.0ms

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
56.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
49.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
21.0ms
(* 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)))

series439.0ms

Calls
4 calls:
Slowest
172.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
119.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
77.0ms
(* 9 (- a (/ 1.0 3.0)))
71.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify28.4s

Calls
262 calls:
Slowest
557.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
470.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
405.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
382.0ms
(* (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)
372.0ms
(* (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))) 9)

prune3.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite527.0ms

Algorithm
rewrite-expression-head
Rules
392×add-sqr-sqrt
257×sqrt-prod
237×*-un-lft-identity
231×times-frac
225×add-cube-cbrt
164×distribute-rgt-in distribute-lft-in
156×prod-diff
150×associate-*r*
82×unswap-sqr
72×associate-*l*
39×associate-/r*
15×pow1
13×div-inv
12×associate-*r/ *-commutative difference-of-squares
11×add-cbrt-cube add-exp-log
7×rem-sqrt-square
6×pow-prod-down distribute-lft-out--
4×expm1-log1p-u sub-neg sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 flip3-- prod-exp cbrt-unprod flip-- associate-/l*
2×associate-/r/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp fma-udef
Calls
4 calls:
Slowest
219.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
187.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
98.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
0.0ms
(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series397.0ms

Calls
4 calls:
Slowest
144.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
114.0ms
(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
74.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
65.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

simplify1.4m

Calls
547 calls:
Slowest
741.0ms
(* (sqrt 9) (* (sqrt 9) (fma (- (/ 1.0 3.0)) (/ 1 1) (* (/ 1.0 3.0) (/ 1 1)))))
694.0ms
(* (* (sqrt 9) (fma (- (/ 1.0 3.0)) 1 (* (/ 1.0 3.0) 1))) (sqrt 9))
671.0ms
(* (* (sqrt 9) (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0))))) (sqrt 9))
664.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)))
644.0ms
(* (* (sqrt 9) (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0))))) (sqrt 9))

prune5.9s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 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)))

rewrite94.0ms

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
54.0ms
(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3)
23.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
11.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series411.0ms

Calls
4 calls:
Slowest
151.0ms
(/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3)
115.0ms
(fma (/ (/ rand (sqrt (- a (/ 1.0 3.0)))) 3) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
99.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
47.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify19.2s

Calls
338 calls:
Slowest
488.0ms
(/ (/ (* (cbrt rand) (cbrt rand)) (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0))))) (* (cbrt 3) (cbrt 3)))
451.0ms
(/ (/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))) (* (* 3 3) 3))
376.0ms
(/ (/ (* (cbrt rand) (cbrt rand)) (* (cbrt (sqrt (- a (/ 1.0 3.0)))) (cbrt (sqrt (- a (/ 1.0 3.0)))))) (* (cbrt 3) (cbrt 3)))
323.0ms
(/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
322.0ms
(/ (/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))) (* (cbrt 3) (cbrt 3)))

prune3.1s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
0.2b
(* (/ 1 (fabs (cbrt 9))) (/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
0.2b
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
0.1b
(* (cbrt 9) (- a (/ 1.0 3.0)))

rewrite381.0ms

Algorithm
rewrite-expression-head
Rules
514×add-sqr-sqrt
351×sqrt-prod
329×associate-/r* *-un-lft-identity
285×add-cube-cbrt
252×frac-times
236×times-frac
186×associate-*r*
127×associate-*l*
121×associate-/l*
80×cbrt-prod
78×prod-diff
61×unswap-sqr
41×distribute-rgt-in clear-num distribute-lft-in
40×frac-2neg
38×difference-of-squares
36×associate-*r/
30×add-exp-log
21×add-cbrt-cube
20×*-commutative
19×distribute-lft-out--
11×pow1
9×div-exp associate-*l/ prod-exp div-inv
6×sqrt-div cbrt-unprod
5×cbrt-undiv
4×expm1-log1p-u flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip-- add-log-exp
3×rem-sqrt-square pow-prod-down
2×rec-exp sub-neg sqrt-pow1 1-exp un-div-inv
1×pow1/2
Calls
4 calls:
Slowest
217.0ms
(* (/ 1 (fabs (cbrt 9))) (/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
58.0ms
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
45.0ms
(/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
36.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))

series1.5s

Calls
4 calls:
Slowest
713.0ms
(* (/ 1 (fabs (cbrt 9))) (/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
458.0ms
(/ rand (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
201.0ms
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
135.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))

simplify1.6m

Calls
970 calls:
Slowest
770.0ms
(* (cbrt 9) (fma (- (/ (sqrt 1.0) (cbrt 3.0))) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (sqrt 1.0) (cbrt 3.0)) (/ (sqrt 1.0) (* (cbrt 3.0) (cbrt 3.0))))))
751.0ms
(- (/ (* rand (sqrt (/ -3.0 (cbrt 9)))) (fabs (cbrt 9))) (+ (* 4.5 (/ (* a rand) (* (fabs (cbrt 9)) (* (sqrt (/ -3.0 (cbrt 9))) (cbrt 9))))) (+ (* 10.125 (/ (* (pow a 2) rand) (* (fabs (cbrt 9)) (* (pow (cbrt 9) 2) (pow (sqrt (/ -3.0 (cbrt 9))) 3))))) (* 13.5 (/ (* (pow a 2) rand) (* (fabs (cbrt 9)) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9))))))))))
654.0ms
(* (* (* (cbrt 9) (cbrt 9)) (cbrt 9)) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
551.0ms
(- (* rand (sqrt (/ -3.0 (cbrt 9)))) (+ (* 13.5 (/ (* (pow a 2) rand) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9)))))) (+ (* 10.125 (/ (* (pow a 2) rand) (* (pow (sqrt (/ -3.0 (cbrt 9))) 3) (pow (cbrt 9) 2)))) (* 4.5 (/ (* a rand) (* (cbrt 9) (sqrt (/ -3.0 (cbrt 9)))))))))
528.0ms
(* (/ (fabs (cbrt 9)) 1) (sqrt (* (cbrt (cbrt 9)) (- a (/ 1.0 3.0)))))

prune9.5s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.0b

regimes238.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
4.6s27536×body80nan
1.2s9135×body80valid