Details

Time bar (total: 3.7m)

sample192.0ms

Algorithm
intervals
Results
125.0ms918×body80nan
32.0ms292×body80valid

simplify606.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
606.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.4b
(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)))

rewrite101.0ms

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
44.0ms
(* 9 (- a (/ 1.0 3.0)))
25.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms
(/ 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)))

series401.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
136.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
100.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
93.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
72.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify22.9s

Counts
148 → 183
Calls
148 calls:
Slowest
605.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
412.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
399.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
392.0ms
(* (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))) 9)
389.0ms
(* 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))))))

prune2.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

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)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
177×add-sqr-sqrt
164×*-un-lft-identity
160×add-cube-cbrt
156×prod-diff
135×times-frac
82×distribute-rgt-in distribute-lft-in
21×associate-*l*
14×div-inv
13×add-cbrt-cube add-exp-log
12×associate-*r*
11×pow1
10×associate-*r/
8×sqrt-prod
6×flip3-- sqrt-div flip--
4×expm1-log1p-u associate-/r* sub-neg associate-/r/ insert-posit16 log1p-expm1-u add-log-exp difference-of-squares
3×pow-prod-down prod-exp cbrt-unprod associate-/l* unswap-sqr
2×frac-times cbrt-undiv sqrt-pow1 div-exp *-commutative distribute-lft-out--
1×clear-num frac-2neg pow1/2 associate-*l/
Counts
4 → 289
Calls
4 calls:
Slowest
109.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
29.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
28.0ms
(* 9 (- a (/ 1.0 3.0)))
24.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series476.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
174.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
148.0ms
(* (/ rand (sqrt (* 9 (- 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)))

simplify48.4s

Counts
268 → 301
Calls
268 calls:
Slowest
642.0ms
(* 9 (fma (- (/ (sqrt 1.0) (sqrt 3.0))) (/ (sqrt 1.0) (sqrt 3.0)) (* (/ (sqrt 1.0) (sqrt 3.0)) (/ (sqrt 1.0) (sqrt 3.0)))))
604.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
580.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (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))))))
441.0ms
(* rand (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
439.0ms
(* (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)

prune3.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.9b
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.2b
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
0.1b
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

rewrite49.0ms

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
20.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
16.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
11.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
0.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series605.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
217.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
164.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
143.0ms
(fma (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
81.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify17.8s

Counts
171 → 166
Calls
171 calls:
Slowest
624.0ms
(/ (* (* 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)))
512.0ms
(/ (sqrt 1) (/ (sqrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt rand)))
436.0ms
(/ (* (cbrt 1) (cbrt 1)) (/ (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (cbrt rand) (cbrt rand))))
394.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
378.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))

prune1.7s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize44.0ms

Local error

Found 4 expressions with local error:

6.8b
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
0.3b
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.0b
(sqrt (- a (/ 1.0 3.0)))
0.0b
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))

rewrite245.0ms

Algorithm
rewrite-expression-head
Rules
930×times-frac
774×add-sqr-sqrt
611×*-un-lft-identity
514×add-cube-cbrt
452×sqrt-prod
204×associate-*l*
195×prod-diff
94×difference-of-squares
82×distribute-rgt-in associate-+l+ distribute-lft-in
48×distribute-lft-out--
41×associate-+r+
36×div-inv
22×associate-/l*
18×add-cbrt-cube add-exp-log
14×flip3-- flip--
10×frac-add
9×associate-/r* add-log-exp
7×pow1 unswap-sqr
6×frac-times cbrt-undiv sqrt-div div-exp associate-*r* associate-*r/
5×sub-neg
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u
3×associate-*l/ prod-exp cbrt-unprod
2×sum-log distribute-rgt-out
1×+-commutative rem-sqrt-square clear-num associate-+r- fma-def frac-2neg distribute-lft1-in sqrt-pow1 flip3-+ pow1/2 diff-log pow-prod-down *-commutative flip-+ associate-/l/
Counts
4 → 745
Calls
4 calls:
Slowest
112.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
49.0ms
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
32.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
25.0ms
(sqrt (- a (/ 1.0 3.0)))

series489.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
138.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
119.0ms
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
70.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify1.8m

Counts
924 → 757
Calls
924 calls:
Slowest
879.0ms
(* (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))))) (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))))
668.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (fma 1 a (- (* (/ 1.0 3.0) 1))))
625.0ms
(+ (* (* (/ rand (sqrt 9)) (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (* (sqrt (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
569.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (fma (- (/ (cbrt 1.0) 3.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) 1) (* (/ (cbrt 1.0) 3.0) (/ (* (cbrt 1.0) (cbrt 1.0)) 1))))
562.0ms
(+ (* (* (/ rand (sqrt 9)) (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ a (/ 1.0 3.0))) (* (* (sqrt (- a (/ 1.0 3.0))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune10.0s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes125.0ms

Accuracy

0% (0.1b remaining)

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

bsearch5.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.6s27373×body80nan
1.3s9112×body80valid