Details

Time bar (total: 42.5s)

sample158.0ms

Algorithm
intervals
Results
102.0ms922×body80nan
29.0ms291×body80valid

simplify259.0ms

Calls
1 calls:
Slowest
259.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

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)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity associate-*r/ add-cube-cbrt
4×expm1-log1p-u pow1 associate-/r* add-cbrt-cube sqrt-div add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*r* flip--
2×distribute-rgt-in sub-neg distribute-lft-in associate-/r/ sqrt-prod
1×clear-num frac-2neg pow1/2 *-commutative fma-udef div-inv
Calls
4 calls:
Slowest
4.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
3.0ms
(* 9 (- a (/ 1.0 3.0)))
2.0ms
(/ 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)))

series147.0ms

Calls
4 calls:
Slowest
56.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
46.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
27.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
17.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify2.0s

Calls
30 calls:
Slowest
405.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
243.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
131.0ms
(- (* 1/3 (* (sqrt -3.0) rand)) (+ (* 4.5 (/ (* (pow a 2) rand) (sqrt -3.0))) (+ (* 1.5 (/ (* a rand) (sqrt -3.0))) (* 3.375 (/ (* (pow a 2) rand) (pow (sqrt -3.0) 3))))))
130.0ms
(sqrt (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
130.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))

prune717.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.2b
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.1b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×associate-*r/
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×pow1 flip3-- add-cbrt-cube sqrt-div associate-*r* associate-*l* add-exp-log flip--
4×distribute-rgt-in expm1-log1p-u associate-/r* sub-neg distribute-lft-in associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
2×frac-times *-commutative sqrt-prod div-inv
1×clear-num frac-2neg pow1/2 pow-prod-down associate-*l/ prod-exp cbrt-unprod
Calls
4 calls:
Slowest
12.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
2.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
2.0ms
(* 9 (- a (/ 1.0 3.0)))
1.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series181.0ms

Calls
4 calls:
Slowest
65.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
55.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
34.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
27.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify5.7s

Calls
51 calls:
Slowest
470.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
397.0ms
(* rand (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
382.0ms
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
373.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
329.0ms
(* (sqrt (* 9 (- a (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune1.0s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)))
0.5b
(/ 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))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube associate-*r/
5×associate-*l*
4×expm1-log1p-u associate-/r* flip3-- sqrt-div insert-posit16 log1p-expm1-u div-inv flip-- associate-/l* add-log-exp
3×associate-*r*
2×distribute-rgt-in frac-times rec-exp clear-num sub-neg frac-2neg distribute-lft-in prod-exp associate-/r/ sqrt-prod associate-/l/
1×pow1/2 pow-prod-down associate-*l/ *-commutative cbrt-unprod pow-flip inv-pow
Calls
4 calls:
Slowest
10.0ms
(* (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)))
3.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
2.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
1.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))

series249.0ms

Calls
4 calls:
Slowest
92.0ms
(/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand))
63.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)
62.0ms
(* (/ 1 (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) rand)) (- a (/ 1.0 3.0)))
33.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify6.0s

Calls
46 calls:
Slowest
445.0ms
(* 1 (- (pow a 3) (pow (/ 1.0 3.0) 3)))
413.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
406.0ms
(- (+ (* 3/2 (/ a (* (sqrt (- 0.3333333333333333)) rand))) (* 3 (/ (sqrt (- 0.3333333333333333)) rand))) (* 3/8 (/ (pow a 2) (* (pow (sqrt (- 0.3333333333333333)) 3) rand))))
387.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
372.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune856.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

8.3b
(* (/ (/ 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)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
39×add-sqr-sqrt *-un-lft-identity
38×add-cube-cbrt
30×associate-*l* sqrt-prod
15×div-inv
14×flip3-- flip--
11×add-cbrt-cube add-exp-log
10×frac-add
6×frac-times pow1 associate-/r* sqrt-div associate-*r/ add-log-exp
5×sub-neg
4×distribute-rgt-in expm1-log1p-u associate-+l+ distribute-lft-in associate-/r/ insert-posit16 log1p-expm1-u associate-/l*
3×associate-*r* associate-*l/
2×cbrt-undiv associate-+r+ div-exp prod-exp cbrt-unprod
1×+-commutative rem-sqrt-square clear-num associate-+r- sum-log fma-def frac-2neg distribute-lft1-in flip3-+ distribute-rgt-out pow1/2 pow-prod-down *-commutative flip-+ associate-/l/
Calls
4 calls:
Slowest
12.0ms
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
8.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
4.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series196.0ms

Calls
4 calls:
Slowest
68.0ms
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
58.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
47.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
23.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify16.9s

Calls
158 calls:
Slowest
816.0ms
(+ (* (* (/ rand (sqrt 9)) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (* (sqrt (- a (/ 1.0 3.0))) (+ a (/ 1.0 3.0))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
546.0ms
(+ (* (* (/ 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))))
528.0ms
(+ (* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (+ a (/ 1.0 3.0)) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
495.0ms
(+ (* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))) (+ (* 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)) (* a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
448.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))

prune1.8s

Pruning

5 alts after pruning (4 fresh and 1 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

bsearch3.0ms

end0.0ms

sample6.0s

Algorithm
intervals
Results
4.0s26886×body80nan
1.3s9160×body80valid