Details

Time bar (total: 57.2s)

sample192.0ms

Algorithm
intervals
Results
117.0ms804×body80nan
40.0ms292×body80valid

simplify341.0ms

Calls
1 calls:
Slowest
341.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 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)))

rewrite6.0ms

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
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)))))
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
152.0ms
(/ 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)))
95.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
50.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify2.0s

Calls
30 calls:
Slowest
383.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
205.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
156.0ms
(- (* 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))))))
134.0ms
(+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))
127.0ms
(sqrt (* 9 (- (pow a 3) (pow (/ 1.0 3.0) 3))))

prune656.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.3b
(/ 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)))

rewrite25.0ms

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
14.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
4.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
4.0ms
(* 9 (- a (/ 1.0 3.0)))
2.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series475.0ms

Calls
4 calls:
Slowest
164.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
139.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
95.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
77.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify5.8s

Calls
51 calls:
Slowest
440.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))
430.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
405.0ms
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
348.0ms
(* rand (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
243.0ms
(* (sqrt (* 9 (- a (/ 1.0 3.0)))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

8.9b
(* (/ (/ 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)))

rewrite29.0ms

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)))
9.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
5.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series499.0ms

Calls
4 calls:
Slowest
168.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
139.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
111.0ms
(+ (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0)))
82.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify17.5s

Calls
158 calls:
Slowest
654.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
581.0ms
(+ (* (* (/ (/ 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))))
522.0ms
(* (/ (* (* (/ 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))))) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
522.0ms
(+ (* (* (/ 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))))
497.0ms
(+ (* (* (/ (/ 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))))

prune1.8s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize8.0ms

Local error

Found 4 expressions with local error:

8.6b
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
0.4b
(* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
0.3b
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
42×add-sqr-sqrt
41×*-un-lft-identity add-cube-cbrt
36×sqrt-prod
34×sqrt-div
31×associate-*l*
20×add-cbrt-cube add-exp-log
18×frac-times
17×flip3-- flip--
15×div-inv
12×associate-*r*
11×pow1
10×associate-*r/
9×associate-*l/
7×prod-exp cbrt-unprod
6×associate-/r*
4×expm1-log1p-u pow-prod-down associate-/r/ insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×cbrt-undiv div-exp
2×*-commutative
1×rem-sqrt-square clear-num frac-2neg pow1/2 associate-/l/
Calls
4 calls:
Slowest
25.0ms
(* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
9.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
4.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
1.0ms
(sqrt (- a (/ 1.0 3.0)))

series385.0ms

Calls
4 calls:
Slowest
168.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
147.0ms
(* (* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))
58.0ms
(sqrt (- a (/ 1.0 3.0)))
12.0ms
(* (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))

simplify17.2s

Calls
167 calls:
Slowest
741.0ms
(+ (+ (- (log (/ rand (sqrt 9))) (log (sqrt (- a (/ 1.0 3.0))))) (log (sqrt (- a (/ 1.0 3.0))))) (log (sqrt (- a (/ 1.0 3.0)))))
633.0ms
(+ (log (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))) (log (sqrt (- a (/ 1.0 3.0)))))
480.0ms
(+ (+ (log (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))) (log (sqrt (- a (/ 1.0 3.0))))) (log (sqrt (- a (/ 1.0 3.0)))))
456.0ms
(* (* (/ (* (* (/ 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))))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0))))) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
451.0ms
(- (+ (* 1/3 (* (sqrt (- 0.3333333333333333)) rand)) (* 1/6 (/ (* a rand) (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (* (pow a 2) rand) (pow (sqrt (- 0.3333333333333333)) 3))))

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

regimes138.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample6.1s

Algorithm
intervals
Results
3.8s27078×body80nan
1.2s9094×body80valid