Details

Time bar (total: 7.7m)

sample230.0ms

Algorithm
intervals
Results
147.0ms925×body80nan
43.0ms301×body80valid

simplify248.0ms

Calls
1 calls:
Slowest
247.0ms
(* (- 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

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.2b
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite425.0ms

Algorithm
rewrite-expression-head
Rules
422×add-sqr-sqrt
273×times-frac
227×sqrt-prod
216×*-un-lft-identity
210×associate-*r*
108×difference-of-squares
105×add-cube-cbrt
55×distribute-lft-out--
51×associate-*l*
37×associate-*r/
36×associate-/r*
22×unswap-sqr
17×*-commutative
14×associate-/l*
13×add-cbrt-cube add-exp-log
11×pow1
6×flip3-- sqrt-div flip--
4×associate-/r/ insert-posit16 add-log-exp associate-/l/
3×clear-num pow-prod-down prod-exp un-div-inv cbrt-unprod
2×distribute-rgt-in cbrt-undiv rem-sqrt-square sub-neg frac-2neg distribute-lft-in sqrt-pow1 div-exp div-inv
1×pow1/2 div-sub
Calls
4 calls:
Slowest
216.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
95.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
59.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
38.0ms
(* 9 (- a (/ 1.0 3.0)))

series365.0ms

Calls
4 calls:
Slowest
132.0ms
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0))))))
85.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* 9 (- a (/ 1.0 3.0)))))
80.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
66.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify34.3s

Calls
458 calls:
Slowest
499.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
427.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
356.0ms
(- (+ (* 1/3 (sqrt (- 0.3333333333333333))) (* 1/6 (/ a (sqrt (- 0.3333333333333333))))) (* 1/24 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
348.0ms
(- (+ (* 3 (sqrt (- 0.3333333333333333))) (* 3/2 (/ a (sqrt (- 0.3333333333333333))))) (* 3/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
332.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

prune4.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
0.2b
(/ rand (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
0.0b
(* 9 (- a (/ 1.0 3.0)))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
1049×add-sqr-sqrt
1008×times-frac
600×*-un-lft-identity
495×sqrt-prod
348×add-cube-cbrt
252×difference-of-squares
204×associate-*r*
126×associate-/r* distribute-lft-out--
102×associate-*l*
39×associate-/r/ associate-/l*
35×unswap-sqr
34×*-commutative
13×add-cbrt-cube add-exp-log
9×pow1 flip3-- flip--
8×associate-*r/
6×sqrt-div div-inv
4×cbrt-undiv div-exp insert-posit16 add-log-exp associate-/l/
3×clear-num frac-2neg
2×distribute-rgt-in rem-sqrt-square sub-neg distribute-lft-in sqrt-pow1 pow-prod-down
1×pow1/2 prod-exp cbrt-unprod
Calls
4 calls:
Slowest
80.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
75.0ms
(/ rand (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
33.0ms
(* 9 (- a (/ 1.0 3.0)))
33.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series458.0ms

Calls
4 calls:
Slowest
158.0ms
(/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
134.0ms
(/ rand (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
95.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
71.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify2.0m

Calls
1130 calls:
Slowest
661.0ms
(/ (* (* rand rand) rand) (* (* (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))) (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))) (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))))
635.0ms
(/ (* (cbrt rand) (cbrt rand)) (/ (* (cbrt (sqrt (* 9 (- a (/ 1.0 3.0))))) (cbrt (sqrt (* 9 (- a (/ 1.0 3.0)))))) 1))
534.0ms
(/ (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
485.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
480.0ms
(/ (* (cbrt rand) (cbrt rand)) (/ (sqrt (* 9 (- a (/ 1.0 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))

prune8.5s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 3 (sqrt (- a (/ 1.0 3.0))))
0.3b
(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
0.2b
(/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
0.0b
(+ (/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))

rewrite676.0ms

Algorithm
rewrite-expression-head
Rules
1539×add-sqr-sqrt
1340×times-frac
830×*-un-lft-identity
449×add-cube-cbrt
405×associate-*r*
382×associate-/r*
364×difference-of-squares
315×sqrt-prod
252×frac-add
187×distribute-lft-out--
136×flip3-- flip--
135×associate-*l*
90×unswap-sqr
57×associate-/r/
47×associate-/l*
45×*-commutative
20×add-cbrt-cube add-exp-log
10×distribute-rgt-out
9×add-log-exp
8×div-inv
7×cbrt-undiv div-exp
6×pow1 sqrt-div associate-*r/
5×clear-num frac-2neg
4×insert-posit16 associate-/l/
3×distribute-lft1-in prod-exp cbrt-unprod
2×associate-+r+ sum-log distribute-lft-out
1×+-commutative associate-+r- sub-neg flip3-+ diff-log pow-prod-down flip-+
Calls
4 calls:
Slowest
391.0ms
(+ (/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
116.0ms
(/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
64.0ms
(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
42.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))

series462.0ms

Calls
4 calls:
Slowest
144.0ms
(+ (/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
128.0ms
(/ rand (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0))))
106.0ms
(/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)))
84.0ms
(* 3 (sqrt (- a (/ 1.0 3.0))))

simplify4.6m

Calls
1702 calls:
Slowest
906.0ms
(/ (cbrt rand) (/ (* (sqrt 3) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
844.0ms
(/ (sqrt rand) (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
840.0ms
(/ (sqrt rand) (/ (* (sqrt 3) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
838.0ms
(+ (* (/ rand (/ (* 3 (sqrt (+ (sqrt a) (sqrt (/ 1.0 3.0))))) (+ (sqrt a) (/ (sqrt 1.0) (sqrt 3.0))))) (+ (* a a) (+ (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0))))) (* (/ (sqrt (- (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (/ (sqrt 1.0) (sqrt 3.0)))) (- (pow a 3) (pow (/ 1.0 3.0) 3))))
811.0ms
(/ (cbrt rand) (/ (* 3 (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))

prune12.1s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
0.3b
(* (/ rand (sqrt (* (cbrt 9) (cbrt 9)))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
0.3b
(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
0.1b
(* (cbrt 9) (- a (/ 1.0 3.0)))

rewrite543.0ms

Algorithm
rewrite-expression-head
Rules
2204×add-sqr-sqrt
2046×sqrt-prod
1856×associate-/r*
1188×frac-times
1050×*-un-lft-identity
842×cbrt-prod
779×add-cube-cbrt
672×associate-*r*
628×associate-*l*
582×times-frac
351×unswap-sqr
332×associate-/l*
268×difference-of-squares
232×swap-sqr
135×distribute-lft-out--
95×*-commutative
76×associate-/l/
73×clear-num
72×frac-2neg
42×flip3-- flip--
41×associate-*r/
36×associate-*l/
21×add-cbrt-cube
20×add-exp-log
11×pow1
6×sqrt-div cbrt-unprod
5×cbrt-undiv div-exp prod-exp
4×associate-/r/ insert-posit16 add-log-exp
3×rem-sqrt-square pow-prod-down un-div-inv div-inv
2×distribute-rgt-in sub-neg distribute-lft-in sqrt-pow1
1×pow1/2 div-sub
Calls
4 calls:
Slowest
261.0ms
(* (/ rand (sqrt (* (cbrt 9) (cbrt 9)))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
72.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
42.0ms
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
41.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))

series999.0ms

Calls
4 calls:
Slowest
398.0ms
(* (/ rand (sqrt (* (cbrt 9) (cbrt 9)))) (/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))))
314.0ms
(/ (- a (/ 1.0 3.0)) (sqrt (* (cbrt 9) (- a (/ 1.0 3.0)))))
175.0ms
(sqrt (* (cbrt 9) (- a (/ 1.0 3.0))))
112.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))