Details

Time bar (total: 1.7m)

sample208.0ms

Algorithm
intervals
Results
129.0ms866×body80nan
37.0ms284×body80valid

simplify261.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
261.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

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)))

rewrite61.0ms

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
22.0ms
(* 9 (- a (/ 1.0 3.0)))
20.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
14.0ms
(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)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
206.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
116.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
79.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
62.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.4s

Counts
148 → 183
Calls
148 calls:
Slowest
792.0ms
(* (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)
681.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
460.0ms
(* 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))))))
454.0ms
(* 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))))))
431.0ms
(* (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))) 9)

prune1.9s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))
0.0b
(- a (/ 1.0 3.0))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
430×times-frac
342×add-sqr-sqrt
266×*-un-lft-identity
234×sqrt-prod
216×add-cube-cbrt
50×difference-of-squares
39×prod-diff
25×distribute-lft-out--
22×associate-/l*
14×div-inv
9×associate-/r* add-cbrt-cube add-exp-log
6×add-log-exp
5×pow1
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×cbrt-undiv flip3-- fma-neg div-exp flip--
2×associate-/r/
1×rem-sqrt-square clear-num sub-neg frac-2neg sqrt-pow1 pow1/2 diff-log fma-udef associate-/l/
Counts
4 → 341
Calls
4 calls:
Slowest
29.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
18.0ms
(- a (/ 1.0 3.0))
18.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series314.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
159.0ms
(/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0))))
85.0ms
(fma (/ (/ rand (sqrt 9)) (sqrt (- a (/ 1.0 3.0)))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
41.0ms
(sqrt (- a (/ 1.0 3.0)))
29.0ms
(- a (/ 1.0 3.0))

simplify40.5s

Counts
539 → 353
Calls
539 calls:
Slowest
1.0s
(fma (* (cbrt a) (cbrt a)) (cbrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
627.0ms
(fma (sqrt a) (sqrt a) (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
597.0ms
(fma (- (/ 1.0 (cbrt 3.0))) (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))))
554.0ms
(fma 1 a (- (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0))))))
548.0ms
(fma (- (/ 1.0 (cbrt 3.0))) (/ 1 (* (cbrt 3.0) (cbrt 3.0))) (* (/ 1.0 (cbrt 3.0)) (/ 1 (* (cbrt 3.0) (cbrt 3.0)))))

prune4.4s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
0.3b
(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
139×add-sqr-sqrt
102×times-frac
74×*-un-lft-identity
68×sqrt-prod
52×add-cube-cbrt
33×associate-*r*
30×add-exp-log
22×associate-*l*
18×add-cbrt-cube
16×difference-of-squares
15×unswap-sqr
10×div-exp
9×pow1 associate-/r*
8×prod-exp distribute-lft-out--
6×sqrt-div
5×cbrt-undiv
4×expm1-log1p-u associate-/r/ cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp flip3-- 1-exp div-inv pow-flip flip-- associate-/l*
2×sqrt-pow1 pow1/2
1×frac-times rem-sqrt-square clear-num frac-2neg pow-prod-down associate-*l/ associate-*r/ un-div-inv *-commutative fma-udef inv-pow
Counts
4 → 192
Calls
4 calls:
Slowest
36.0ms
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
23.0ms
(sqrt (- a (/ 1.0 3.0)))
12.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
0.0ms
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series391.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0)))))
104.0ms
(fma (* (/ rand (sqrt 9)) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
84.0ms
(/ 1 (sqrt (- a (/ 1.0 3.0))))
50.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify12.7s

Counts
196 → 204
Calls
196 calls:
Slowest
588.0ms
(* (* (* (/ rand (sqrt 9)) (/ rand (sqrt 9))) (/ rand (sqrt 9))) (* (* (/ 1 (sqrt (- a (/ 1.0 3.0)))) (/ 1 (sqrt (- a (/ 1.0 3.0))))) (/ 1 (sqrt (- a (/ 1.0 3.0))))))
455.0ms
(- (sqrt -3.0) (+ (* 4.5 (/ a (sqrt -3.0))) (+ (* 13.5 (/ (pow a 2) (sqrt -3.0))) (* 10.125 (/ (pow a 2) (pow (sqrt -3.0) 3))))))
348.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
312.0ms
(+ (log (/ rand (sqrt 9))) (- 0 (log (sqrt (- a (/ 1.0 3.0))))))
286.0ms
(+ (- (log rand) (log (sqrt 9))) (- 0 (log (sqrt (- a (/ 1.0 3.0))))))

prune2.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
0.3b
(/ rand (sqrt (- a (/ 1.0 3.0))))
0.1b
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
0.0b
(sqrt (- a (/ 1.0 3.0)))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
89×add-sqr-sqrt
64×times-frac
56×*-un-lft-identity
49×sqrt-prod
40×add-cube-cbrt
33×associate-*r*
16×difference-of-squares
11×add-cbrt-cube add-exp-log
9×associate-/r*
8×distribute-lft-out--
7×pow1
6×sqrt-div
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- associate-*l* flip-- associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down associate-*r/ *-commutative fma-udef
Counts
4 → 144
Calls
4 calls:
Slowest
25.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
11.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
10.0ms
(sqrt (- a (/ 1.0 3.0)))
0.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
130.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
99.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
53.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify6.5s

Counts
138 → 156
Calls
138 calls:
Slowest
580.0ms
(- (* (sqrt -3.0) rand) (+ (* 13.5 (/ (* (pow a 2) rand) (sqrt -3.0))) (+ (* 4.5 (/ (* a rand) (sqrt -3.0))) (* 10.125 (/ (* (pow a 2) rand) (pow (sqrt -3.0) 3))))))
369.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
332.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
310.0ms
(* (* (* 1/3 1/3) 1/3) (* (* (/ rand (sqrt (- a (/ 1.0 3.0)))) (/ rand (sqrt (- a (/ 1.0 3.0))))) (/ rand (sqrt (- a (/ 1.0 3.0))))))
250.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))

prune1.8s

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

0% (0.1b remaining)

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

bsearch2.0ms

end0.0ms

sample6.2s

Algorithm
intervals
Results
4.1s27374×body80nan
1.3s9125×body80valid