Details

Time bar (total: 3.3m)

sample211.0ms

Algorithm
intervals
Results
108.0ms973×body80nan
34.0ms293×body80valid

simplify266.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
266.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune26.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.4b
(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)))

rewrite70.0ms

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
39.0ms
(* 9 (- a (/ 1.0 3.0)))
17.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
11.0ms
(/ 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)))

series402.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
98.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
73.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
65.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.7s

Counts
148 → 183
Calls
148 calls:
Slowest
723.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt (* 9 (- a (/ 1.0 3.0))))))
639.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
435.0ms
(* 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))))))
424.0ms
(* (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)
423.0ms
(* 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))))))

prune2.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize24.0ms

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)))

rewrite148.0ms

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
73.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
36.0ms
(* 9 (- a (/ 1.0 3.0)))
21.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
11.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series417.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
145.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
140.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
87.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
45.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify48.9s

Counts
268 → 301
Calls
268 calls:
Slowest
930.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
552.0ms
(* (* (* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))) (/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
414.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
413.0ms
(* (/ rand (sqrt (* 9 (- 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))))
402.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (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))))))

prune3.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 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)))

rewrite64.0ms

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
38.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
12.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
11.0ms
(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)))

series446.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
153.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
130.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
115.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
49.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify6.2s

Counts
138 → 156
Calls
138 calls:
Slowest
336.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
329.0ms
(* (* (* 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))))))
289.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
270.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
221.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* 9 (- a (/ 1.0 3.0))))
0.3b
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
0.3b
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
0.2b
(* rand (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
239×add-sqr-sqrt
234×prod-diff
230×*-un-lft-identity
227×add-cube-cbrt
205×distribute-rgt-in distribute-lft-in
189×times-frac
32×add-exp-log
21×associate-*l*
20×add-cbrt-cube div-inv
18×pow1
15×associate-*r/
13×prod-exp
8×sqrt-prod
7×flip3-- associate-*r* cbrt-unprod flip--
6×sub-neg sqrt-div div-exp pow-prod-down
4×expm1-log1p-u frac-times associate-/r* sqrt-pow1 associate-/r/ insert-posit16 log1p-expm1-u pow-flip add-log-exp
3×cbrt-undiv rec-exp 1-exp associate-/l* unswap-sqr
2×pow1/2 associate-*l/ *-commutative difference-of-squares
1×clear-num frac-2neg distribute-lft-out-- inv-pow
Counts
4 → 385
Calls
4 calls:
Slowest
250.0ms
(* rand (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
104.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
23.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
15.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

series813.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
497.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
119.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
116.0ms
(* rand (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
81.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify1.6m

Counts
362 → 397
Calls
362 calls:
Slowest
981.0ms
(* rand (* (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))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))
735.0ms
(* (* (/ 1 (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)))))) rand)
704.0ms
(* (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))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))))
688.0ms
(* rand (* (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))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))
670.0ms
(* rand (* (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))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))

prune5.4s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes166.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
3.9s27088×body80nan
2.1s9131×body80valid