Details

Time bar (total: 3.2m)

sample205.0ms

Algorithm
intervals
Results
123.0ms841×body80nan
41.0ms293×body80valid

simplify306.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
306.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

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)))

rewrite77.0ms

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
28.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
25.0ms
(* 9 (- a (/ 1.0 3.0)))
20.0ms
(/ 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)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
83.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
71.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
47.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.2s

Counts
148 → 183
Calls
148 calls:
Slowest
502.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
434.0ms
(* (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)
429.0ms
(* (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)
397.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
387.0ms
(* 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))))))

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.4b
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
0.2b
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
0.2b
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
0.1b
(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

rewrite564.0ms

Algorithm
rewrite-expression-head
Rules
164×distribute-rgt-in distribute-lft-in
156×prod-diff
151×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
120×times-frac
15×pow1
13×div-inv
12×associate-*r/
11×add-cbrt-cube add-exp-log
8×sqrt-prod
6×associate-*l* pow-prod-down
4×expm1-log1p-u associate-/r* sub-neg sqrt-div insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 flip3-- prod-exp cbrt-unprod flip-- associate-/l*
2×associate-/r/
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp associate-*r* *-commutative fma-udef
Counts
4 → 254
Calls
4 calls:
Slowest
428.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
66.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
56.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
0.0ms
(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))

series455.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
167.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
120.0ms
(fma (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
109.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
59.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

simplify54.1s

Counts
230 → 266
Calls
230 calls:
Slowest
748.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)))
719.0ms
(* (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)) (sqrt 9))
669.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)))
637.0ms
(* (* (sqrt 9) (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0))))) (sqrt 9))
618.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 3.0)) 1 (* (/ 1.0 3.0) 1)) (sqrt 9)))

prune3.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

8.8b
(* (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
0.4b
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
0.2b
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))
0.2b
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))

rewrite342.0ms

Algorithm
rewrite-expression-head
Rules
238×add-sqr-sqrt
234×prod-diff
230×*-un-lft-identity
228×add-cube-cbrt
205×distribute-rgt-in distribute-lft-in
188×times-frac
24×associate-*l*
20×div-inv
18×associate-*r/
17×pow1
16×add-cbrt-cube add-exp-log
11×sqrt-prod
7×associate-*r* pow-prod-down
6×sub-neg flip3-- sqrt-div flip--
5×prod-exp cbrt-unprod
4×expm1-log1p-u associate-/r* associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×sqrt-pow1 associate-/l*
2×frac-times cbrt-undiv div-exp *-commutative difference-of-squares unswap-sqr
1×clear-num frac-2neg pow1/2 associate-*l/ distribute-lft-out--
Counts
4 → 372
Calls
4 calls:
Slowest
178.0ms
(* (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
60.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
49.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
37.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

series495.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
164.0ms
(/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))))
157.0ms
(* (/ rand (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))) (- a (/ 1.0 3.0)))
99.0ms
(sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))
75.0ms
(* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0))))

simplify1.4m

Counts
350 → 384
Calls
350 calls:
Slowest
957.0ms
(* (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)) (sqrt 9))
879.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)))
647.0ms
(* (* (sqrt 9) (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0))))) (sqrt 9))
639.0ms
(* (sqrt 9) (* (fma (- (/ 1.0 (sqrt 3.0))) (/ 1 (sqrt 3.0)) (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0)))) (sqrt 9)))
625.0ms
(* (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 (sqrt (* (sqrt 9) (* (sqrt 9) (- a (/ 1.0 3.0)))))))

prune5.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
0.2b
(/ 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)))

rewrite63.0ms

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
33.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
18.0ms
(/ 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)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
173.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
124.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
111.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
46.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify6.1s

Counts
138 → 156
Calls
138 calls:
Slowest
348.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
287.0ms
(/ (* (* rand rand) rand) (* (* (sqrt (- a (/ 1.0 3.0))) (sqrt (- a (/ 1.0 3.0)))) (sqrt (- a (/ 1.0 3.0)))))
264.0ms
(* (* (* 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))))))
263.0ms
(sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
235.0ms
(sqrt (- (pow a 3) (pow (/ 1.0 3.0) 3)))

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes179.0ms

Accuracy

0% (0.1b remaining)

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

bsearch3.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
4.7s27957×body80nan
1.4s9122×body80valid