Details

Time bar (total: 4.4m)

sample234.0ms

Algorithm
intervals
Results
133.0ms1018×body80nan
60.0ms300×body80valid

simplify288.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
288.0ms
(* (- 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

localize22.0ms

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)))

rewrite56.0ms

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
23.0ms
(* 9 (- a (/ 1.0 3.0)))
15.0ms
(/ 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)))

series381.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
156.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
94.0ms
(fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
68.0ms
(* 9 (- a (/ 1.0 3.0)))
62.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify54.2s

Counts
280 → 183
Calls
280 calls:
Slowest
844.0ms
(* (* (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (fma (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
756.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
660.0ms
(* (fma (sqrt a) (sqrt a) (- (* (/ 1.0 (sqrt 3.0)) (/ 1 (sqrt 3.0))))) 9)
594.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
549.0ms
(* (* (* 9 (- a (/ 1.0 3.0))) (* 9 (- a (/ 1.0 3.0)))) (* 9 (- a (/ 1.0 3.0))))

prune1.9s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite210.0ms

Algorithm
rewrite-expression-head
Rules
234×prod-diff
229×add-sqr-sqrt
222×*-un-lft-identity
220×add-cube-cbrt
205×distribute-rgt-in distribute-lft-in
175×times-frac
31×pow1
20×add-exp-log
19×div-inv
17×pow-prod-down
14×associate-*r/
13×add-cbrt-cube
9×prod-exp cbrt-unprod
7×associate-*r* associate-*l*
6×sub-neg
5×sqrt-pow1 sqrt-prod
4×cbrt-prod expm1-log1p-u associate-/r* flip3-- sqrt-div insert-posit16 log1p-expm1-u flip-- add-log-exp
3×associate-/l*
2×associate-/r/ *-commutative difference-of-squares unswap-sqr
1×cbrt-undiv clear-num frac-2neg pow1/2 div-exp distribute-lft-out--
Counts
4 → 358
Calls
4 calls:
Slowest
55.0ms
(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))
52.0ms
(sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))
50.0ms
(/ rand (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))))
40.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))

series694.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
252.0ms
(/ rand (sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))))
193.0ms
(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0))))
136.0ms
(* (cbrt 9) (- a (/ 1.0 3.0)))
113.0ms
(sqrt (* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (- a (/ 1.0 3.0)))))

simplify2.6m

Counts
631 → 370
Calls
631 calls:
Slowest
833.0ms
(* (* (cbrt 9) (cbrt 9)) (* (fma (sqrt a) (sqrt a) (- (* (/ (cbrt 1.0) 3.0) (/ (* (cbrt 1.0) (cbrt 1.0)) 1)))) (cbrt 9)))
785.0ms
(* (* (* (cbrt 9) (- a (/ 1.0 3.0))) (* (cbrt 9) (- a (/ 1.0 3.0)))) (* (cbrt 9) (- a (/ 1.0 3.0))))
754.0ms
(* (* (fma (sqrt a) (sqrt a) (- (* (/ 1.0 3.0) (/ 1 1)))) (cbrt 9)) (* (cbrt 9) (cbrt 9)))
723.0ms
(* (cbrt 9) (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))))))
689.0ms
(* (* (cbrt 9) (cbrt 9)) (* (cbrt 9) (fma (- (/ (cbrt 1.0) (cbrt 3.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 3.0) (cbrt 3.0))) (* (/ (cbrt 1.0) (cbrt 3.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt 3.0) (cbrt 3.0)))))))

prune4.0s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize38.0ms

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)))

rewrite103.0ms

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
56.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
23.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
20.0ms
(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)))

series465.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
163.0ms
(* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))
138.0ms
(/ rand (sqrt (- a (/ 1.0 3.0))))
101.0ms
(fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))
62.0ms
(sqrt (- a (/ 1.0 3.0)))

simplify14.1s

Counts
192 → 156
Calls
192 calls:
Slowest
1.2s
(* (* (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0)))) (fma (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))))
385.0ms
(- (+ (sqrt (- 0.3333333333333333)) (* 1/2 (/ a (sqrt (- 0.3333333333333333))))) (* 1/8 (/ (pow a 2) (pow (sqrt (- 0.3333333333333333)) 3))))
332.0ms
(* (* (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))) (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0)))))) (* 1/3 (/ rand (sqrt (- a (/ 1.0 3.0))))))
315.0ms
(/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
312.0ms
(* 1/3 (/ rand (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))

prune2.2s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize50.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))
0.3b
(* 1/3 (/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))))
0.2b
(/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0))))))
0.1b
(sqrt (sqrt (- a (/ 1.0 3.0))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
114×sqrt-prod
84×add-sqr-sqrt
76×sqrt-div
39×*-un-lft-identity
36×sqrt-pow1
31×pow1
27×associate-*r*
23×add-cube-cbrt
20×add-cbrt-cube swap-sqr add-exp-log
19×flip3-- flip--
18×pow1/2
16×associate-/r/
15×associate-*l*
12×frac-times times-frac
11×unswap-sqr
10×difference-of-squares
9×pow-prod-up
7×associate-*r/ distribute-lft-out--
6×pow-prod-down associate-*l/ prod-exp cbrt-unprod
5×pow-sqr
4×expm1-log1p-u cbrt-undiv div-exp insert-posit16 log1p-expm1-u add-log-exp
3×associate-/l*
2×rem-sqrt-square *-commutative div-inv
1×pow2 clear-num associate-/r* rem-square-sqrt frac-2neg pow-plus sqrt-unprod
Counts
4 → 195
Calls
4 calls:
Slowest
82.0ms
(* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))
78.0ms
(* 1/3 (/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))))
19.0ms
(/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0))))))
8.0ms
(sqrt (sqrt (- a (/ 1.0 3.0))))

series474.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
166.0ms
(* 1/3 (/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))))
140.0ms
(sqrt (sqrt (- a (/ 1.0 3.0))))
124.0ms
(/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0))))))
44.0ms
(* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))

simplify20.7s

Counts
250 → 207
Calls
250 calls:
Slowest
447.0ms
(* (sqrt (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))) (sqrt (sqrt (- a (/ 1.0 3.0)))))
445.0ms
(/ rand (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))))
445.0ms
(/ rand (* (sqrt (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))) (sqrt (sqrt (- a (/ 1.0 3.0))))))
445.0ms
(/ (* (* rand rand) rand) (* (* (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0))))) (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))) (* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- a (/ 1.0 3.0)))))))
432.0ms
(* (sqrt (sqrt (- a (/ 1.0 3.0)))) (sqrt (sqrt (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))

prune2.5s

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (0.1b remaining)

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

bsearch4.0ms

end0.0ms

sample7.0s

Algorithm
intervals
Results
4.4s27411×body80nan
1.7s9123×body80valid