Details

Time bar (total: 3.6m)

sample190.0ms

Algorithm
intervals
Results
125.0ms917×body80nan
34.0ms290×body80valid

simplify261.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
260.0ms
(* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand)))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize33.0ms

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)))

rewrite92.0ms

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
37.0ms
(* 9 (- a (/ 1.0 3.0)))
27.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms
(/ 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)))

series378.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
142.0ms
(/ 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)))
88.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
53.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify23.5s

Counts
148 → 183
Calls
148 calls:
Slowest
651.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
642.0ms
(* 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))))))
417.0ms
(* 9 (fma (- (/ (sqrt 1.0) 3.0)) (/ (sqrt 1.0) 1) (* (/ (sqrt 1.0) 3.0) (/ (sqrt 1.0) 1))))
407.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
407.0ms
(* (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)

prune2.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

6.0b
(* (/ 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)))

rewrite180.0ms

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
109.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
25.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
21.0ms
(* 9 (- a (/ 1.0 3.0)))
19.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))

series416.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
178.0ms
(/ rand (sqrt (* 9 (- a (/ 1.0 3.0)))))
116.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
76.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
46.0ms
(* 9 (- a (/ 1.0 3.0)))

simplify48.6s

Counts
268 → 301
Calls
268 calls:
Slowest
750.0ms
(* (/ rand (sqrt (* 9 (- a (/ 1.0 3.0))))) (fma (- (/ (cbrt 1.0) (sqrt 3.0))) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 3.0)) (* (/ (cbrt 1.0) (sqrt 3.0)) (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt 3.0)))))
714.0ms
(* 9 (fma (- (/ (sqrt 1.0) (sqrt 3.0))) (/ (sqrt 1.0) (sqrt 3.0)) (* (/ (sqrt 1.0) (sqrt 3.0)) (/ (sqrt 1.0) (sqrt 3.0)))))
543.0ms
(* (* (* 9 9) 9) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
476.0ms
(* (/ (* (* rand rand) rand) (* (* (sqrt (* 9 (- a (/ 1.0 3.0)))) (sqrt (* 9 (- a (/ 1.0 3.0))))) (sqrt (* 9 (- a (/ 1.0 3.0)))))) (* (* (- a (/ 1.0 3.0)) (- a (/ 1.0 3.0))) (- a (/ 1.0 3.0))))
422.0ms
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))

prune3.8s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize46.0ms

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

rewrite518.0ms

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
285.0ms
(* rand (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
146.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
35.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))
33.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))

series424.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
124.0ms
(* rand (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0))))
110.0ms
(/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))
103.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (- a (/ 1.0 3.0)))
87.0ms
(sqrt (* 9 (- a (/ 1.0 3.0))))

simplify1.6m

Counts
362 → 397
Calls
362 calls:
Slowest
881.0ms
(* rand (* (/ 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)))))))
795.0ms
(* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) (fma (- (/ (sqrt 1.0) (sqrt 3.0))) (/ (sqrt 1.0) (sqrt 3.0)) (* (/ (sqrt 1.0) (sqrt 3.0)) (/ (sqrt 1.0) (sqrt 3.0)))))
687.0ms
(* rand (* (fma (- (sqrt (/ 1.0 3.0))) (sqrt (/ 1.0 3.0)) (* (sqrt (/ 1.0 3.0)) (sqrt (/ 1.0 3.0)))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))))
658.0ms
(* (* (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))))) (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0)))))) rand)
641.0ms
(* 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)))))))

prune5.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize52.0ms

Local error

Found 4 expressions with local error:

25.6b
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
8.3b
(* (/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (sqrt (+ a (/ 1.0 3.0))))
0.2b
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
0.2b
(* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
27×*-un-lft-identity
26×times-frac
25×add-cube-cbrt
21×associate-*l*
14×sqrt-prod
13×add-cbrt-cube add-exp-log
11×pow1 associate-*r*
10×sqrt-div associate-*r/
5×unswap-sqr
4×expm1-log1p-u associate-/r* flip3-- associate-/r/ insert-posit16 log1p-expm1-u flip-- add-log-exp
3×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod associate-/l*
2×frac-times cbrt-undiv sub-neg sqrt-pow1 flip3-+ div-exp prod-diff *-commutative flip-+ div-inv
1×clear-num frac-2neg pow1/2 associate-*l/ distribute-lft-out difference-of-squares
Counts
4 → 132
Calls
4 calls:
Slowest
98.0ms
(* (/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (sqrt (+ a (/ 1.0 3.0))))
46.0ms
(* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))
27.0ms
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
19.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))

series581.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
210.0ms
(* (/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (sqrt (+ a (/ 1.0 3.0))))
163.0ms
(/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))
107.0ms
(sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))
101.0ms
(* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))

simplify27.6s

Counts
113 → 144
Calls
113 calls:
Slowest
604.0ms
(sqrt (+ (* a a) (- (* (/ 1.0 3.0) (/ 1.0 3.0)) (* a (/ 1.0 3.0)))))
578.0ms
(* (/ (* (* rand rand) rand) (* (* (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))) (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))) (* (* (sqrt (+ a (/ 1.0 3.0))) (sqrt (+ a (/ 1.0 3.0)))) (sqrt (+ a (/ 1.0 3.0)))))
491.0ms
(* (/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (sqrt (+ a (/ 1.0 3.0))))
463.0ms
(/ (* (cbrt rand) (cbrt rand)) (* (cbrt (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0)))))) (cbrt (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))))
460.0ms
(* (sqrt (/ rand (sqrt (* 9 (- (* a a) (* (/ 1.0 3.0) (/ 1.0 3.0))))))) (sqrt (sqrt (+ a (/ 1.0 3.0)))))

prune1.8s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes167.0ms

Accuracy

0% (0.1b remaining)

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

bsearch6.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
4.8s28027×body80nan
1.2s9213×body80valid