Details

Time bar (total: 50.5s)

sample270.0ms

Algorithm
intervals
Results
66.0ms322×body80nan
22.0ms34×body1280valid
20.0ms155×body80valid
18.0ms34×body640valid
14.0ms22×body1280nan
10.0ms21×body640nan
8.0ms21×body320valid
7.0ms14×body320nan
3.0ms12×body160valid
2.0ms8×body160nan

simplify240.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
239.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.7b

localize72.0ms

Local error

Found 4 expressions with local error:

14.7b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.1b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.3b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×*-un-lft-identity add-cube-cbrt
11×add-cbrt-cube add-exp-log
7×pow1
6×associate-/r* times-frac associate-*l* add-log-exp
4×expm1-log1p-u sqrt-div insert-posit16 log1p-expm1-u
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down *-commutative div-inv associate-/l*
Counts
4 → 94
Calls
4 calls:
Slowest
86.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
79.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
26.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
8.0ms
(* (sqrt 2) t)

series2.2s

Counts
4 → 12
Calls
4 calls:
Slowest
1.5s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
451.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
250.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
48.0ms
(* (sqrt 2) t)

simplify8.7s

Counts
64 → 106
Calls
64 calls:
Slowest
448.0ms
(sqrt (+ (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (+ (* (* l l) (* l l)) (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
362.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
348.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
316.0ms
(/ (* (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* t t) t)) (* (* (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))))
307.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.8b

localize61.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
2.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt add-cbrt-cube add-exp-log
10×*-un-lft-identity add-cube-cbrt
7×pow1 sqrt-prod
6×associate-*l*
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp associate-*r*
2×unswap-sqr
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 pow-prod-down *-commutative fma-udef div-inv associate-/l*
Counts
4 → 78
Calls
4 calls:
Slowest
35.0ms
(/ (* (* t t) 4) x)
24.0ms
(* (sqrt 2) t)
3.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series603.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
426.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
88.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
58.0ms
(* (sqrt 2) t)
31.0ms
(/ (* (* t t) 4) x)

simplify2.6s

Counts
46 → 90
Calls
46 calls:
Slowest
233.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
217.0ms
(sqrt (* (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (cbrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
212.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
200.0ms
(/ (* (* (* (* t t) t) (* (* t t) t)) (* (* 4 4) 4)) (* (* x x) x))
187.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.7b

localize58.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
2.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
31×add-exp-log
25×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity prod-exp add-cube-cbrt cbrt-unprod
9×associate-/r* times-frac sqrt-prod
8×cbrt-undiv div-exp
5×pow1
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 89
Calls
4 calls:
Slowest
46.0ms
(/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
20.0ms
(/ (* (* t t) 4) x)
1.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series810.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
471.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
212.0ms
(/ (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
92.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
34.0ms
(/ (* (* t t) 4) x)

simplify10.9s

Counts
61 → 101
Calls
61 calls:
Slowest
982.0ms
(/ (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t)) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))) (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) t))) (* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
813.0ms
(- (+ (log (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (log (* (cbrt (sqrt 2)) t))) (log (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
577.0ms
(/ (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t))) (* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
548.0ms
(/ (* (* (* (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (cbrt (sqrt 2)) (cbrt (sqrt 2)))) (* (sqrt 2) (* (* t t) t))) (* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
499.0ms
(- (+ (+ (log (cbrt (sqrt 2))) (log (cbrt (sqrt 2)))) (log (* (cbrt (sqrt 2)) t))) (log (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.7b

localize39.0ms

Local error

Found 4 expressions with local error:

22.8b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.1b
(/ (* (* t t) 4) x)
2.6b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.6b
(/ (* (cbrt (sqrt 2)) t) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
17×add-cbrt-cube
12×add-sqr-sqrt
11×*-un-lft-identity add-cube-cbrt
9×associate-/r* times-frac sqrt-prod
5×pow1 cbrt-undiv div-exp
4×expm1-log1p-u prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg div-inv associate-/l*
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 83
Calls
4 calls:
Slowest
30.0ms
(/ (* (* t t) 4) x)
21.0ms
(/ (* (cbrt (sqrt 2)) t) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
1.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
0.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

series980.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
460.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
378.0ms
(/ (* (cbrt (sqrt 2)) t) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
107.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
34.0ms
(/ (* (* t t) 4) x)

simplify7.1s

Counts
55 → 95
Calls
55 calls:
Slowest
464.0ms
(/ (* (sqrt 2) (* (* t t) t)) (* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
313.0ms
(/ (* (* (* (cbrt (sqrt 2)) t) (* (cbrt (sqrt 2)) t)) (* (cbrt (sqrt 2)) t)) (* (* (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))) (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))))
256.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
249.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
241.0ms
(cbrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.7b

regimes557.0ms

Accuracy

77% (5.4b remaining)

Error of 9.1b against oracle of 3.7b and baseline of 27.2b

bsearch410.0ms

end0.0ms

sample8.8s

Algorithm
intervals
Results
2.1s10056×body80nan
1.2s5166×body80valid
1.1s999×body640valid
1.1s588×body1280nan
961.0ms614×body640nan
818.0ms822×body1280valid
363.0ms646×body320valid
206.0ms343×body320nan
164.0ms207×body160nan
153.0ms367×body160valid