Details

Time bar (total: 42.7s)

sample382.0ms

Algorithm
intervals
Results
81.0ms338×body80nan
79.0ms176×body80valid
51.0ms22×body1280valid
23.0ms27×body640nan
22.0ms28×body640valid
19.0ms17×body1280nan
14.0ms22×body320valid
6.0ms8×body320nan
4.0ms8×body160valid
1.0ms2×body160nan

simplify855.0ms

Calls
1 calls:
Slowest
855.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 38.3b

localize53.0ms

Local error

Found 4 expressions with local error:

19.8b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
11.7b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.4b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite224.0ms

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*
Calls
4 calls:
Slowest
88.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
64.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
53.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
15.0ms
(* (sqrt 2) t)

series2.2s

Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
435.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
259.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
54.0ms
(* (sqrt 2) t)

simplify8.9s

Calls
64 calls:
Slowest
414.0ms
(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)))))
372.0ms
(/ (* (* (* (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)))))
353.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
320.0ms
(/ (* (* (* (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)))))
317.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))

prune1.4s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.3b

localize69.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.4b
(* (sqrt 2) t)

rewrite41.0ms

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*
Calls
4 calls:
Slowest
29.0ms
(/ (* (* t t) 4) x)
8.0ms
(* (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))

series692.0ms

Calls
4 calls:
Slowest
519.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
78.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
53.0ms
(* (sqrt 2) t)
42.0ms
(/ (* (* t t) 4) x)

simplify2.8s

Calls
46 calls:
Slowest
255.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
222.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
220.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
209.0ms
(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)))))
191.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))

prune1.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize67.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube add-exp-log
12×sqrt-prod
11×add-sqr-sqrt
10×pow1 *-un-lft-identity add-cube-cbrt
9×associate-*l*
6×prod-exp cbrt-unprod
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* times-frac div-exp pow-prod-down
1×rem-sqrt-square clear-num frac-2neg sqrt-pow1 pow1/2 associate-*r* *-commutative fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
36.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
34.0ms
(/ (* (* t t) 4) x)
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))

series618.0ms

Calls
4 calls:
Slowest
408.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
87.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
79.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
43.0ms
(/ (* (* t t) 4) x)

simplify3.3s

Calls
46 calls:
Slowest
318.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
244.0ms
(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)))))
236.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
235.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
216.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune1.5s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.3b

localize41.0ms

Local error

Found 4 expressions with local error:

26.4b
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
8.3b
(/ (* (* t t) 4) x)
3.0b
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
1.0b
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
69×sqrt-prod
50×add-sqr-sqrt
33×sqrt-pow1
28×pow1
19×*-un-lft-identity add-cube-cbrt
17×pow1/2
15×add-cbrt-cube swap-sqr add-exp-log
9×associate-*r* associate-*l* pow-prod-up unswap-sqr
5×pow-prod-down pow-sqr
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
1×pow2 rem-sqrt-square clear-num rem-square-sqrt frac-2neg pow-plus sqrt-unprod *-commutative fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
28.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))
23.0ms
(/ (* (* 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))

series630.0ms

Calls
4 calls:
Slowest
474.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))
108.0ms
(fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))
48.0ms
(/ (* (* t t) 4) x)
0.0ms
(* (sqrt (sqrt 2)) (sqrt (sqrt 2)))

simplify3.4s

Calls
128 calls:
Slowest
232.0ms
(/ (* (* (* (* t t) 4) (* (* t t) 4)) (* (* t t) 4)) (* (* x x) x))
217.0ms
(sqrt (sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x))))
213.0ms
(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)))))
189.0ms
(/ (* (* (* (* t t) (* t t)) (* t t)) (* (* 4 4) 4)) (* (* x x) x))
171.0ms
(sqrt (fma (fma (/ l x) l (* t t)) 2 (/ (* (* t t) 4) x)))

prune2.0s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.3b

regimes884.0ms

Accuracy

77.9% (5.2b remaining)

Error of 9.2b against oracle of 3.9b and baseline of 27.6b

bsearch2.2s

end0.0ms

sample9.0s

Algorithm
intervals
Results
2.4s10149×body80nan
1.3s1042×body640valid
1.1s5145×body80valid
958.0ms588×body640nan
937.0ms795×body1280valid
813.0ms568×body1280nan
512.0ms661×body320valid
264.0ms372×body320nan
198.0ms357×body160valid
70.0ms178×body160nan