Details

Time bar (total: 35.5s)

sample621.0ms

Algorithm
intervals
Results
177.0ms317×body80nan
74.0ms164×body80valid
69.0ms26×body1280valid
63.0ms24×body1280nan
40.0ms37×body640valid
37.0ms10×body160nan
21.0ms17×body640nan
12.0ms17×body320valid
7.0ms12×body160valid
7.0ms9×body320nan

simplify330.0ms

Calls
1 calls:
Slowest
329.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune38.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.4b

localize44.0ms

Local error

Found 4 expressions with local error:

19.7b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
13.0b
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
0.5b
(* (sqrt 2) t)
0.0b
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac add-cbrt-cube add-exp-log add-log-exp
4×expm1-log1p-u pow1 sqrt-div insert-posit16 log1p-expm1-u
3×flip3-- associate-*l* flip--
2×associate--l+ associate-/r/
1×distribute-rgt-in cbrt-undiv rem-sqrt-square clear-num sub-neg frac-2neg distribute-lft-in pow1/2 fma-neg diff-log div-exp prod-diff *-commutative div-inv associate-/l*
Calls
4 calls:
Slowest
31.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
25.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
11.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
5.0ms
(* (sqrt 2) t)

series2.2s

Calls
4 calls:
Slowest
1.4s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
484.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
258.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
56.0ms
(* (sqrt 2) t)

simplify7.4s

Calls
49 calls:
Slowest
327.0ms
(* (* l l) (/ (+ x 1) (- x 1)))
302.0ms
(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)))))
300.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
285.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
274.0ms
(sqrt (- (* (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (* (* l l) (* l l))))

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.2b

localize40.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
5.3b
(/ (* l l) x)
1.0b
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
0.5b
(* (sqrt 2) t)

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
6×*-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* sqrt-prod
1×rem-sqrt-square clear-num frac-2neg pow1/2 *-commutative fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
3.0ms
(/ (* l l) x)
3.0ms
(* (sqrt 2) t)
2.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
0.0ms
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))

series681.0ms

Calls
4 calls:
Slowest
506.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
83.0ms
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
72.0ms
(* (sqrt 2) t)
20.0ms
(/ (* l l) x)

simplify1.1s

Calls
18 calls:
Slowest
213.0ms
(sqrt (* (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))) (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))))
206.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
185.0ms
(sqrt (sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))))
164.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
160.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune858.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize30.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
1.0b
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))
0.5b
(* (sqrt 2) t)
0.1b
(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
9×sqrt-prod
6×associate-/r* times-frac add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l*
1×cbrt-undiv rem-sqrt-square clear-num frac-2neg pow1/2 div-exp *-commutative fma-udef div-inv associate-/l*
Calls
4 calls:
Slowest
15.0ms
(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))))
6.0ms
(* (sqrt 2) t)
3.0ms
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
0.0ms
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))

series810.0ms

Calls
4 calls:
Slowest
468.0ms
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
209.0ms
(/ (* (sqrt 2) t) (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))))
74.0ms
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))
58.0ms
(* (sqrt 2) t)

simplify4.8s

Calls
39 calls:
Slowest
278.0ms
(- (log (* (sqrt 2) t)) (log (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))))
247.0ms
(/ t (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))))
246.0ms
(sqrt (* (cbrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))) (cbrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))))
231.0ms
(/ (sqrt 2) (sqrt (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))))
225.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))) (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))) (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))))

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

28.1b
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
1.0b
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))
0.3b
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
0.2b
(* (sqrt (sqrt 2)) t)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
12×associate-*l*
10×add-sqr-sqrt
9×*-un-lft-identity add-cube-cbrt sqrt-prod
6×pow1 add-cbrt-cube add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×*-commutative
1×rem-sqrt-square pow1/2 associate-*r* pow-prod-down prod-exp cbrt-unprod fma-udef
Calls
4 calls:
Slowest
15.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))
7.0ms
(* (sqrt (sqrt 2)) t)
1.0ms
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
0.0ms
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))

series699.0ms

Calls
4 calls:
Slowest
461.0ms
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))
95.0ms
(fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))
91.0ms
(* (sqrt (sqrt 2)) t)
52.0ms
(* (sqrt (sqrt 2)) (* (sqrt (sqrt 2)) t))

simplify1.7s

Calls
29 calls:
Slowest
378.0ms
(* (* (* (sqrt (sqrt 2)) (sqrt (sqrt 2))) (sqrt (sqrt 2))) (* (* (* (sqrt (sqrt 2)) t) (* (sqrt (sqrt 2)) t)) (* (sqrt (sqrt 2)) t)))
236.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
207.0ms
(sqrt (sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t)))))
203.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
184.0ms
(sqrt (fma (/ l (/ x l)) 2 (* (+ 2 (/ 4 x)) (* t t))))

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

regimes543.0ms

Accuracy

73.7% (6.1b remaining)

Error of 9.9b against oracle of 3.8b and baseline of 27.0b

bsearch1.6s

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.1s10013×body80nan
1.5s5092×body80valid
928.0ms863×body1280valid
906.0ms1018×body640valid
705.0ms339×body320nan
538.0ms640×body640nan
532.0ms588×body1280nan
439.0ms654×body320valid
152.0ms373×body160valid
64.0ms185×body160nan