Details

Time bar (total: 32.1s)

sample441.0ms

Algorithm
intervals
Results
128.0ms317×body80nan
91.0ms36×body640valid
68.0ms155×body80valid
26.0ms26×body1280valid
20.0ms16×body1280nan
14.0ms25×body320valid
8.0ms10×body640nan
6.0ms14×body160valid
3.0ms7×body320nan
3.0ms5×body160nan

simplify778.0ms

Calls
1 calls:
Slowest
778.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 42.6b

localize61.0ms

Local error

Found 4 expressions with local error:

19.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
14.2b
(- (* (/ (+ 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))))

rewrite92.0ms

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
34.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
29.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
21.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
5.0ms
(* (sqrt 2) t)

series2.0s

Calls
4 calls:
Slowest
1.3s
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
434.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
240.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
48.0ms
(* (sqrt 2) t)

simplify7.4s

Calls
49 calls:
Slowest
338.0ms
(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)))))
332.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
295.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
268.0ms
(* (* l l) (/ (+ x 1) (- x 1)))
247.0ms
(/ (exp (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (exp (* l l)))

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 7.2b

localize18.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
6.0b
(/ (* l l) x)
1.0b
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
0.4b
(* (sqrt 2) t)

rewrite7.0ms

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)
1.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
0.0ms
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))

series675.0ms

Calls
4 calls:
Slowest
474.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
103.0ms
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
57.0ms
(* (sqrt 2) t)
41.0ms
(/ (* l l) x)

simplify1.1s

Calls
18 calls:
Slowest
214.0ms
(sqrt (sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))))
205.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
199.0ms
(sqrt (* (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))) (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))))
189.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
154.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))

prune841.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize33.0ms

Local error

Found 4 expressions with local error:

27.6b
(sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))
8.4b
(fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))
0.4b
(* (sqrt 2) t)
0.1b
(/ (* (sqrt 2) t) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* times-frac associate-*l* sqrt-prod
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
13.0ms
(/ (* (sqrt 2) t) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))
5.0ms
(* (sqrt 2) t)
2.0ms
(sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))
0.0ms
(fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))

series439.0ms

Calls
4 calls:
Slowest
220.0ms
(sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))
87.0ms
(fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))
83.0ms
(/ (* (sqrt 2) t) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))
48.0ms
(* (sqrt 2) t)

simplify4.5s

Calls
30 calls:
Slowest
357.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
321.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
285.0ms
(/ (* (* (* (sqrt 2) t) (* (sqrt 2) t)) (* (sqrt 2) t)) (* (* (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))))) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))))))
234.0ms
(/ (* t (sqrt 2)) (fabs (sqrt (fma (pow t 2) (/ 4 x) (* 2 (fma (/ l x) l (pow t 2)))))))
224.0ms
(- (log (* (sqrt 2) t)) (log (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))))))

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2) t)
0.4b
(* (sqrt 2) t)
0.4b
(/ t (sqrt 2))
0.4b
(/ t (sqrt 2))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×associate-/r* associate-*l*
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg *-commutative div-inv
Calls
4 calls:
Slowest
3.0ms
(* (sqrt 2) t)
3.0ms
(* (sqrt 2) t)
1.0ms
(/ t (sqrt 2))
0.0ms
(/ t (sqrt 2))

series260.0ms

Calls
4 calls:
Slowest
82.0ms
(/ t (sqrt 2))
69.0ms
(* (sqrt 2) t)
60.0ms
(/ t (sqrt 2))
48.0ms
(* (sqrt 2) t)

simplify120.0ms

Calls
22 calls:
Slowest
9.0ms
(sqrt (sqrt 2))
8.0ms
(/ t (sqrt 2))
8.0ms
(* t (sqrt 2))
8.0ms
(* t (sqrt 2))
7.0ms
(* t (sqrt 2))

prune883.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 4.4b

regimes948.0ms

Accuracy

54.4% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 15.5b

bsearch492.0ms

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.2s10002×body80nan
1.4s832×body1280valid
1.1s5172×body80valid
1.1s1006×body640valid
929.0ms606×body1280nan
463.0ms585×body640nan
460.0ms617×body320valid
238.0ms373×body320nan
135.0ms373×body160valid
119.0ms190×body160nan