Details

Time bar (total: 36.8s)

sample253.0ms

Algorithm
intervals
Results
50.0ms25×body1280valid
39.0ms324×body80nan
21.0ms169×body80valid
20.0ms37×body640valid
11.0ms20×body640nan
9.0ms15×body1280nan
6.0ms17×body320valid
6.0ms17×body320nan
2.0ms8×body160nan
2.0ms8×body160valid

simplify673.0ms

Calls
1 calls:
Slowest
672.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 37.5b

localize62.0ms

Local error

Found 4 expressions with local error:

17.6b
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
10.4b
(- (* (/ (+ 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))))

rewrite84.0ms

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
36.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
30.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
10.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
3.0ms
(* (sqrt 2) t)

series1.3s

Calls
4 calls:
Slowest
874.0ms
(sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l)))
290.0ms
(/ (* (sqrt 2) t) (sqrt (- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))))
135.0ms
(- (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) (* l l))
32.0ms
(* (sqrt 2) t)

simplify7.2s

Calls
49 calls:
Slowest
347.0ms
(- (+ (* 2 (pow t 2)) (+ (* 2 (* x (pow l 2))) (* 2 (pow l 2)))))
316.0ms
(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)))))
292.0ms
(/ (* (* (* (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)))))
274.0ms
(sqrt (- (pow (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t)))) 3) (pow (* l l) 3)))
273.0ms
(/ (exp (* (/ (+ x 1) (- x 1)) (+ (* l l) (* 2 (* t t))))) (exp (* l l)))

prune1.3s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.8b

localize38.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
4.9b
(/ (* l l) x)
0.6b
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
0.4b
(* (sqrt 2) t)

rewrite15.0ms

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
6.0ms
(* (sqrt 2) t)
6.0ms
(/ (* l l) x)
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)))

series354.0ms

Calls
4 calls:
Slowest
260.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
42.0ms
(fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))
35.0ms
(* (sqrt 2) t)
16.0ms
(/ (* l l) x)

simplify1.2s

Calls
18 calls:
Slowest
211.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
203.0ms
(sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))
198.0ms
(+ (* 2 (pow t 2)) (+ (* 2 (/ (pow l 2) x)) (* 4 (/ (pow t 2) x))))
176.0ms
(sqrt (* (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))) (cbrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t))))))
169.0ms
(sqrt (sqrt (fma (/ (* l l) x) 2 (* (+ 2 (/ 4 x)) (* t t)))))

prune828.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))
5.6b
(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)))))))

rewrite11.0ms

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
7.0ms
(/ (* (sqrt 2) t) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))
3.0ms
(* (sqrt 2) t)
1.0ms
(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))))

series242.0ms

Calls
4 calls:
Slowest
108.0ms
(sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))
58.0ms
(/ (* (sqrt 2) t) (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))
41.0ms
(fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))
35.0ms
(* (sqrt 2) t)

simplify4.3s

Calls
30 calls:
Slowest
344.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
302.0ms
(/ (* (* (* (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))))))))
295.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
228.0ms
(/ (* t (sqrt 2)) (fabs (sqrt (fma (pow t 2) (/ 4 x) (* 2 (fma (/ l x) l (pow t 2)))))))
222.0ms
(/ (sqrt 2) (* (cbrt (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t))))))) (cbrt (fabs (sqrt (fma (* t t) (/ 4 x) (* 2 (fma (/ l x) l (* t t)))))))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize42.0ms

Local error

Found 4 expressions with local error:

24.7b
(sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))
6.7b
(/ (* t t) x)
3.8b
(fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))
0.4b
(/ (sqrt 2) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
9×times-frac
6×add-cbrt-cube add-exp-log
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l* add-log-exp
3×associate-/r* sqrt-prod
2×clear-num frac-2neg div-inv
1×cbrt-undiv rem-sqrt-square pow1/2 div-exp fma-udef
Calls
4 calls:
Slowest
6.0ms
(/ (sqrt 2) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))))
5.0ms
(/ (* t t) x)
2.0ms
(sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))
0.0ms
(fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))

series188.0ms

Calls
4 calls:
Slowest
101.0ms
(sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))
40.0ms
(/ (sqrt 2) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))))
37.0ms
(fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))
10.0ms
(/ (* t t) x)

simplify6.3s

Calls
41 calls:
Slowest
367.0ms
(- (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))) (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))))
341.0ms
(/ (* (* (sqrt 2) (sqrt 2)) (sqrt 2)) (* (* (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))))) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))))))
313.0ms
(- (* 2 (/ t (* (pow (sqrt 2) 3) (pow x 2)))) (+ (* t (sqrt 2)) (* 2 (/ t (* (sqrt 2) x)))))
244.0ms
(/ (cbrt (sqrt 2)) (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))))
222.0ms
(/ (* (cbrt (sqrt 2)) (cbrt (sqrt 2))) (* (cbrt (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2))))) (cbrt (fabs (sqrt (fma (/ (* t t) x) 4 (* (fma (/ l x) l (* t t)) 2)))))))

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

regimes558.0ms

Accuracy

41.5% (6.7b remaining)

Error of 10.5b against oracle of 3.9b and baseline of 15.3b

bsearch1.5s

end0.0ms

sample8.2s

Algorithm
intervals
Results
2.6s10058×body80nan
1.3s855×body1280valid
1.1s5089×body80valid
857.0ms1041×body640valid
637.0ms585×body1280nan
464.0ms595×body640nan
395.0ms641×body320valid
192.0ms323×body320nan
132.0ms374×body160valid
62.0ms171×body160nan