Details

Time bar (total: 21.8s)

sample252.0ms

Algorithm
intervals
Results
86.0ms338×body80nan
19.0ms156×body80valid
18.0ms40×body640valid
13.0ms24×body1280valid
9.0ms19×body1280nan
9.0ms20×body320nan
7.0ms24×body320valid
6.0ms14×body640nan
2.0ms12×body160valid
1.0ms5×body160nan

simplify1.5s

Counts
1 → 1

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.1b

localize70.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.5b
(* (sqrt 2.0) t)
13.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
77.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
11.0ms
(* (sqrt 2.0) t)
46.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
55.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts
4 → 12
Calls
4 calls:
688.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
78.0ms
(* (sqrt 2.0) t)
329.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.7s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.0s

Counts
92 → 92

prune511.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.5b

localize45.0ms

Local error

Found 4 expressions with local error:

5.3b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.9b
(/ (pow l 2) x)
9.5b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
24.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
18.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
47.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series442.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
41.0ms
(/ (pow l 2) x)
34.0ms
(/ (pow t 2) x)
263.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify1.1s

Counts
142 → 142

prune640.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
5.3b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
9.5b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
14.0ms
(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
21.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
15.0ms
(/ (pow t 2) x)
30.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

series409.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(+ (pow t 2) (* (fabs l) (/ (fabs l) x)))
84.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))))
34.0ms
(/ (pow t 2) x)
247.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))

simplify1.0s

Counts
104 → 104

prune667.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize41.0ms

Local error

Found 4 expressions with local error:

9.5b
(/ (pow t 2) x)
28.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
28.4b
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
28.4b
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×sqrt-div
24×add-cube-cbrt *-un-lft-identity times-frac
18×associate-*r/
12×unpow-prod-down
9×add-exp-log flip3-+ sqrt-prod flip-+
8×frac-add associate-/l*
7×pow1
6×add-cbrt-cube
4×frac-times unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
2×associate-*l/
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 102
Calls
4 calls:
9.0ms
(/ (pow t 2) x)
54.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
15.0ms
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
15.0ms
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))

series396.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ (pow t 2) x)
204.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x)))) (sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))))))
86.0ms
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))
69.0ms
(sqrt (+ (pow t 2) (* (fabs l) (/ (fabs l) x))))

simplify1.1s

Counts
114 → 114

prune688.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

regimes705.0ms

Accuracy

76.6% (5.6b remaining)

Error of 9.5b against oracle of 3.9b and baseline of 27.9b

bsearch371.0ms

Steps
ItersRangePoint
9
9.324172023423285e+142
1.1012045087961449e+149
1.6421833813677545e+146
10
-1.1979006433782284e+85
-5.09199279650327e+67
-2.8442338941596414e+80

simplify657.0ms

end0.0ms

sample6.8s

Algorithm
intervals
Results
1.4s10110×body80nan
1.4s1030×body640valid
745.0ms5091×body80valid
620.0ms847×body1280valid
552.0ms381×body320nan
343.0ms656×body320valid
335.0ms601×body1280nan
294.0ms584×body640nan
77.0ms376×body160valid
35.0ms183×body160nan