Details

Time bar (total: 25.2s)

sample306.0ms

Algorithm
intervals
Results
97.0ms361×body80nan
24.0ms182×body80valid
16.0ms23×body1280valid
14.0ms27×body640valid
12.0ms19×body1280nan
7.0ms13×body320valid
7.0ms15×body640nan
4.0ms11×body320nan
3.0ms11×body160valid
1.0ms4×body160nan

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
01827
14126
210026
323426
453126
5105126
6192926
7459326
done500026

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.4b

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
11.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite242.0ms

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×expm1-log1p-u sqrt-div 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 sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 90
Calls
4 calls:
99.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
10.0ms
(* (sqrt 2.0) t)
43.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
83.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.9s

Counts
4 → 12
Calls
4 calls:
655.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
51.0ms
(* (sqrt 2.0) t)
300.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.9s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify2.2s

Counts
102 → 102
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01792660
14842380
227402183
done50012176

prune542.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.1b

localize30.0ms

Local error

Found 4 expressions with local error:

3.9b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
4.7b
(/ (pow l 2) x)
11.3b
(/ (pow t 2) x)
27.7b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

rewrite30.0ms

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×add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r*
5×pow1
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×sqrt-prod
2×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
1×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 127
Calls
4 calls:
0.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
9.0ms
(/ (pow l 2) x)
12.0ms
(/ (pow t 2) x)
4.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

series428.0ms

Counts
4 → 12
Calls
4 calls:
101.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x))))
34.0ms
(/ (pow l 2) x)
36.0ms
(/ (pow t 2) x)
256.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify885.0ms

Counts
139 → 139
Iterations

Useful iterations: done (878.0ms)

IterNodesCost
02161767
13981621
215761429
done50001426

prune757.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.6b

localize47.0ms

Local error

Found 4 expressions with local error:

0.5b
(fma t t (/ l (/ x l)))
3.9b
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
11.3b
(/ (pow t 2) x)
27.7b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

rewrite25.0ms

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-/l*
6×add-cbrt-cube
5×pow1
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×div-exp associate-/r* sqrt-prod
2×fma-udef
1×cbrt-undiv pow-to-exp rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 86
Calls
4 calls:
1.0ms
(fma t t (/ l (/ x l)))
1.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
17.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

series438.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(fma t t (/ l (/ x l)))
98.0ms
(fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l)))))
30.0ms
(/ (pow t 2) x)
244.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (fma t t (/ l (/ x l))))))

simplify620.0ms

Counts
98 → 98
Iterations

Useful iterations: done (612.0ms)

IterNodesCost
01581364
12931266
211241124
done50001119

prune610.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.6b

localize45.0ms

Local error

Found 4 expressions with local error:

11.3b
(/ (pow t 2) x)
27.7b
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))
28.1b
(sqrt (fma t t (/ l (/ x l))))
28.1b
(sqrt (fma t t (/ l (/ x l))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
24×add-cube-cbrt *-un-lft-identity times-frac
12×unpow-prod-down
9×add-exp-log sqrt-prod
8×associate-/l*
7×pow1
6×add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 96
Calls
4 calls:
11.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))
2.0ms
(sqrt (fma t t (/ l (/ x l))))
2.0ms
(sqrt (fma t t (/ l (/ x l))))

series521.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ (pow t 2) x)
242.0ms
(sqrt (fma 4.0 (/ (pow t 2) x) (* 2.0 (* (sqrt (fma t t (/ l (/ x l)))) (sqrt (fma t t (/ l (/ x l))))))))
124.0ms
(sqrt (fma t t (/ l (/ x l))))
133.0ms
(sqrt (fma t t (/ l (/ x l))))

simplify594.0ms

Counts
108 → 108
Iterations

Useful iterations: done (590.0ms)

IterNodesCost
01551536
12901194
210071088
done50011086

prune709.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.6b

regimes588.0ms

Accuracy

72.5% (6.7b remaining)

Error of 10.4b against oracle of 3.7b and baseline of 28.0b

bsearch1.7s

Steps
ItersRangePoint
9
120598577249.33295
4.0571253922894675e+17
3.996178578621348e+17
7
2.350322407405638e-155
1.4722807743973814e-153
2.3938287644345074e-155
9
1.0833252341973962e-258
2.7305213248627865e-250
4.761463376941263e-255
4
2.4448033833944457e-307
3.792221310577071e-307
2.483283582103816e-307
7
-1.0924451814151017e-167
-1.515188990120532e-169
-2.7475651167318553e-168
8
-2.766418797691212e+17
-341683923293129.4
-2.739099727305944e+17

simplify11.0ms

Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
063295
175257
done75257

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.3s10120×body80nan
834.0ms5129×body80valid
506.0ms835×body1280valid
435.0ms994×body640valid
338.0ms577×body1280nan
253.0ms662×body320valid
226.0ms597×body640nan
159.0ms380×body160valid
141.0ms359×body320nan
34.0ms186×body160nan