Details

Time bar (total: 25.0s)

sample328.0ms

Algorithm
intervals
Results
34.0ms318×body80nan
19.0ms166×body80valid
16.0ms32×body1280valid
13.0ms34×body640nan
11.0ms21×body1280nan
10.0ms24×body640valid
8.0ms27×body320valid
3.0ms9×body320nan
2.0ms7×body160valid
0.0ms4×body160nan

simplify4.7s

Counts
1 → 1
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
01827
14126
210026
323426
453126
5105126
6192926
7459326
done500026

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.5b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
0.5b
(* (sqrt 2.0) t)
12.5b
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
23.8b
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

rewrite188.0ms

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-/r/ cbrt-unprod unswap-sqr
1×sub-neg rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 fma-neg diff-log prod-diff pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 88
Calls
4 calls:
81.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
11.0ms
(* (sqrt 2.0) t)
24.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
66.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

series1.6s

Counts
4 → 12
Calls
4 calls:
706.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))))
62.0ms
(* (sqrt 2.0) t)
320.0ms
(- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l))
507.0ms
(sqrt (- (* (fma l l (* 2.0 (* t t))) (/ (+ x 1.0) (- x 1.0))) (* l l)))

simplify1.5s

Counts
100 → 100
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01552445
13732263
219182071
done50012066

prune659.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 32.7b

localize32.0ms

Local error

Found 4 expressions with local error:

4.7b
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l 2) x))))
5.3b
(/ (pow l 2) x)
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (fma (/ (pow t 2) x) 4.0 (* 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:
1.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l 2) x))))
10.0ms
(/ (pow l 2) x)
9.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l 2) x)))))

series500.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l 2) x))))
26.0ms
(/ (pow l 2) x)
40.0ms
(/ (pow t 2) x)
321.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l 2) x)))))

simplify1.0s

Counts
139 → 139
Iterations

Useful iterations: done (1.0s)

IterNodesCost
02171767
13991621
216061425
done50001420

prune805.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize54.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
4.7b
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

rewrite26.0ms

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 (/ (pow l (/ 2 2)) (/ x l)))
1.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
17.0ms
(/ (pow t 2) x)
3.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

series508.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(fma t t (/ (pow l (/ 2 2)) (/ x l)))
102.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l)))))
25.0ms
(/ (pow t 2) x)
290.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow l (/ 2 2)) (/ x l))))))

simplify661.0ms

Counts
98 → 98
Iterations

Useful iterations: done (656.0ms)

IterNodesCost
01601532
13001346
211761122
done50011117

prune584.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.9b

localize57.0ms

Local error

Found 4 expressions with local error:

1.0b
(fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
4.7b
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
10.2b
(/ (pow t 2) x)
30.5b
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

rewrite31.0ms

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 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
1.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
20.0ms
(/ (pow t 2) x)
4.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

series586.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
191.0ms
(fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
24.0ms
(/ (pow t 2) x)
270.0ms
(sqrt (fma (/ (pow t 2) x) 4.0 (* 2.0 (fma t t (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

simplify676.0ms

Counts
98 → 98
Iterations

Useful iterations: done (671.0ms)

IterNodesCost
01631742
13031586
212211334
done50001294

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.9b

regimes664.0ms

Accuracy

68.8% (7.4b remaining)

Error of 11.3b against oracle of 3.9b and baseline of 27.5b

bsearch2.0s

Steps
ItersRangePoint
8
1.6408579458501768e-121
4.556522159544336e-119
4.517101072782233e-119
9
2.0972313946662681e-184
1.2402052730190393e-177
5.156014301754716e-183
9
7.118961009208154e-257
8.264861022207576e-250
1.2838506268746495e-253
9
-3.148120069625892e-299
-2.2879652291577596e-306
-3.973880744580358e-300
8
-4.004652054920314e-256
-4.149126620126526e-259
-4.702934921132744e-259
10
-1.5855763995020358e-183
-8.487635768128844e-198
-3.093321223031471e-189
9
-2.9914453904952074e-147
-2.9474571731553717e-155
-2.995919227120962e-155
10
-1.0062559782947483e+141
-3.931503708037643e+123
-2.893044424140444e+127

simplify18.0ms

Iterations

Useful iterations: done (18.0ms)

IterNodesCost
059283
168248
273218
376218
done76217

end0.0ms

sample6.7s

Algorithm
intervals
Results
1.8s10100×body80nan
780.0ms640×body320valid
650.0ms630×body1280nan
635.0ms5124×body80valid
579.0ms838×body1280valid
495.0ms1025×body640valid
406.0ms583×body640nan
124.0ms169×body160nan
98.0ms305×body320nan
75.0ms373×body160valid