Details

Time bar (total: 13.0s)

sample108.0ms

Algorithm
intervals
Results
27.0ms23×body1280nan
16.0ms322×body80nan
9.0ms156×body80valid
8.0ms32×body1280valid
7.0ms38×body640valid
4.0ms22×body640nan
3.0ms18×body320valid
2.0ms10×body320nan
1.0ms12×body160valid
0.0ms5×body160nan

simplify93.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04114
110114
223414
352514
4101614
5170114
6362614
7500214
done500214

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize18.0ms

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))))
0.4b
(* (sqrt 2.0) t)
13.9b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.6b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite149.0ms

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:
53.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
9.0ms
(* (sqrt 2.0) t)
32.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
51.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
439.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
46.0ms
(* (sqrt 2.0) t)
224.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.2s
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify62.0ms

Counts
102 → 102
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04461290
122061177
250021172
done50021172

prune358.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.6b

localize24.0ms

Local error

Found 4 expressions with local error:

4.4b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
7.8b
(/ (pow l 2) x)
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

rewrite22.0ms

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 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
8.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

series387.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x))))
19.0ms
(/ (pow l 2) x)
19.0ms
(/ (pow t 2) x)
275.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow l 2) x) (* 4.0 (/ (pow t 2) x)))))

simplify43.0ms

Counts
139 → 139
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0377811
11351724
25001715
done5001715

prune463.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.0b

localize24.0ms

Local error

Found 4 expressions with local error:

2.0b
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
4.4b
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x))))
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x)))))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
477×times-frac
208×add-sqr-sqrt
207×add-cube-cbrt *-un-lft-identity
176×unpow-prod-down
63×cbrt-prod unpow2 sqr-pow
49×add-exp-log
40×associate-/r*
31×div-exp
14×associate-/l*
13×pow-exp
11×add-cbrt-cube
9×pow-to-exp div-inv
5×pow1
4×cbrt-undiv expm1-log1p-u prod-exp log1p-expm1-u add-log-exp
3×sqrt-prod
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2 associate-/r/ fma-udef
Counts
4 → 372
Calls
4 calls:
26.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
0.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x))))
8.0ms
(/ (pow t 2) x)
2.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x)))))

series447.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
91.0ms
(fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x))))
18.0ms
(/ (pow t 2) x)
288.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))) (* 4.0 (/ (pow t 2) x)))))

simplify67.0ms

Counts
384 → 384
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
014775550
150024324
done50024324

prune1.3s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.0b

localize31.0ms

Local error

Found 4 expressions with local error:

27.3b
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))))
31.2b
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
31.2b
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
31.2b
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
1260×times-frac
843×cbrt-prod
498×add-sqr-sqrt
497×add-cube-cbrt *-un-lft-identity
435×unpow-prod-down
165×unpow2 sqr-pow
21×div-inv
5×pow1
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cbrt-div pow1/3 sqrt-prod associate-/r/
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 729
Calls
4 calls:
1.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))))
18.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
18.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
21.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))

series637.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(sqrt (fma 2.0 (pow t 2) (fma 2.0 (* (* (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))) (* 4.0 (/ (pow t 2) x)))))
94.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
92.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
98.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))

simplify139.0ms

Counts
741 → 741
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
0154714364
1500114009
done500114009

prune3.2s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.0b

regimes485.0ms

Accuracy

71.2% (7.1b remaining)

Error of 11.0b against oracle of 3.9b and baseline of 28.4b

bsearch688.0ms

Steps
ItersRangePoint
9
3.5307849290302813e-79
1.4309834081351868e-71
1.4086343395051824e-71
8
1.9331730416670513e-145
3.203389628538628e-142
1.96678984226064e-145
7
2.9864185856163577e-279
3.6043515955327495e-277
3.155486028136924e-278
7
-4.881804416771232e-192
-8.553073611070034e-194
-1.8378980932293354e-192
10
-2.153678170399452e-149
-7.582263287327444e-161
-2.7094616069098305e-160
7
-3.61369871224165e+84
-8.523850575778694e+82
-3.489486864712887e+84

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
074137
174137
done74137

end0.0ms

sample2.3s

Algorithm
intervals
Results
495.0ms10246×body80nan
258.0ms5071×body80valid
221.0ms895×body1280valid
206.0ms1045×body640valid
143.0ms605×body1280nan
113.0ms603×body640nan
85.0ms603×body320valid
43.0ms320×body320nan
37.0ms386×body160valid
16.0ms175×body160nan