Details

Time bar (total: 12.5s)

sample105.0ms

Algorithm
intervals
Results
27.0ms23×body1280nan
15.0ms322×body80nan
8.0ms156×body80valid
8.0ms32×body1280valid
8.0ms38×body640valid
4.0ms22×body640nan
3.0ms18×body320valid
2.0ms10×body320nan
1.0ms12×body160valid
1.0ms5×body160nan

simplify83.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114
done500114

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize19.0ms

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)))

rewrite145.0ms

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:
52.0ms
(/ (* (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)
31.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
49.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series1.9s

Counts
4 → 12
Calls
4 calls:
436.0ms
(/ (* (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)))

simplify60.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (49.0ms)

IterNodesCost
04171207
120511099
250021094
done50021094

prune302.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 5.6b

localize18.0ms

Local error

Found 4 expressions with local error:

4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
7.8b
(/ (pow l 2) x)
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite59.0ms

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:
21.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.0ms
(/ (pow l 2) x)
8.0ms
(/ (pow t 2) x)
17.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series273.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
19.0ms
(/ (pow l 2) x)
24.0ms
(/ (pow t 2) x)
160.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify61.0ms

Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261093
12235984
25001978
done5001978

prune432.0ms

Pruning

8 alts after pruning (7 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)))
4.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
9.2b
(/ (pow t 2) x)
27.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

rewrite94.0ms

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
8×associate-*r/
6×add-log-exp
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add prod-exp flip-+
3×sqrt-prod
2×associate-+r+ frac-2neg clear-num
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log associate-/r/
Counts
4 → 375
Calls
4 calls:
23.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
17.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
8.0ms
(/ (pow t 2) x)
20.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

series346.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))
91.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))))
18.0ms
(/ (pow t 2) x)
189.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2)))))))

simplify72.0ms

Counts
387 → 387
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
016225971
150014790
done50014790

prune1.2s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.0b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

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 sqrt-div associate-*r/ add-cbrt-cube add-log-exp
3×cbrt-div pow1/3 sqrt-prod associate-/r/
2×flip3-+ frac-add flip-+
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 725
Calls
4 calls:
19.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 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))))) (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))))
18.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
22.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))

series528.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 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))))) (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))))
92.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))
95.0ms
(cbrt (/ (pow (* (cbrt l) (cbrt l)) 2) (/ x (pow (cbrt l) 2))))

simplify153.0ms

Counts
737 → 737
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0169914875
1500214508
done500214508

prune3.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 4.0b

regimes443.0ms

Accuracy

71.2% (7.1b remaining)

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

bsearch705.0ms

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
090144
190144
done90144

end0.0ms

sample2.2s

Algorithm
intervals
Results
501.0ms10246×body80nan
257.0ms5071×body80valid
226.0ms895×body1280valid
208.0ms1045×body640valid
141.0ms605×body1280nan
112.0ms603×body640nan
86.0ms603×body320valid
43.0ms320×body320nan
37.0ms386×body160valid
18.0ms175×body160nan