Details

Time bar (total: 1.1m)

sample234.0ms

Algorithm
intervals
Results
101.0ms521×body80nan
45.0ms299×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.8b

localize46.0ms

Local error

Found 4 expressions with local error:

7.3b
(/ (* l l) Om)
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite542.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
30×prod-diff
26×add-sqr-sqrt *-un-lft-identity
25×pow1
24×add-cube-cbrt
23×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
16×prod-exp
13×pow-prod-down
11×flip3-- flip--
10×associate--l+ cbrt-unprod
8×associate-*r* frac-sub
6×sub-neg sqrt-div
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp
3×times-frac div-exp associate-/r*
2×cbrt-undiv associate-*l* pow-exp *-commutative
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 141
Calls
4 calls:
21.0ms
(/ (* l l) Om)
96.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
204.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
208.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.1s

Counts
4 → 12
Calls
4 calls:
24.0ms
(/ (* l l) Om)
548.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.8s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ (* l l) Om))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify2.8s

Counts
153 → 153
Iterations

Useful iterations: 2 (1.3s)

IterNodesCost
04114799
111414430
246813850
done50003850

prune786.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 26.9b

localize21.0ms

Local error

Found 4 expressions with local error:

5.7b
(* n (pow (/ l Om) 2.0))
7.7b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

rewrite500.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
35×add-exp-log
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×add-cbrt-cube
19×prod-exp
15×unpow-prod-down
13×pow-prod-down
11×flip3-- flip--
10×times-frac associate--l+ cbrt-unprod
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×pow-to-exp div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 157
Calls
4 calls:
39.0ms
(* n (pow (/ l Om) 2.0))
80.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
210.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
164.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

series9.6s

Counts
4 → 12
Calls
4 calls:
265.0ms
(* n (pow (/ l Om) 2.0))
670.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
1.9s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*))))
6.8s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* n (pow (/ l Om) 2.0)) (- U U*)))))

simplify3.3s

Counts
169 → 169
Iterations

Useful iterations: 2 (1.5s)

IterNodesCost
04435038
111974647
247024089
done50004089

prune984.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 25.6b

localize53.0ms

Local error

Found 4 expressions with local error:

7.7b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
8.0b
(* n (pow (/ l Om) (/ 2.0 2)))
12.4b
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

rewrite748.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
41×add-sqr-sqrt
33×*-un-lft-identity
31×add-cube-cbrt
30×prod-diff
25×pow1 associate-*r*
24×add-cbrt-cube
22×associate-*r/
21×distribute-rgt-in distribute-lft-in
20×pow-exp
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×flip3-- flip--
10×pow-to-exp times-frac div-exp associate--l+
8×frac-sub
6×sub-neg sqrt-div
5×associate-*l*
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×*-commutative
2×sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 174
Calls
4 calls:
238.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
30.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
280.0ms
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
191.0ms
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

series10.5s

Counts
4 → 12
Calls
4 calls:
522.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
260.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
2.1s
(* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
7.6s
(sqrt (* (* (* 2.0 n) U) (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))))

simplify978.0ms

Counts
186 → 186
Iterations

Useful iterations: done (965.0ms)

IterNodesCost
04797307
112905730
done50005038

prune1.2s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 25.5b

localize73.0ms

Local error

Found 4 expressions with local error:

16.4b
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
16.4b
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
16.4b
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
20.8b
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

rewrite881.0ms

Algorithm
rewrite-expression-head
Rules
158×associate-*r/
148×cbrt-div
94×flip3-- flip--
76×frac-times
62×sqrt-div
40×frac-sub
34×pow1
22×pow-prod-down associate-*l/
13×cbrt-prod
11×add-sqr-sqrt *-un-lft-identity
8×sqrt-pow1
7×add-cube-cbrt
4×add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
2×distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod
Counts
4 → 134
Calls
4 calls:
4.0ms
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
5.0ms
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
54.0ms
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
805.0ms
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

series6.0s

Counts
4 → 12
Calls
4 calls:
1.0s
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
1.2s
(cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))
1.0s
(cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))
2.8s
(sqrt (* (* (* 2.0 n) (* (* U (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2))))))))) (cbrt (- t (fma 2.0 (/ l (/ Om l)) (* (- U U*) (* n (pow (/ l Om) (* 2 (/ 2.0 2)))))))))) (cbrt (- (- t (* 2.0 (/ l (/ Om l)))) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))))

simplify2.4s

Counts
146 → 146
Iterations

Useful iterations: done (2.4s)

IterNodesCost
053619420
1133717447
2432015673
done500015534

prune2.1s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 24.9b

regimes1.1s

Accuracy

14% (8.6b remaining)

Error of 29.8b against oracle of 21.3b and baseline of 31.2b

bsearch637.0ms

Steps
ItersRangePoint
6
1.8201656030287107e+147
8.233449218191808e+147
1.8470005031618575e+147
10
8.558334221433006e+131
2.157787304016569e+145
1.0381668918954598e+145
6
-1.8074549885472418e-147
-1.327451324818211e-148
-1.7708242025566493e-147

simplify13.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
077357
1102357
done102357

end0.0ms

sample7.1s

Algorithm
intervals
Results
3.6s14816×body80nan
1.4s9208×body80valid