Details

Time bar (total: 40.8s)

sample179.0ms

Algorithm
intervals
Results
75.0ms354×body80nan
36.0ms279×body80valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02128
14928
215427
364227
4323927
done500027

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.5b

localize33.0ms

Local error

Found 4 expressions with local error:

7.8b
(/ (* l l) Om)
8.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0b
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
20.9b
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite263.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
25×pow1
24×add-sqr-sqrt *-un-lft-identity
23×add-cbrt-cube
20×add-cube-cbrt
18×prod-diff
16×prod-exp
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×cbrt-unprod
6×associate-*r* associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×flip3-- times-frac div-exp associate-/r* flip--
2×cbrt-undiv sub-neg sqrt-div associate-*r/ pow-exp *-commutative distribute-lft-out-- difference-of-squares
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod div-inv associate-/l*
Counts
4 → 115
Calls
4 calls:
20.0ms
(/ (* l l) Om)
57.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
91.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
88.0ms
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.1s

Counts
4 → 12
Calls
4 calls:
29.0ms
(/ (* l l) Om)
473.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
998.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.5s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify1.8s

Counts
127 → 127
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02813038
17062772
225452368
done50022339

prune528.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 22.4b

localize41.0ms

Local error

Found 4 expressions with local error:

6.9b
(* n (pow (/ l Om) 2.0))
8.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
10.0b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
20.9b
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite262.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
35×add-exp-log
31×*-un-lft-identity
27×add-cube-cbrt
25×pow1
23×associate-*r*
20×add-cbrt-cube
19×prod-exp
18×prod-diff
15×unpow-prod-down
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×times-frac cbrt-unprod
9×associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ pow-exp log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sub-neg sqrt-div associate-*r/ div-exp distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 131
Calls
4 calls:
29.0ms
(* n (pow (/ l Om) 2.0))
70.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
87.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
68.0ms
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.2s

Counts
4 → 12
Calls
4 calls:
196.0ms
(* n (pow (/ l Om) 2.0))
481.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
939.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.6s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify1.6s

Counts
143 → 143
Iterations

Useful iterations: done (1.6s)

IterNodesCost
03133277
17622989
225612595
done50012566

prune699.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 20.8b

localize33.0ms

Local error

Found 4 expressions with local error:

5.6b
(* n (pow (/ l Om) (/ 2.0 2)))
8.0b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
10.0b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
20.9b
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

rewrite403.0ms

Algorithm
rewrite-expression-head
Rules
99×add-exp-log
67×prod-exp
39×add-sqr-sqrt
31×*-un-lft-identity
27×add-cube-cbrt
25×pow1
24×add-cbrt-cube
23×associate-*r*
20×pow-exp
18×prod-diff
15×unpow-prod-down
13×pow-prod-down cbrt-unprod
11×distribute-rgt-in distribute-lft-in
10×pow-to-exp times-frac div-exp
9×associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×sub-neg sqrt-div associate-*r/ distribute-lft-out-- difference-of-squares sqr-pow
1×pow1/2 sqrt-prod div-inv
Counts
4 → 148
Calls
4 calls:
25.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
192.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
122.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
57.0ms
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

series4.6s

Counts
4 → 12
Calls
4 calls:
256.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
563.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
975.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
2.8s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

simplify2.0s

Counts
160 → 160
Iterations

Useful iterations: done (2.0s)

IterNodesCost
03485166
18533924
229473412
done50003383

prune899.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 20.6b

localize32.0ms

Local error

Found 4 expressions with local error:

5.6b
(* n (pow (/ l Om) (/ 2.0 2)))
6.2b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
10.0b
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U))
20.9b
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))

rewrite255.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
39×*-un-lft-identity
35×add-cube-cbrt
30×unpow-prod-down
29×add-exp-log
25×associate-*l*
23×pow1 associate-*r*
20×times-frac
18×prod-diff
17×add-cbrt-cube
14×prod-exp
12×pow-prod-down
11×distribute-rgt-in distribute-lft-in
8×cbrt-unprod unswap-sqr
4×expm1-log1p-u sqrt-pow1 associate-*l/ pow-exp log1p-expm1-u add-log-exp sqr-pow
3×flip3-- *-commutative flip--
2×pow-to-exp sub-neg sqrt-div associate-*r/ div-exp div-inv distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod
Counts
4 → 148
Calls
4 calls:
37.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
58.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
74.0ms
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U))
76.0ms
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))

series4.7s

Counts
4 → 12
Calls
4 calls:
223.0ms
(* n (pow (/ l Om) (/ 2.0 2)))
527.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
1.1s
(* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U))
2.8s
(sqrt (* (- t (fma 2.0 (* l (/ l Om)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))) (* (* 2.0 n) U)))

simplify1.8s

Counts
160 → 160
Iterations

Useful iterations: done (1.8s)

IterNodesCost
03564184
18033860
226213116
done50003087

prune834.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 20.3b

regimes1.1s

Accuracy

11.5% (10.0b remaining)

Error of 30.3b against oracle of 20.3b and baseline of 31.6b

bsearch695.0ms

Steps
ItersRangePoint
8
5.15625872640778e+143
9.21690699377622e+147
5.8658338131557224e+144
9
1.024298677426481e-58
1.930139365993194e-53
1.201900539256645e-58
7
5.447741291244494e-280
9.489145446758533e-278
4.693776387210434e-278

simplify16.0ms

Iterations

Useful iterations: done (15.0ms)

IterNodesCost
046172
161141
26494
36794
done6793

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.6s14686×body80nan
2.5s9192×body80valid