Details

Time bar (total: 2.8m)

sample223.0ms

Algorithm
intervals
Results
91.0ms532×body80nan
35.0ms305×body80valid

simplify6.5s

Counts
1 → 1
Iterations
IterNodes
done5002
42913
3614
2150
149
021

prune77.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize112.0ms

Local error

Found 4 expressions with local error:

6.2b
(* n (pow (/ l Om) 2.0))
7.3b
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
8.0b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
20.1b
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

rewrite539.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
35×add-exp-log
29×*-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 associate-*r/ cbrt-unprod
7×associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ pow-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- *-commutative flip--
2×pow-to-exp sub-neg sqrt-div div-exp sqr-pow
1×pow1/2 sqrt-prod div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 133
Calls
4 calls:
65.0ms
(* n (pow (/ l Om) 2.0))
203.0ms
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
128.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
120.0ms
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

series27.9s

Counts
4 → 12
Calls
4 calls:
479.0ms
(* n (pow (/ l Om) 2.0))
3.2s
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0))
1.1s
(* (* n (pow (/ l Om) 2.0)) (- U U*))
23.2s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) 2.0)) (- U U*))))) 2.0)))

simplify5.7s

Counts
145 → 145
Iterations
IterNodes
done5005
23310
1978
0357

prune2.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 22.6b

localize133.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
7.3b
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
8.0b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
20.1b
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

rewrite700.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
63×prod-exp
25×pow1
22×add-cbrt-cube
20×add-sqr-sqrt *-un-lft-identity
18×prod-diff pow-exp add-cube-cbrt
13×pow-prod-down
12×cbrt-unprod
11×distribute-rgt-in distribute-lft-in
10×associate-*r/
9×pow-to-exp div-exp
6×associate-*r*
4×expm1-log1p-u sqrt-pow1 associate-*l* associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg sqrt-div *-commutative
1×pow1/2 sqrt-prod fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 121
Calls
4 calls:
1.0ms
(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
158.0ms
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
389.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
134.0ms
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

series28.6s

Counts
4 → 12
Calls
4 calls:
926.0ms
(fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
3.2s
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0))
1.2s
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
23.2s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))))) 2.0)))

simplify6.4s

Counts
133 → 133
Iterations
IterNodes
done5004
23584
1954
0335

prune2.3s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 21.9b

localize99.0ms

Local error

Found 4 expressions with local error:

4.1b
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
4.8b
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
7.3b
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
20.1b
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

rewrite374.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
28×*-un-lft-identity
26×add-cube-cbrt
23×pow1
21×add-exp-log
20×associate-*l*
18×prod-diff
15×unpow-prod-down add-cbrt-cube
12×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×times-frac prod-exp associate-*r/
7×cbrt-unprod
6×associate-*r*
4×expm1-log1p-u sqrt-pow1 associate-*l/ insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- flip--
2×sub-neg sqrt-div pow-exp *-commutative sqr-pow
1×pow-to-exp pow1/2 div-exp sqrt-prod fma-udef div-inv distribute-lft-out-- difference-of-squares
Counts
4 → 121
Calls
4 calls:
1.0ms
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
76.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
158.0ms
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
129.0ms
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

series28.2s

Counts
4 → 12
Calls
4 calls:
925.0ms
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*))))
952.0ms
(* (pow (/ l Om) (/ 2.0 2)) (- U U*))
3.5s
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0))
22.9s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ l Om) (/ 2.0 2)) (- U U*)))))) 2.0)))

simplify5.4s

Counts
133 → 133
Iterations
IterNodes
done5008
23167
1899
0354

prune2.8s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 21.1b

localize327.0ms

Local error

Found 4 expressions with local error:

4.0b
(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
4.1b
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
7.3b
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0))
20.1b
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

rewrite391.0ms

Algorithm
rewrite-expression-head
Rules
25×pow1
23×add-sqr-sqrt
21×*-un-lft-identity
19×add-cube-cbrt
18×prod-diff
15×add-cbrt-cube add-exp-log
13×pow-prod-down
11×distribute-rgt-in distribute-lft-in
10×associate-*r/
7×prod-exp cbrt-unprod
6×associate-*r* associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ insert-posit16 log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg sqrt-div *-commutative
1×pow1/2 sqrt-prod fma-udef distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 102
Calls
4 calls:
66.0ms
(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
2.0ms
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
147.0ms
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0))
161.0ms
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

series30.3s

Counts
4 → 12
Calls
4 calls:
2.6s
(* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))))
992.0ms
(fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*)))))
3.1s
(* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0))
23.6s
(sqrt (* U (* (* n (- t (fma (/ l Om) (* 2.0 l) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (pow (/ (* (cbrt l) (cbrt l)) (* (cbrt Om) (cbrt Om))) (/ 2.0 2)) (* (pow (/ (cbrt l) (cbrt Om)) (/ 2.0 2)) (- U U*))))))) 2.0)))

simplify5.6s

Counts
114 → 114
Iterations
IterNodes
done5006
22655
1748
0286

prune2.6s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 20.7b

regimes4.4s

Accuracy

30.3% (7.4b remaining)

Error of 27.3b against oracle of 19.9b and baseline of 30.6b

bsearch223.0ms

Steps
ItersRangePoint
9
-1.8258581717670128e-306
1.8155718285527778e-305
-5.889660218949e-311

simplify50.0ms

Iterations
IterNodes
done61
161
044

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.8s15197×body80nan
1.8s9217×body80valid