Details

Time bar (total: 45.1s)

sample473.0ms

Algorithm
intervals
Results
102.0ms293×body80valid
92.0ms517×body80nan

simplify3.7s

Counts
1 → 1
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
02128
14928
215427
366427
4414327
done500027

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.4b

localize45.0ms

Local error

Found 4 expressions with local error:

6.7b
(* n (pow (/ l Om) 2.0))
6.8b
(/ (* l l) Om)
9.1b
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
20.0b
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite265.0ms

Algorithm
rewrite-expression-head
Rules
26×add-exp-log add-sqr-sqrt
23×pow1
20×add-cbrt-cube
18×*-un-lft-identity associate-*r*
16×add-cube-cbrt
15×unpow-prod-down
13×times-frac
12×pow-prod-down
11×prod-exp
8×associate-*l* cbrt-unprod
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp unswap-sqr
3×div-exp associate-/r*
2×cbrt-undiv flip3-- sqrt-div pow-exp *-commutative flip-- div-inv sqr-pow
1×pow-to-exp frac-2neg pow1/2 clear-num sqrt-prod associate-/l* distribute-lft-out-- difference-of-squares
Counts
4 → 106
Calls
4 calls:
51.0ms
(* n (pow (/ l Om) 2.0))
21.0ms
(/ (* l l) Om)
119.0ms
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
62.0ms
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.3s

Counts
4 → 12
Calls
4 calls:
211.0ms
(* n (pow (/ l Om) 2.0))
22.0ms
(/ (* l l) Om)
1.1s
(* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.9s
(sqrt (* (- t (fma 2.0 (/ (* l l) Om) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify2.2s

Counts
118 → 118
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02512234
16452134
233481861
done50021856

prune884.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 23.1b

localize35.0ms

Local error

Found 4 expressions with local error:

6.3b
(* (* n (pow (/ l Om) 2.0)) (- U U*))
6.7b
(* n (pow (/ l Om) 2.0))
9.1b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
20.0b
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

rewrite258.0ms

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:
62.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
36.0ms
(* n (pow (/ l Om) 2.0))
92.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
59.0ms
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

series4.8s

Counts
4 → 12
Calls
4 calls:
533.0ms
(* (* n (pow (/ l Om) 2.0)) (- U U*))
209.0ms
(* n (pow (/ l Om) 2.0))
1.1s
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U))
2.9s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) 2.0)) (- U U*)))) (* (* 2.0 n) U)))

simplify3.0s

Counts
143 → 143
Iterations

Useful iterations: done (3.0s)

IterNodesCost
03143277
18373008
244642607
done50002603

prune1.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 21.2b

localize47.0ms

Local error

Found 4 expressions with local error:

4.3b
(fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
6.3b
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
9.1b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
20.0b
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

rewrite419.0ms

Algorithm
rewrite-expression-head
Rules
91×add-exp-log
63×prod-exp
25×pow1
22×add-sqr-sqrt *-un-lft-identity add-cbrt-cube
18×add-cube-cbrt prod-diff pow-exp
13×pow-prod-down
12×cbrt-unprod
11×distribute-rgt-in distribute-lft-in
9×pow-to-exp div-exp
6×associate-*r* associate-*l*
4×expm1-log1p-u sqrt-pow1 associate-*l/ log1p-expm1-u add-log-exp
3×flip3-- flip--
2×sub-neg sqrt-div associate-*r/ *-commutative distribute-lft-out-- difference-of-squares
1×pow1/2 sqrt-prod fma-udef
Counts
4 → 119
Calls
4 calls:
1.0ms
(fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
210.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
101.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
93.0ms
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* 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:
457.0ms
(fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))
508.0ms
(* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*))
1.1s
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U))
2.7s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* (* n (pow (/ l Om) (/ 2.0 2))) (pow (/ l Om) (/ 2.0 2))) (- U U*)))) (* (* 2.0 n) U)))

simplify3.0s

Counts
131 → 131
Iterations

Useful iterations: done (3.0s)

IterNodesCost
02895065
18143755
245913278
done50003277

prune638.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 20.7b

localize53.0ms

Local error

Found 4 expressions with local error:

4.3b
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
5.8b
(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
9.1b
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U))
20.0b
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U)))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
23×pow1
21×add-exp-log
18×*-un-lft-identity associate-*r*
15×unpow-prod-down add-cbrt-cube
14×add-cube-cbrt
12×pow-prod-down
10×times-frac associate-*l* prod-exp
7×cbrt-unprod
6×associate-*l/
4×expm1-log1p-u sqrt-pow1 log1p-expm1-u add-log-exp unswap-sqr
3×flip3-- flip--
2×sqrt-div pow-exp *-commutative distribute-lft-out-- difference-of-squares sqr-pow
1×pow-to-exp pow1/2 div-exp sqrt-prod fma-udef div-inv
Counts
4 → 97
Calls
4 calls:
0.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
61.0ms
(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
93.0ms
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U))
76.0ms
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U)))

series5.0s

Counts
4 → 12
Calls
4 calls:
488.0ms
(fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))
831.0ms
(* (- U U*) (pow (/ l Om) (/ 2.0 2)))
1.0s
(* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U))
2.7s
(sqrt (* (- t (fma 2.0 (/ l (/ Om l)) (* (* n (pow (/ l Om) (/ 2.0 2))) (* (- U U*) (pow (/ l Om) (/ 2.0 2)))))) (* (* 2.0 n) U)))

simplify2.2s

Counts
109 → 109
Iterations

Useful iterations: done (2.2s)

IterNodesCost
02613298
16473106
231222425
done50022418

prune698.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 20.5b

regimes736.0ms

Accuracy

4.9% (10.1b remaining)

Error of 30.1b against oracle of 20.1b and baseline of 30.6b

bsearch447.0ms

Steps
ItersRangePoint
9
2.658816743878136e-228
1.8887405497938054e-221
1.7515352123828318e-224
7
-3.448883255124923e-114
-1.4192910650674533e-116
-2.391153254400287e-114

simplify13.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
038113
15277
done5277

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.8s15067×body80nan
1.4s9221×body80valid