Details

Time bar (total: 15.0s)

sample51.0ms

Algorithm
intervals
Results
33.0ms256×body80valid

simplify1.7s

Counts
1 → 1
Iterations
IterNodes
done2000
71989
61145
5750
4496
3200
279
133
016

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 24.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ y x) z)
0.3b
(fma a t (* (+ y x) z))
1.5b
(fma y (- a b) (fma a t (* (+ y x) z)))
24.5b
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (+ x (+ y t)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
18×add-sqr-sqrt
16×add-cube-cbrt
15×times-frac
13×distribute-lft-out
8×add-cbrt-cube add-exp-log
6×pow1
5×associate-/r*
4×expm1-log1p-u associate-*l* insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r* associate-/l*
2×flip3-+ associate-*l/ associate-/r/ flip-+ fma-udef
1×cbrt-undiv clear-num frac-2neg div-exp pow-prod-down prod-exp *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 86
Calls
4 calls:
15.0ms
(* (+ y x) z)
0.0ms
(fma a t (* (+ y x) z))
0.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
29.0ms
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (+ x (+ y t)))

series424.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (+ y x) z)
63.0ms
(fma a t (* (+ y x) z))
140.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
187.0ms
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (+ x (+ y t)))

simplify518.0ms

Counts
98 → 98
Iterations
IterNodes
done2004
2867
1278
0131

prune700.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ x (+ y t)))
0.3b
(fma a t (* (+ y x) z))
1.5b
(fma y (- a b) (fma a t (* (+ y x) z)))
24.6b
(* (fma y (- a b) (fma a t (* (+ y x) z))) (/ 1 (+ x (+ y t))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
32×times-frac
31×add-sqr-sqrt
24×add-cube-cbrt
21×associate-*r* distribute-lft-out
17×add-exp-log
11×add-cbrt-cube
7×pow1
5×associate-/r*
4×expm1-log1p-u div-exp prod-exp associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp flip3-+ 1-exp cbrt-unprod flip-+ fma-udef div-inv
1×clear-num frac-2neg pow-prod-down associate-*r/ un-div-inv *-commutative pow-flip inv-pow
Counts
4 → 113
Calls
4 calls:
26.0ms
(/ 1 (+ x (+ y t)))
0.0ms
(fma a t (* (+ y x) z))
0.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
57.0ms
(* (fma y (- a b) (fma a t (* (+ y x) z))) (/ 1 (+ x (+ y t))))

series461.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ 1 (+ x (+ y t)))
54.0ms
(fma a t (* (+ y x) z))
134.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
201.0ms
(* (fma y (- a b) (fma a t (* (+ y x) z))) (/ 1 (+ x (+ y t))))

simplify875.0ms

Counts
125 → 125
Iterations
IterNodes
done2000
2925
1301
0136

prune640.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.8b

localize36.0ms

Local error

Found 4 expressions with local error:

24.5b
(/ (* (* (cbrt (fma y (- a b) (fma a t (* (+ y x) z)))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (+ x (+ y t)))
25.2b
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
25.2b
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
25.2b
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
13×add-exp-log
9×cbrt-prod add-sqr-sqrt add-cbrt-cube add-cube-cbrt
6×distribute-lft-out
5×associate-/r* times-frac
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv pow1/3 div-exp prod-exp cbrt-unprod
2×associate-/r/
1×clear-num frac-2neg flip3-+ flip-+ div-inv associate-/l*
Counts
4 → 74
Calls
4 calls:
38.0ms
(/ (* (* (cbrt (fma y (- a b) (fma a t (* (+ y x) z)))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (+ x (+ y t)))
1.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
1.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
1.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))

series804.0ms

Counts
4 → 12
Calls
4 calls:
202.0ms
(/ (* (* (cbrt (fma y (- a b) (fma a t (* (+ y x) z)))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (cbrt (fma y (- a b) (fma a t (* (+ y x) z))))) (+ x (+ y t)))
247.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
174.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))
180.0ms
(cbrt (fma y (- a b) (fma a t (* (+ y x) z))))

simplify581.0ms

Counts
86 → 86
Iterations
IterNodes
done2004
21042
1330
0129

prune455.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 6.8b

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (+ x (+ y t)))
1.5b
(fma y (- a b) (fma a t (* (+ y x) z)))
9.9b
(/ (/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t))))) (cbrt (+ x (+ y t))))
14.6b
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
142×*-un-lft-identity
124×cbrt-div
85×cbrt-prod
82×associate-/r/
62×flip3-+ flip-+
57×add-sqr-sqrt add-cube-cbrt
51×distribute-lft-out
40×frac-times
20×associate-*l/ associate-*r/
18×add-exp-log associate-/l*
11×add-cbrt-cube div-inv
9×associate-/r*
7×cbrt-undiv div-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u add-log-exp
2×clear-num frac-2neg prod-exp cbrt-unprod
1×pow1/3 fma-udef associate-/l/
Counts
4 → 226
Calls
4 calls:
8.0ms
(cbrt (+ x (+ y t)))
0.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
50.0ms
(/ (/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t))))) (cbrt (+ x (+ y t))))
23.0ms
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))))

series3.6s

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (+ x (+ y t)))
104.0ms
(fma y (- a b) (fma a t (* (+ y x) z)))
181.0ms
(/ (/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t))))) (cbrt (+ x (+ y t))))
3.1s
(/ (fma y (- a b) (fma a t (* (+ y x) z))) (* (cbrt (+ x (+ y t))) (cbrt (+ x (+ y t)))))

simplify620.0ms

Counts
238 → 238
Iterations
IterNodes
done2002
1818
0341

prune1.0s

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 6.8b

regimes614.0ms

Accuracy

51.1% (9.3b remaining)

Error of 14.8b against oracle of 5.5b and baseline of 24.6b

bsearch98.0ms

Steps
ItersRangePoint
9
520296.8443274253
10943861951524.459
10735475308532.344
6
-2.9863469966991447e+83
-2.8770639793914173e+82
-1.2841481611231983e+83

simplify5.0ms

Iterations
IterNodes
done35
135
024

end0.0ms

sample1.5s

Algorithm
intervals
Results
847.0ms7997×body80valid
1.0ms2×body320valid
0.0ms1×body1280valid