Details

Time bar (total: 23.7s)

sample33.0ms

Algorithm
intervals
Results
8.0ms211×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
3.0ms17×body640valid
1.0ms7×body320valid
1.0ms7×body160valid

simplify53.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214
done500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
45×add-sqr-sqrt add-cube-cbrt fma-def
24×associate-/r/
21×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
15×add-log-exp
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* sum-log
4×pow1 expm1-log1p-u frac-times log1p-expm1-u
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 179
Calls
4 calls:
123.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
178.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
635.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
58.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series652.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
246.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
292.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
85.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify104.0ms

Counts
191 → 191
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
07582073
142381870
250011858
done50011858

prune591.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
0.1b
(pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)
2.1b
(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
11.2b
(cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

rewrite194.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
48×add-sqr-sqrt
44×times-frac
29×add-exp-log add-cbrt-cube
28×add-cube-cbrt
26×associate-*r* associate-*l*
23×distribute-lft-out
16×cbrt-prod
11×fma-def
9×pow1
8×cbrt-undiv div-exp prod-exp cbrt-unprod
6×cube-div add-log-exp
5×pow-exp rem-cube-cbrt
4×expm1-log1p-u associate-/r/ log1p-expm1-u distribute-lft-out-- difference-of-squares unswap-sqr
3×cube-mult frac-times unpow-prod-down pow-unpow cbrt-div flip3-+ unpow3 cube-prod associate-*r/ associate-*l/ flip-+ sqr-pow
2×pow-pow pow-prod-down div-inv
1×+-commutative pow-to-exp pow1/3 sum-log *-commutative rem-cbrt-cube
Counts
4 → 158
Calls
4 calls:
129.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
41.0ms
(pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)
15.0ms
(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
3.0ms
(cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

series4.1s

Counts
4 → 12
Calls
4 calls:
407.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
3.1s
(pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)
311.0ms
(+ (cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3)) 1.0)
305.0ms
(cbrt (pow (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 3))

simplify100.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07621916
139081788
250011786
done50011786

prune571.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
0.1b
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
2.1b
(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)
2.2b
(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)))

rewrite345.0ms

Algorithm
rewrite-expression-head
Rules
107×*-un-lft-identity
67×add-sqr-sqrt
64×times-frac
37×add-cube-cbrt
28×distribute-lft-out
26×associate-*r* associate-*l*
18×add-exp-log add-cbrt-cube
9×distribute-lft-out-- difference-of-squares
7×pow1
6×associate-/r/ add-log-exp
5×cbrt-undiv div-exp associate-/l*
4×expm1-log1p-u log-prod flip3-+ prod-exp associate-/r* log-pow cbrt-unprod flip-+ log1p-expm1-u unswap-sqr
3×exp-prod div-inv
2×associate-/l/
1×+-commutative frac-times flip3-- fma-def frac-2neg div-sub associate-*r/ rem-log-exp exp-sum pow-prod-down associate-*l/ clear-num sum-log *-commutative flip--
Counts
4 → 158
Calls
4 calls:
23.0ms
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
128.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
39.0ms
(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)
145.0ms
(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)))

series942.0ms

Counts
4 → 12
Calls
4 calls:
84.0ms
(/ (- beta alpha) (+ (fma 2.0 i beta) alpha))
253.0ms
(* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
306.0ms
(+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)
299.0ms
(log (exp (+ (* (/ (+ alpha beta) (+ (+ alpha beta) (fma 2.0 i 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) 1.0)))

simplify86.0ms

Counts
170 → 170
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06971918
131741747
250021741
done50021741

prune569.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
0.3b
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
3.4b
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
12400×times-frac
9469×*-un-lft-identity
5477×add-sqr-sqrt
4067×add-cube-cbrt
1996×distribute-lft-out
1418×fma-def
705×distribute-lft-out-- difference-of-squares
400×associate-/r/
378×associate-/l*
205×div-inv
164×flip3-+ flip-+
125×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3880
Calls
4 calls:
272.0ms
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
44.0ms
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
53.0ms
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
1.5s
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series674.0ms

Counts
4 → 12
Calls
4 calls:
307.0ms
(/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
76.0ms
(/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))
155.0ms
(/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha)))
135.0ms
(+ (/ (/ 1 (/ (/ (+ (fma 2.0 i beta) alpha) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify506.0ms

Counts
3892 → 3892
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500155522
done500155522

prune9.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

regimes280.0ms

Accuracy

0% (6.3b remaining)

Error of 12.1b against oracle of 5.7b and baseline of 12.1b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02614
12614
done2614

end0.0ms

sample853.0ms

Algorithm
intervals
Results
246.0ms6404×body80valid
110.0ms8000×pre80true
104.0ms512×body1280valid
85.0ms551×body640valid
40.0ms332×body320valid
15.0ms201×body160valid