Details

Time bar (total: 20.5s)

sample34.0ms

Algorithm
intervals
Results
9.0ms220×body80valid
4.0ms256×pre80true
3.0ms14×body1280valid
2.0ms10×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize13.0ms

Local error

Found 3 expressions with local error:

0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
95.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
357.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series591.0ms

Counts
3 → 9
Calls
3 calls:
227.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
283.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
80.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07011971
137401800
250011782

prune550.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.5b
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0b
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
5.5b
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite716.0ms

Algorithm
rewrite-expression-head
Rules
80×add-exp-log add-cbrt-cube
61×*-un-lft-identity
58×times-frac
49×add-sqr-sqrt
41×add-cube-cbrt sqrt-prod
34×cbrt-undiv div-exp
27×associate-*r*
24×prod-exp cbrt-unprod
14×associate-/r*
13×associate-*l*
10×distribute-lft-out
8×sqrt-div associate-/r/
6×pow1 add-log-exp
5×flip3-+ flip-+ associate-/l/
4×expm1-log1p-u log1p-expm1-u div-inv associate-/l*
3×unswap-sqr
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×+-commutative flip3-- fma-def div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 187
Calls
4 calls:
84.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
103.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
372.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
148.0ms
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
353.0ms
(/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
163.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
244.0ms
(* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
295.0ms
(+ (* (/ (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- (+ alpha beta) (* 2.0 i)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify74.0ms

Algorithm
egg-herbie
Counts
199 → 199
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
010765004
150014219

prune656.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.5b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
2.1b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×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 → 3236
Calls
4 calls:
173.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
33.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.1s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series659.0ms

Counts
4 → 12
Calls
4 calls:
309.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
71.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
150.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
130.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify473.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (26.0ms)

IterNodesCost
0500147194

prune9.7s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.5b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
8.7b
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
1062×times-frac
759×*-un-lft-identity
595×add-sqr-sqrt
413×add-cube-cbrt
105×associate-/r*
91×distribute-lft-out-- difference-of-squares
82×distribute-lft-out
65×associate-/r/
34×add-exp-log
33×div-inv
27×flip3-+ flip-+
24×associate-/l*
20×div-exp add-cbrt-cube
10×cbrt-undiv
6×pow1
5×flip3-- flip--
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×pow-flip inv-pow
1×fma-udef associate-/l/
Counts
4 → 595
Calls
4 calls:
68.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
16.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
30.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
0.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series372.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
65.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
156.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
86.0ms
(fma (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (/ 1 (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify123.0ms

Algorithm
egg-herbie
Counts
607 → 607
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
017348804
150018297

prune1.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.5b

regimes253.0ms

Accuracy

13.8% (5.8b remaining)

Error of 11.4b against oracle of 5.6b and baseline of 12.4b

bsearch75.0ms

Steps
ItersRangePoint
8
4.691534427487681e+136
1.114487485779193e+140
3.9671665599107027e+139

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05038
15038

end0.0ms

sample829.0ms

Algorithm
intervals
Results
256.0ms6356×body80valid
129.0ms8000×pre80true
105.0ms534×body1280valid
87.0ms544×body640valid
46.0ms345×body320valid
17.0ms221×body160valid