Details

Time bar (total: 9.5s)

sample34.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
5.0ms13×body640valid
4.0ms256×pre80true
3.0ms17×body1280valid
2.0ms13×body320valid
0.0ms6×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.2b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.8b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite469.0ms

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:
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
342.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
27.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series567.0ms

Counts
3 → 9
Calls
3 calls:
221.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
267.0ms
(+ (/ (/ (* (+ 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)))

simplify98.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07011971
137401800
250011782

prune514.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))
0.1b
(/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.3b
(+ (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite658.0ms

Algorithm
rewrite-expression-head
Rules
123×*-un-lft-identity
106×add-sqr-sqrt
103×times-frac
58×sqrt-prod
57×add-cube-cbrt
41×associate-*l*
36×add-exp-log add-cbrt-cube
18×distribute-lft-out
16×associate-*r*
15×distribute-lft-out-- difference-of-squares
14×cbrt-undiv div-exp associate-/r*
13×fma-def
8×sqrt-div prod-exp associate-/r/ cbrt-unprod
6×pow1 associate-/l* add-log-exp unswap-sqr
5×flip3-+ flip-+ div-inv associate-/l/
4×expm1-log1p-u log1p-expm1-u
2×frac-times frac-2neg associate-*r/ associate-*l/ clear-num
1×+-commutative flip3-- div-sub pow-prod-down sum-log *-commutative flip--
Counts
4 → 220
Calls
4 calls:
166.0ms
(* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))
107.0ms
(/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
72.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
303.0ms
(+ (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series808.0ms

Counts
4 → 12
Calls
4 calls:
291.0ms
(* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))))
217.0ms
(/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
123.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
176.0ms
(+ (/ (* (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify119.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
09533596
143663232
250013214

prune729.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.6b
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
6.1b
(+ (/ (* (* (/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1)) (/ (- beta alpha) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite526.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log *-un-lft-identity
13×fma-def
11×add-sqr-sqrt add-cube-cbrt
10×times-frac
9×add-cbrt-cube
8×cbrt-prod
7×pow1
6×1-exp div-exp prod-exp add-log-exp
4×expm1-log1p-u cbrt-div flip3-+ sqrt-prod flip-+ log1p-expm1-u distribute-lft-out
3×rec-exp associate-/l*
2×cbrt-undiv pow-flip pow1/3 sqrt-div associate-/r/ div-inv
1×+-commutative frac-2neg pow-prod-down clear-num associate-/r* sum-log cbrt-unprod inv-pow
Counts
4 → 92
Calls
4 calls:
4.0ms
(/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1))
32.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
456.0ms
(+ (/ (* (* (/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1)) (/ (- beta alpha) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1))
176.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
177.0ms
(cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1s
(+ (/ (* (* (/ 1 (* (fabs (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1)) (/ (- beta alpha) (sqrt (cbrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))) (/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify52.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
05191426
116311273
250011242

prune510.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
0.4b
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.7b
(fma (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt 1)) (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
255×times-frac
249×*-un-lft-identity
147×add-sqr-sqrt
131×add-cube-cbrt
92×sqrt-prod
51×distribute-lft-out
25×associate-/l*
17×associate-/r*
13×add-exp-log add-cbrt-cube
11×div-inv
8×distribute-lft-out-- difference-of-squares
5×cbrt-undiv div-exp associate-/l/
4×pow1 expm1-log1p-u sqrt-div associate-/r/ log1p-expm1-u add-log-exp
3×frac-2neg flip3-+ clear-num flip-+
1×flip3-- div-sub flip-- fma-udef
Counts
4 → 265
Calls
4 calls:
8.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
77.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
74.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt 1)) (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series644.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(/ (+ alpha beta) (fma i 2.0 (+ alpha beta)))
225.0ms
(/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
129.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
228.0ms
(fma (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (sqrt 1)) (/ (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify107.0ms

Algorithm
egg-herbie
Counts
277 → 277
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
08554511
133334234
250014231

prune791.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

regimes221.0ms

Accuracy

17.6% (5.5b remaining)

Error of 11.0b against oracle of 5.5b and baseline of 12.2b

bsearch75.0ms

Steps
ItersRangePoint
7
1.4116812876132222e+209
2.791389625835243e+210
1.5371929371909745e+209

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04843
14843

end0.0ms

sample802.0ms

Algorithm
intervals
Results
254.0ms6387×body80valid
124.0ms8000×pre80true
108.0ms532×body1280valid
80.0ms529×body640valid
39.0ms341×body320valid
16.0ms211×body160valid