Details

Time bar (total: 8.7s)

sample33.0ms

Algorithm
intervals
Results
7.0ms207×body80valid
4.0ms256×pre80true
3.0ms20×body640valid
2.0ms12×body1280valid
1.0ms10×body320valid
1.0ms7×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.6b

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))
2.1b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
18.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite888.0ms

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:
173.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
653.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
55.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series552.0ms

Counts
3 → 9
Calls
3 calls:
219.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
260.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
73.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify95.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune524.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.3b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.7b
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite394.0ms

Algorithm
rewrite-expression-head
Rules
490×times-frac
410×*-un-lft-identity
284×add-sqr-sqrt
228×add-cube-cbrt
156×sqrt-prod
63×distribute-lft-out
42×associate-/l*
28×distribute-lft-out-- difference-of-squares
22×associate-/r/
19×div-inv
18×add-exp-log
17×associate-/r*
16×add-cbrt-cube
11×flip3-+ flip-+
9×div-exp
7×cbrt-undiv
4×pow1 expm1-log1p-u sqrt-div log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg div-sub clear-num
1×flip3-- 1-exp flip-- fma-udef
Counts
4 → 402
Calls
4 calls:
45.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
181.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
144.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series650.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
217.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
135.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
223.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify94.0ms

Algorithm
egg-herbie
Counts
414 → 414
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012837520
150026956

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
0.3b
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.7b
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite395.0ms

Algorithm
rewrite-expression-head
Rules
226×times-frac
203×*-un-lft-identity
123×add-sqr-sqrt
114×add-cube-cbrt
76×sqrt-prod
43×distribute-lft-out
35×add-exp-log
23×add-cbrt-cube
17×associate-/l*
15×associate-*r*
14×div-exp associate-/r*
11×div-inv
8×cbrt-undiv prod-exp
7×associate-/l/
6×pow1 associate-/r/
5×associate-*l*
4×expm1-log1p-u frac-times flip3-- sqrt-div associate-*l/ flip-- cbrt-unprod log1p-expm1-u add-log-exp
3×flip3-+ 1-exp flip-+ unswap-sqr
2×rec-exp frac-2neg associate-*r/ clear-num un-div-inv
1×pow-prod-down *-commutative fma-udef distribute-lft-out-- difference-of-squares
Counts
4 → 254
Calls
4 calls:
87.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
150.0ms
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
143.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series648.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
216.0ms
(/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
136.0ms
(/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
221.0ms
(fma (/ (/ (+ alpha beta) 1) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (* (- beta alpha) (/ 1 (+ (+ alpha beta) (* 2.0 i)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify58.0ms

Algorithm
egg-herbie
Counts
266 → 266
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010473796
150013330

prune647.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.7b

localize163.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.0b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
11.8b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite234.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
162×*-un-lft-identity
118×add-sqr-sqrt
80×add-cube-cbrt
26×associate-/l*
22×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
10×add-exp-log add-cbrt-cube
7×flip3-+ associate-/r* flip-+ div-inv
4×cbrt-undiv div-exp
3×pow1 expm1-log1p-u div-sub log1p-expm1-u associate-/l/ add-log-exp
2×frac-2neg clear-num
1×flip3-- flip-- fma-udef
Counts
3 → 181
Calls
3 calls:
43.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
179.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series470.0ms

Counts
3 → 9
Calls
3 calls:
70.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
150.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
249.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify90.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
07273112
132592892
250022876

prune563.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.7b

regimes274.0ms

Accuracy

18.6% (5.3b remaining)

Error of 11.0b against oracle of 5.7b and baseline of 12.2b

bsearch23.0ms

Steps
ItersRangePoint
3
2.3450662147457176e+164
3.073975176359863e+164
2.3906230248466014e+164

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04231
14431
24431

end0.0ms

sample843.0ms

Algorithm
intervals
Results
240.0ms6391×body80valid
118.0ms8000×pre80true
97.0ms511×body1280valid
85.0ms579×body640valid
41.0ms325×body320valid
14.0ms194×body160valid