Details

Time bar (total: 7.4s)

sample37.0ms

Algorithm
intervals
Results
8.0ms202×body80valid
7.0ms256×pre80true
3.0ms16×body1280valid
2.0ms13×body640valid
2.0ms16×body320valid
1.0ms9×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
46×fma-def
45×add-sqr-sqrt add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
12×div-inv
11×add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
4×pow1 expm1-log1p-u frac-times sum-log 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 → 178
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* 2.0 i))
21.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
36.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
16.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series751.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* 2.0 i))
235.0ms
(/ (/ (* (+ 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)
214.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
07242051
141011860
250011852

prune609.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.9b
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
87×add-exp-log
70×times-frac
52×add-sqr-sqrt add-cube-cbrt
49×add-cbrt-cube
48×sqrt-prod
36×prod-exp
29×div-exp
27×associate-*l*
20×distribute-lft-out
18×cbrt-unprod
15×cbrt-undiv
14×associate-/r*
11×pow1
7×associate-/l*
6×rec-exp sqrt-div 1-exp associate-/r/ add-log-exp
5×frac-times flip3-+ associate-*r/ flip-+
4×expm1-log1p-u log1p-expm1-u
3×pow-flip pow-prod-down associate-*l/ div-inv
2×frac-2neg clear-num associate-/l/
1×+-commutative fma-def sqrt-pow1 pow1/2 associate-*r* sum-log *-commutative inv-pow
Counts
4 → 201
Calls
4 calls:
41.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
14.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
11.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
34.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

series797.0ms

Counts
4 → 12
Calls
4 calls:
239.0ms
(* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))
137.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
129.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
291.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

simplify118.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
08973539
147403012
250012990

prune580.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))
0.3b
(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.2b
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
263×times-frac
259×*-un-lft-identity
137×add-sqr-sqrt add-cube-cbrt
100×sqrt-prod
61×distribute-lft-out
45×associate-/r*
21×add-exp-log
13×associate-/r/ add-cbrt-cube associate-/l*
10×div-exp
8×flip3-+ flip-+
7×pow1 div-inv
6×add-log-exp
5×cbrt-undiv
4×expm1-log1p-u pow-flip sqrt-div log1p-expm1-u
3×rec-exp frac-2neg 1-exp clear-num
2×associate-/l/ inv-pow
1×+-commutative fma-def sqrt-pow1 pow1/2 sum-log
Counts
4 → 286
Calls
4 calls:
13.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))
17.0ms
(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta)))
11.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
43.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

series693.0ms

Counts
4 → 12
Calls
4 calls:
140.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))
141.0ms
(/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta)))
125.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
287.0ms
(+ (* (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (+ alpha beta))) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))) 1.0)

simplify115.0ms

Algorithm
egg-herbie
Counts
298 → 298
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08764233
141653755
250023724

prune739.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
0.6b
(cbrt (+ (+ alpha beta) (* 2.0 i)))
12.5b
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×cbrt-div
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+
1×fma-udef
Counts
4 → 55
Calls
4 calls:
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
5.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
1.0ms
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series934.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
161.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
159.0ms
(cbrt (+ (+ alpha beta) (* 2.0 i)))
456.0ms
(fma (/ (/ (+ alpha beta) (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i))))) 1) (/ (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify78.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0242782
1714703
23079693
35002682

prune294.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.9b

regimes205.0ms

Accuracy

15.6% (5.5b remaining)

Error of 11.6b against oracle of 6.1b and baseline of 12.6b

bsearch83.0ms

Steps
ItersRangePoint
9
1.3435221939027013e+243
5.3992141672933e+250
1.8224494697960075e+245

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04435
14435

end0.0ms

sample833.0ms

Algorithm
intervals
Results
255.0ms6355×body80valid
132.0ms8000×pre80true
104.0ms522×body1280valid
83.0ms534×body640valid
49.0ms399×body320valid
17.0ms190×body160valid