Details

Time bar (total: 7.6s)

sample34.0ms

Algorithm
intervals
Results
8.0ms203×body80valid
5.0ms24×body1280valid
4.0ms256×pre80true
2.0ms13×body640valid
1.0ms9×body320valid
1.0ms7×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: 24.1b

localize18.0ms

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))
1.8b
(+ (/ (/ (* (+ 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)))

rewrite77.0ms

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:
20.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
15.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series599.0ms

Counts
3 → 9
Calls
3 calls:
231.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
288.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune548.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
9.0b
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
326×times-frac
306×*-un-lft-identity
228×add-sqr-sqrt
156×add-cube-cbrt
124×sqrt-prod
50×associate-/l*
39×distribute-lft-out
36×distribute-lft-out-- difference-of-squares
17×associate-/r*
13×add-exp-log add-cbrt-cube
12×sqrt-div associate-/r/
8×flip3-+ flip-+
7×div-inv
6×add-log-exp
5×cbrt-undiv div-exp associate-/l/
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg div-sub clear-num
1×+-commutative flip3-- fma-def sum-log flip--
Counts
4 → 322
Calls
4 calls:
19.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))
13.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
14.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
39.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

series788.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))
143.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
131.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
291.0ms
(+ (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify132.0ms

Algorithm
egg-herbie
Counts
334 → 334
Iterations

Useful iterations: 2 (76.0ms)

IterNodesCost
011045715
142475427
250015390

prune963.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
12.9b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite38.0ms

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:
10.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series517.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
165.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
274.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify98.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07273112
132592892
250022876

prune632.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b
(pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)
12.9b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
13.5b
(cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
398×times-frac
370×*-un-lft-identity
274×add-sqr-sqrt
264×cbrt-prod
190×add-cube-cbrt
133×unpow-prod-down cube-prod
48×distribute-lft-out
47×associate-/l*
42×distribute-lft-out-- difference-of-squares
15×div-inv
9×add-exp-log
8×add-cbrt-cube
7×cube-mult unpow3 sqr-pow
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×cube-div pow-unpow
2×cbrt-undiv cbrt-div div-exp pow-exp associate-/r/ rem-cube-cbrt
1×pow-to-exp pow-pow frac-2neg flip3-+ pow1/3 clear-num rem-cbrt-cube flip-+ fma-udef associate-/l/
Counts
4 → 382
Calls
4 calls:
22.0ms
(/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
7.0ms
(pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)
1.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
12.0ms
(cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3))

series695.0ms

Counts
4 → 12
Calls
4 calls:
171.0ms
(/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
163.0ms
(pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)
276.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
85.0ms
(cbrt (pow (/ (- beta alpha) (fma i 2.0 (+ alpha beta))) 3))

simplify140.0ms

Algorithm
egg-herbie
Counts
394 → 394
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
07696542
133905805
250015780

prune795.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.9b

regimes282.0ms

Accuracy

17.1% (5.6b remaining)

Error of 11.6b against oracle of 6.1b and baseline of 12.8b

bsearch49.0ms

Steps
ItersRangePoint
5
1.2908541269997071e+138
3.532287159096209e+138
1.5322107907580335e+138

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14225

end0.0ms

sample845.0ms

Algorithm
intervals
Results
255.0ms6300×body80valid
128.0ms8000×pre80true
119.0ms530×body1280valid
95.0ms582×body640valid
45.0ms380×body320valid
16.0ms208×body160valid