Details

Time bar (total: 15.4s)

sample32.0ms

Algorithm
intervals
Results
8.0ms210×body80valid
4.0ms256×pre80true
3.0ms18×body640valid
2.0ms11×body1280valid
1.0ms11×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: 21.3b

localize16.0ms

Local error

Found 3 expressions with local error:

0.3b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.1b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite80.0ms

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:
21.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
32.0ms
(+ (/ (/ (* (+ 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)))

series587.0ms

Counts
3 → 9
Calls
3 calls:
228.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
281.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
77.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify96.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune548.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
0.3b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b
(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b
(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
2284×times-frac
1863×*-un-lft-identity
1165×add-sqr-sqrt
803×add-cube-cbrt
386×fma-def
349×distribute-lft-out
181×distribute-lft-out-- difference-of-squares
118×associate-/r/
103×associate-/l*
64×div-inv
55×flip3-+ flip-+
26×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×div-sub
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num associate-/l/
1×+-commutative associate-+l- flip3-- sum-log flip--
Counts
4 → 1070
Calls
4 calls:
12.0ms
(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
35.0ms
(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
151.0ms
(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series560.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)))
49.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
231.0ms
(/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
195.0ms
(+ (/ (/ (- beta alpha) (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify168.0ms

Algorithm
egg-herbie
Counts
1082 → 1082
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0195513486
1500113315

prune3.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.3b
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
3100×times-frac
2455×*-un-lft-identity
1481×add-sqr-sqrt
1467×add-cube-cbrt
726×prod-diff
493×distribute-lft-out
242×fma-neg
161×associate-/r/
91×div-inv
70×flip3-+ flip-+
65×associate-/l*
17×add-exp-log add-cbrt-cube
12×associate-/r*
8×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×frac-2neg clear-num
1×sub-neg flip3-- diff-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 1377
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
26.0ms
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
119.0ms
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series547.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
49.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
158.0ms
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
288.0ms
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify323.0ms

Algorithm
egg-herbie
Counts
1389 → 1389
Iterations

Useful iterations: 1 (43.0ms)

IterNodesCost
0259832465
1500128487

prune3.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
0.3b
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.4b
(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
1.3b
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite331.0ms

Algorithm
rewrite-expression-head
Rules
3102×times-frac
2454×*-un-lft-identity
1488×add-sqr-sqrt
1467×add-cube-cbrt
726×prod-diff
492×distribute-lft-out
242×fma-neg
161×associate-/r/
91×div-inv
70×flip3-+ flip-+
62×associate-/l*
24×add-exp-log
20×add-cbrt-cube
18×associate-*r*
9×div-exp
8×cbrt-undiv associate-/r*
6×pow1 add-log-exp
4×expm1-log1p-u prod-exp log1p-expm1-u difference-of-squares
3×associate-*l* unswap-sqr
2×frac-2neg clear-num cbrt-unprod
1×sub-neg rec-exp flip3-- diff-log 1-exp associate-*r/ pow-prod-down un-div-inv *-commutative flip-- associate-/l/ distribute-lft-out--
Counts
4 → 1385
Calls
4 calls:
8.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
26.0ms
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0ms
(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
120.0ms
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series546.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))
161.0ms
(/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
53.0ms
(* (fma i 2.0 (+ alpha beta)) (/ 1 (+ alpha beta)))
283.0ms
(- (/ (/ alpha (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify335.0ms

Algorithm
egg-herbie
Counts
1397 → 1397
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0274632488
1500228471

prune3.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.4b

regimes337.0ms

Accuracy

0% (6.4b remaining)

Error of 11.8b against oracle of 5.4b and baseline of 11.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03131
13131

end0.0ms

sample811.0ms

Algorithm
intervals
Results
248.0ms6404×body80valid
126.0ms8000×pre80true
102.0ms492×body1280valid
86.0ms551×body640valid
42.0ms362×body320valid
15.0ms191×body160valid