Details

Time bar (total: 27.1s)

sample35.0ms

Algorithm
intervals
Results
8.0ms200×body80valid
4.0ms256×pre80true
4.0ms24×body640valid
4.0ms18×body1280valid
1.0ms8×body320valid
0.0ms6×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.1b

localize17.0ms

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))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
20.9b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
47×*-un-lft-identity
25×add-sqr-sqrt add-cube-cbrt
17×add-exp-log add-cbrt-cube
14×associate-/r/
11×flip3-+ flip-+ distribute-lft-out
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
5×add-log-exp
4×frac-times
3×pow1 flip3-- flip--
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 111
Calls
3 calls:
19.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series578.0ms

Counts
3 → 9
Calls
3 calls:
229.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
269.0ms
(+ (/ (/ (* (+ 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)))

simplify92.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (17.0ms)

IterNodesCost
06811905
136221789
250031789

prune339.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.1b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
1.6b
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
2.0b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite681.0ms

Algorithm
rewrite-expression-head
Rules
5126×times-frac
3533×*-un-lft-identity
2233×add-sqr-sqrt
1787×add-cube-cbrt
650×distribute-lft-out
223×distribute-lft-out-- difference-of-squares
183×div-inv
167×associate-/r/
113×associate-/r*
76×flip3-+ flip-+
41×add-exp-log
32×add-cbrt-cube
28×div-exp
25×associate-/l*
19×cbrt-undiv
6×add-log-exp
5×associate-/l/
4×pow1
3×frac-2neg 1-exp clear-num
1×+-commutative flip3-- div-sub sum-log flip--
Counts
4 → 1734
Calls
4 calls:
9.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
20.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
365.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
60.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series725.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
148.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
272.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
229.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

simplify442.0ms

Algorithm
egg-herbie
Counts
1746 → 1746
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
0500148152

prune3.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.2b
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
2.0b
(/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
3.1b
(+ (/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
20651×times-frac
12469×*-un-lft-identity
8457×add-sqr-sqrt
7107×add-cube-cbrt
2006×distribute-lft-out
675×distribute-lft-out-- difference-of-squares
581×associate-/r/
576×div-inv
369×associate-/r*
282×flip3-+ flip-+
136×add-exp-log
113×div-exp
50×add-cbrt-cube
40×associate-/l*
33×cbrt-undiv
22×1-exp
12×rec-exp
6×add-log-exp
5×pow1
3×frac-2neg clear-num
2×div-sub associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 5268
Calls
4 calls:
19.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
31.0ms
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
151.0ms
(/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
1.1s
(+ (/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series811.0ms

Counts
4 → 12
Calls
4 calls:
159.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
149.0ms
(/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
223.0ms
(/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
280.0ms
(+ (/ (/ (+ alpha beta) 1) (/ 1 (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify1.6s

Algorithm
egg-herbie
Counts
5280 → 5280
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
05328174675

prune13.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 6.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
0.6b
(cbrt (+ alpha beta))
9.8b
(+ (* (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
3.0ms
(cbrt (+ alpha beta))
3.0ms
(cbrt (+ alpha beta))
3.0ms
(cbrt (+ alpha beta))
59.0ms
(+ (* (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

series670.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(cbrt (+ alpha beta))
125.0ms
(cbrt (+ alpha beta))
129.0ms
(cbrt (+ alpha beta))
284.0ms
(+ (* (* (/ (* (cbrt (+ alpha beta)) (cbrt (+ alpha beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (* (cbrt (+ (+ alpha beta) (* 2.0 i))) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) (* (/ (cbrt (+ alpha beta)) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (cbrt (+ (+ alpha beta) (* 2.0 i)))))) 1.0)

simplify41.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02771004
11001909
25001899

prune324.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.1b

regimes152.0ms

Accuracy

-11.1% (7.2b remaining)

Error of 13.0b against oracle of 5.8b and baseline of 12.3b

bsearch131.0ms

Steps
ItersRangePoint
7
1.324752331211444e-269
1.2903597111982837e-267
1.3442187960051523e-269
7
2.415342563852309e-292
3.4286620833587e-290
3.071350128137838e-290

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06870
17070
27070

end0.0ms

sample841.0ms

Algorithm
intervals
Results
263.0ms6379×body80valid
130.0ms8000×pre80true
100.0ms504×body1280valid
93.0ms562×body640valid
44.0ms375×body320valid
14.0ms180×body160valid