Details

Time bar (total: 10.2s)

sample32.0ms

Algorithm
intervals
Results
8.0ms202×body80valid
4.0ms256×pre80true
3.0ms16×body1280valid
2.0ms13×body640valid
2.0ms16×body320valid
1.0ms9×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize17.0ms

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)))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
54×times-frac
48×*-un-lft-identity
26×add-sqr-sqrt add-cube-cbrt
18×add-exp-log add-cbrt-cube
14×associate-/r/
12×flip3-+ flip-+
11×distribute-lft-out add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r* div-inv
4×pow1 frac-times sum-log
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 124
Calls
4 calls:
5.0ms
(+ (+ alpha beta) (* 2.0 i))
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)
13.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series595.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(+ (+ alpha beta) (* 2.0 i))
224.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
276.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
75.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify107.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07011981
139801865
250021865

prune375.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
0.1b
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
2.6b
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite282.0ms

Algorithm
rewrite-expression-head
Rules
1580×times-frac
1545×*-un-lft-identity
747×add-sqr-sqrt
537×add-cube-cbrt
399×distribute-lft-out
117×associate-/l*
105×distribute-lft-out-- difference-of-squares
60×associate-/r/
35×associate-/r*
33×div-inv
26×flip3-- flip--
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
5×associate-/l/
4×pow1 flip3-+ flip-+
3×frac-2neg clear-num
1×+-commutative sum-log
Counts
4 → 776
Calls
4 calls:
43.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
16.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
138.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series660.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
77.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
82.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
278.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify185.0ms

Algorithm
egg-herbie
Counts
788 → 788
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0180116134
1500115862

prune1.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.9b
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
650×*-un-lft-identity
646×times-frac
356×add-sqr-sqrt
268×add-cube-cbrt
235×sqrt-prod
176×distribute-lft-out
160×associate-*l*
41×associate-*r*
38×associate-/r/
32×add-exp-log add-cbrt-cube
27×associate-/l*
20×flip3-+ flip-+
19×div-inv
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- div-sub associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 515
Calls
4 calls:
120.0ms
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
23.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
13.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
45.0ms
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series968.0ms

Counts
4 → 12
Calls
4 calls:
219.0ms
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
348.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
127.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
273.0ms
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify127.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0154810983
1500110507

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
0.4b
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.9b
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
650×*-un-lft-identity
646×times-frac
356×add-sqr-sqrt
268×add-cube-cbrt
235×sqrt-prod
176×distribute-lft-out
160×associate-*l*
41×associate-*r*
38×associate-/r/
32×add-exp-log add-cbrt-cube
27×associate-/l*
20×flip3-+ flip-+
19×div-inv
15×distribute-lft-out-- difference-of-squares unswap-sqr
14×associate-/r*
13×cbrt-undiv div-exp
8×sqrt-div
6×pow1 prod-exp cbrt-unprod add-log-exp
3×associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times flip3-- div-sub associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative flip--
Counts
4 → 515
Calls
4 calls:
117.0ms
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
22.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
16.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
40.0ms
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

series836.0ms

Counts
4 → 12
Calls
4 calls:
223.0ms
(* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))
220.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
124.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
268.0ms
(+ (* (/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))) 1.0)

simplify128.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0154810983
1500110507

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

regimes213.0ms

Accuracy

14.5% (5.3b remaining)

Error of 11.5b against oracle of 6.2b and baseline of 12.4b

bsearch92.0ms

Steps
ItersRangePoint
9
1.3435221939027013e+243
5.3992141672933e+250
1.5755879822253269e+243

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05843
15843

end0.0ms

sample812.0ms

Algorithm
intervals
Results
258.0ms6355×body80valid
120.0ms8000×pre80true
108.0ms522×body1280valid
84.0ms534×body640valid
48.0ms399×body320valid
15.0ms190×body160valid