Details

Time bar (total: 10.6s)

sample31.0ms

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

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize16.0ms

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)))

rewrite80.0ms

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:
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))
31.0ms
(+ (/ (/ (* (+ 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)))

series607.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(+ (+ alpha beta) (* 2.0 i))
228.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
280.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
79.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify101.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07011981
139801865
250021865

prune371.0ms

Filtered
136 candidates to 101 candidates (74.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.9b

localize18.0ms

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)

rewrite297.0ms

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:
46.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
11.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
17.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
147.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series668.0ms

Counts
4 → 12
Calls
4 calls:
230.0ms
(/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
78.0ms
(/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))
80.0ms
(/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha)))
280.0ms
(+ (/ (/ (+ alpha beta) (/ (+ alpha (+ (* 2.0 i) beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify172.0ms

Algorithm
egg-herbie
Counts
788 → 788
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0180116134
1500115862

prune1.6s

Filtered
788 candidates to 363 candidates (46.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

localize17.0ms

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)

rewrite252.0ms

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:
129.0ms
(* (/ (/ (+ 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)))
14.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
44.0ms
(+ (* (/ (/ (+ 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)

series889.0ms

Counts
4 → 12
Calls
4 calls:
238.0ms
(* (/ (/ (+ 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))))
223.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
132.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
296.0ms
(+ (* (/ (/ (+ 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)

simplify123.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0154810983
1500110507

prune1.2s

Filtered
527 candidates to 253 candidates (48.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.9b

localize21.0ms

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)

rewrite255.0ms

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:
129.0ms
(* (/ (/ (+ 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)))
14.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
46.0ms
(+ (* (/ (/ (+ 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)

series885.0ms

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (/ (/ (+ 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))))
231.0ms
(/ (/ (+ alpha beta) (+ alpha (+ (* 2.0 i) beta))) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
133.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
285.0ms
(+ (* (/ (/ (+ 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)

simplify130.0ms

Algorithm
egg-herbie
Counts
527 → 527
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
0154810983
1500110507

prune1.4s

Filtered
527 candidates to 254 candidates (48.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.9b

regimes409.0ms

Accuracy

14.1% (5.3b remaining)

Error of 11.5b against oracle of 6.2b and baseline of 12.3b

bsearch92.0ms

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

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05843
15843

end0.0ms

sample811.0ms

Algorithm
intervals
Results
244.0ms6355×body80valid
130.0ms8000×pre80true
109.0ms522×body1280valid
87.0ms534×body640valid
46.0ms399×body320valid
15.0ms190×body160valid