Details

Time bar (total: 16.6s)

sample32.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
4.0ms256×pre80true
3.0ms16×body1280valid
2.0ms15×body640valid
1.0ms11×body320valid
1.0ms7×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110314
245414
3212714
4500114

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.9b

localize13.0ms

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)
18.7b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite428.0ms

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:
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
305.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
27.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series570.0ms

Counts
3 → 9
Calls
3 calls:
222.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
270.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
78.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify93.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
06811905
136221789
250031789

prune347.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.8b

localize14.0ms

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)
3.2b
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

rewrite1.5s

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:
21.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
150.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
957.0ms
(+ (/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))) 1.0)
138.0ms
(/ (/ (+ alpha beta) 1) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))))

series717.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
146.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))))
267.0ms
(+ (/ (/ (+ 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 (25.0ms)

IterNodesCost
0500148152

prune3.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 4.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
0.1b
(* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
1.6b
(+ (* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i)))) 1.0)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
3444×times-frac
2162×*-un-lft-identity
1954×add-sqr-sqrt
1229×add-cube-cbrt
583×sqrt-prod
577×associate-*l*
249×distribute-lft-out
185×distribute-lft-out-- difference-of-squares
151×add-exp-log
105×div-inv
96×associate-/r/
92×div-exp
90×associate-*r*
87×add-cbrt-cube
75×unswap-sqr
48×cbrt-undiv
46×flip3-- flip--
31×associate-/r*
27×prod-exp
26×associate-/l*
15×cbrt-unprod
8×rec-exp 1-exp
6×pow1 add-log-exp
3×flip3-+ flip-+ associate-/l/
2×frac-2neg clear-num
1×+-commutative frac-times associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 1496
Calls
4 calls:
132.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
865.0ms
(* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i))))
89.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
96.0ms
(+ (* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i)))) 1.0)

series685.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))
226.0ms
(* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i))))
85.0ms
(/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha)))
273.0ms
(+ (* (/ (/ 1 (sqrt 1)) (/ (+ (+ (+ alpha beta) (* 2.0 i)) 2.0) (- beta alpha))) (/ (/ (+ alpha beta) (sqrt 1)) (+ (+ alpha beta) (* 2.0 i)))) 1.0)

simplify341.0ms

Algorithm
egg-herbie
Counts
1508 → 1508
Iterations

Useful iterations: 1 (75.0ms)

IterNodesCost
0457431115
1500127669

prune3.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 4.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))
0.3b
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
0.4b
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
6.9b
(+ (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) 1.0)

rewrite558.0ms

Algorithm
rewrite-expression-head
Rules
144×*-un-lft-identity
112×times-frac
108×add-sqr-sqrt
65×add-cube-cbrt
63×sqrt-prod
34×associate-*l*
30×add-exp-log distribute-lft-out
20×add-cbrt-cube
15×associate-*r*
12×associate-/r*
11×associate-/l*
10×div-exp
9×unswap-sqr
8×prod-exp associate-/r/ distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv flip3-+ sqrt-div flip-+ add-log-exp
4×cbrt-unprod div-inv associate-/l/
2×rec-exp frac-2neg 1-exp clear-num
1×+-commutative frac-times flip3-- associate-*r/ pow-prod-down associate-*l/ sum-log un-div-inv *-commutative flip--
Counts
4 → 212
Calls
4 calls:
99.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))
189.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
71.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
188.0ms
(+ (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) 1.0)

series776.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))
216.0ms
(* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))
144.0ms
(/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
276.0ms
(+ (* (/ 1 (/ (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (- beta alpha))) (* (/ (+ alpha beta) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ 1 (+ (+ alpha beta) (* 2.0 i))))) 1.0)

simplify117.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
09663314
141543042
250033025

prune610.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 4.8b

regimes155.0ms

Accuracy

6.1% (6.0b remaining)

Error of 12.0b against oracle of 6.0b and baseline of 12.3b

bsearch197.0ms

Steps
ItersRangePoint
9
8.405953526449568e+193
6.237161537074933e+200
2.135954177821433e+197
3
2.1778918232465144e+119
2.626864871441726e+119
2.2620742697831166e+119
9
2.5525867425499545e+76
5.451460309788243e+83
1.5412307314962603e+80

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07785
17785

end0.0ms

sample807.0ms

Algorithm
intervals
Results
245.0ms6359×body80valid
121.0ms8000×pre80true
103.0ms514×body1280valid
86.0ms549×body640valid
47.0ms375×body320valid
15.0ms203×body160valid