Details

Time bar (total: 14.3s)

sample49.0ms

Algorithm
intervals
Results
12.0ms192×body80valid
8.0ms24×body1280valid
5.0ms22×body640valid
5.0ms256×pre80true
2.0ms10×body320valid
1.0ms8×body160valid

simplify56.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.0b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
24.0b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite907.0ms

Algorithm
rewrite-expression-head
Rules
102×*-un-lft-identity times-frac
62×add-sqr-sqrt
58×add-cube-cbrt
42×fma-def
24×associate-/r/
21×distribute-lft-out
20×add-exp-log add-cbrt-cube
19×flip3-+ flip-+
18×prod-diff
12×div-inv
11×distribute-rgt-in distribute-lft-in
10×associate-/l*
9×associate-/l/
8×frac-times
7×cbrt-undiv div-exp associate-/r*
6×pow1 flip3-- flip-- add-log-exp
5×associate-*r*
4×expm1-log1p-u associate-*r/ associate-*l* associate-*l/ log1p-expm1-u
3×prod-exp cbrt-unprod
2×sub-neg frac-2neg clear-num
1×+-commutative pow-prod-down sum-log *-commutative distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 212
Calls
4 calls:
41.0ms
(* (+ alpha beta) (- beta alpha))
177.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
627.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
53.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series570.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(* (+ alpha beta) (- beta alpha))
207.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
255.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
72.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify56.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
09372463
150022158

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.3b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite557.0ms

Algorithm
rewrite-expression-head
Rules
68×*-un-lft-identity
66×add-sqr-sqrt
58×times-frac
40×add-cube-cbrt
21×associate-*r*
20×add-exp-log add-cbrt-cube
16×associate-*l*
8×associate-/l*
7×associate-/r* distribute-lft-out distribute-lft-out-- difference-of-squares
6×pow1 cbrt-undiv div-exp associate-/r/ add-log-exp
4×expm1-log1p-u flip3-- prod-exp flip-- cbrt-unprod log1p-expm1-u div-inv associate-/l/ unswap-sqr
2×frac-2neg flip3-+ div-sub clear-num flip-+
1×+-commutative frac-times fma-def associate-*r/ pow-prod-down associate-*l/ sum-log *-commutative
Counts
4 → 157
Calls
4 calls:
183.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
46.0ms
(/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))
114.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
209.0ms
(+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series520.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
73.0ms
(/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))
112.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
263.0ms
(+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify106.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
08282197
141061987
250021980

prune1.9s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
0.1b
(exp (log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
2.0b
(+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
2.6b
(log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

rewrite743.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
36×*-un-lft-identity
31×times-frac
24×add-cube-cbrt
21×associate-*r*
17×add-exp-log
16×associate-*l* add-cbrt-cube
8×pow1
6×log-prod add-log-exp
4×cbrt-undiv expm1-log1p-u log-div exp-prod div-exp prod-exp cbrt-unprod log1p-expm1-u unswap-sqr
3×flip3-+ exp-sum flip-+ distribute-lft-out distribute-lft-out-- difference-of-squares
2×exp-diff associate-/r/ log-pow div-inv
1×+-commutative frac-times flip3-- fma-def associate-*r/ rem-log-exp pow-prod-down associate-*l/ sum-log *-commutative flip-- rem-exp-log
Counts
4 → 112
Calls
4 calls:
113.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
206.0ms
(exp (log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
212.0ms
(+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
207.0ms
(log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

series874.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))))
255.0ms
(exp (log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))
255.0ms
(+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
251.0ms
(log (+ (* (* (/ (+ alpha beta) (fma i 2.0 (+ alpha beta))) (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i)))) (/ (- (+ alpha beta) (* 2.0 i)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0))

simplify89.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
06732497
130342238
250012164

prune1.6s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

localize27.0ms

Local error

Found 4 expressions with local error:

2.0b
(log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta))))))
2.6b
(log (log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))))))
3.1b
(* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i)))
3.1b
(/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))

rewrite415.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
33×add-sqr-sqrt
30×add-exp-log
29×add-cbrt-cube
22×add-cube-cbrt
21×associate-*l*
19×times-frac
12×log-prod
11×log-pow
10×cbrt-undiv div-exp
9×pow1
8×exp-prod prod-diff prod-exp cbrt-unprod
7×distribute-rgt-in distribute-lft-in
5×associate-/l/
4×expm1-log1p-u frac-times log1p-expm1-u distribute-lft-out add-log-exp
3×flip3-- associate-*r/ associate-*r* associate-*l/ associate-/r* flip-- distribute-lft-out-- difference-of-squares
2×sub-neg flip3-+ rem-log-exp associate--l+ associate-/r/ flip-+ div-inv unswap-sqr
1×frac-2neg exp-sum pow-prod-down clear-num *-commutative associate-/l*
Counts
4 → 132
Calls
4 calls:
56.0ms
(log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta))))))
23.0ms
(log (log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))))))
170.0ms
(* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i)))
161.0ms
(/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))

series764.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta))))))
266.0ms
(log (log (exp (+ 1.0 (/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))))))
15.0ms
(* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i)))
221.0ms
(/ (* (+ alpha beta) (/ (* (/ (- beta alpha) (- (+ alpha beta) (* 2.0 i))) (- (+ alpha beta) (* 2.0 i))) (+ beta (+ alpha (fma i 2.0 2.0))))) (fma i 2.0 (+ alpha beta)))

simplify123.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08402754
145782042
250012042

prune1.4s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.9b

regimes636.0ms

Accuracy

7.3% (7.4b remaining)

Error of 11.6b against oracle of 4.2b and baseline of 12.2b

bsearch102.0ms

Steps
ItersRangePoint
8
9.718655615369813e+98
2.5950765872405964e+101
2.5729948988409967e+101

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14425
24425

end0.0ms

sample1.1s

Algorithm
intervals
Results
412.0ms6389×body80valid
170.0ms528×body1280valid
135.0ms525×body640valid
131.0ms8000×pre80true
66.0ms353×body320valid
25.0ms205×body160valid