Details

Time bar (total: 11.8s)

sample53.0ms

Algorithm
intervals
Results
15.0ms200×body80valid
9.0ms22×body640valid
7.0ms20×body1280valid
6.0ms256×pre80true
2.0ms7×body320valid
1.0ms7×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ alpha beta) (- beta alpha))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.4b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
21.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite499.0ms

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:
19.0ms
(* (+ alpha beta) (- beta alpha))
92.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
349.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
28.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series611.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (+ alpha beta) (- beta alpha))
222.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
266.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
81.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify47.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09372463
150022158

prune609.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
0.1b
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
1.4b
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite745.0ms

Algorithm
rewrite-expression-head
Rules
2182×times-frac
1819×*-un-lft-identity
1037×add-sqr-sqrt
783×add-cube-cbrt
391×distribute-lft-out
362×fma-def
127×distribute-lft-out-- difference-of-squares
98×associate-/r/
96×associate-/l*
54×div-inv
42×flip3-- flip--
30×associate-/r*
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp
6×add-log-exp
4×pow1 expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×frac-2neg clear-num associate-/l/
1×+-commutative sum-log
Counts
4 → 1013
Calls
4 calls:
5.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
103.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
518.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series648.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
224.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
82.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
270.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify157.0ms

Algorithm
egg-herbie
Counts
1025 → 1025
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
0176912717
1500112362

prune2.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha))))
0.2b
(* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))
2.4b
(+ (/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite421.0ms

Algorithm
rewrite-expression-head
Rules
137×times-frac
129×*-un-lft-identity
69×add-sqr-sqrt
56×add-cube-cbrt
50×add-exp-log
46×fma-def
33×distribute-lft-out
32×add-cbrt-cube
26×associate-/r/
22×div-exp
21×associate-*r*
14×associate-/l*
13×cbrt-undiv div-inv
12×prod-exp
11×associate-*r/ un-div-inv
6×pow1 cbrt-unprod add-log-exp
5×associate-/r*
4×expm1-log1p-u flip3-+ flip-+ log1p-expm1-u
3×rec-exp 1-exp associate-*l* associate-/l/ distribute-lft-out-- difference-of-squares unswap-sqr
2×frac-2neg clear-num
1×+-commutative flip3-- pow-prod-down sum-log *-commutative flip--
Counts
4 → 218
Calls
4 calls:
77.0ms
(/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha))))
16.0ms
(* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))
303.0ms
(+ (/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series686.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
88.0ms
(/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha))))
76.0ms
(* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))
289.0ms
(+ (/ (/ (+ alpha beta) (* (fma i 2.0 (+ alpha beta)) (/ 1 (- beta alpha)))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify106.0ms

Algorithm
egg-herbie
Counts
230 → 230
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
07822334
136882051
250022005

prune611.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
0.1b
(/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.5b
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
13.3b
(fma (/ (+ alpha beta) 1) (/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
950×times-frac
646×*-un-lft-identity
508×add-sqr-sqrt
386×add-cube-cbrt
74×associate-/l*
69×distribute-lft-out
61×distribute-lft-out-- difference-of-squares
48×associate-/r/
36×add-exp-log
30×associate-/r*
27×div-inv
22×div-exp
20×flip3-- add-cbrt-cube flip--
10×cbrt-undiv
5×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×frac-2neg clear-num
1×pow-flip flip3-+ flip-+ fma-udef associate-/l/ inv-pow
Counts
4 → 528
Calls
4 calls:
8.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
91.0ms
(/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
10.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
0.0ms
(fma (/ (+ alpha beta) 1) (/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series806.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
191.0ms
(/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
274.0ms
(/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
268.0ms
(fma (/ (+ alpha beta) 1) (/ (/ 1 (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify119.0ms

Algorithm
egg-herbie
Counts
540 → 540
Iterations

Useful iterations: 1 (34.0ms)

IterNodesCost
016329394
150028715

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.4b

regimes222.0ms

Accuracy

14.9% (5.5b remaining)

Error of 11.3b against oracle of 5.8b and baseline of 12.3b

bsearch37.0ms

Steps
ItersRangePoint
4
3.873380385792731e+160
5.854087725460173e+160
5.737494938052244e+160

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04524
14524

end0.0ms

sample1.3s

Algorithm
intervals
Results
497.0ms6374×body80valid
185.0ms8000×pre80true
183.0ms605×body640valid
173.0ms474×body1280valid
80.0ms348×body320valid
30.0ms199×body160valid