Details

Time bar (total: 45.7s)

sample33.0ms

Algorithm
intervals
Results
8.0ms205×body80valid
4.0ms256×pre80true
3.0ms16×body1280valid
3.0ms17×body640valid
1.0ms10×body320valid
1.0ms8×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.2b

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))
2.0b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite485.0ms

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:
18.0ms
(* (+ alpha beta) (- beta alpha))
90.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
336.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
31.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series620.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(* (+ alpha beta) (- beta alpha))
229.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
272.0ms
(+ (/ (/ (* (+ 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)))

simplify48.0ms

Algorithm
egg-herbie
Counts
224 → 224
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
09372463
150022158

prune656.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.7b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.9b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.8s

Algorithm
rewrite-expression-head
Rules
10036×times-frac
6754×*-un-lft-identity
4612×add-sqr-sqrt
3458×add-cube-cbrt
1178×fma-def
1071×distribute-lft-out
577×distribute-lft-out-- difference-of-squares
400×associate-/r/
314×associate-/l*
205×div-inv
164×flip3-+ flip-+
105×associate-/r*
62×add-exp-log
43×div-exp
32×flip3-- add-cbrt-cube flip--
19×cbrt-undiv
6×rec-exp 1-exp add-log-exp
5×pow1
4×expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num
2×associate-/l/
1×+-commutative pow-flip sum-log inv-pow
Counts
4 → 3236
Calls
4 calls:
161.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
15.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
31.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series613.0ms

Counts
4 → 12
Calls
4 calls:
286.0ms
(/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
64.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
146.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
116.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify462.0ms

Algorithm
egg-herbie
Counts
3248 → 3248
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500147178

prune9.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
0.7b
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
3.9b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
4.0b
(log (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

rewrite4.2s

Algorithm
rewrite-expression-head
Rules
5174×times-frac
3516×*-un-lft-identity
2410×add-sqr-sqrt
1796×add-cube-cbrt
1178×fma-def
553×distribute-lft-out
307×distribute-lft-out-- difference-of-squares
213×associate-/r/
109×div-inv
101×associate-/r*
88×flip3-+ flip-+
30×add-exp-log
21×associate-/l*
18×div-exp add-cbrt-cube
17×flip3-- flip--
9×cbrt-undiv
6×pow1 add-log-exp
5×log-pow
4×expm1-log1p-u log-prod exp-prod log1p-expm1-u
3×rec-exp 1-exp
2×frac-2neg clear-num
1×+-commutative pow-flip rem-log-exp exp-sum sum-log associate-/l/ inv-pow
Counts
4 → 1757
Calls
4 calls:
15.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
31.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
1.2s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
2.7s
(log (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

series443.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))
142.0ms
(/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha)))
115.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
118.0ms
(log (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)))

simplify137.0ms

Algorithm
egg-herbie
Counts
1769 → 1769
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
017048927
150018628

prune5.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize23.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
3.3b
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
3.9b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
3.9b
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite8.0s

Algorithm
rewrite-expression-head
Rules
8248×times-frac
5554×*-un-lft-identity
3654×add-sqr-sqrt
2790×add-cube-cbrt
2356×fma-def
950×distribute-lft-out
432×distribute-lft-out-- difference-of-squares
300×associate-/r/
154×div-inv
124×flip3-+ flip-+
24×flip3-- flip--
14×log-prod log-pow
10×sqrt-pow1
8×pow1 exp-prod sqrt-prod add-log-exp
6×add-exp-log
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×+-commutative pow1/2 rem-log-exp exp-sum sum-log
Counts
4 → 2432
Calls
4 calls:
2.7s
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
2.9s
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
1.0s
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series749.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
260.0ms
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
112.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
116.0ms
(+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify96.0ms

Algorithm
egg-herbie
Counts
2444 → 2444
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
01791632
14611474
219581442
350011406

prune11.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.1b

regimes310.0ms

Accuracy

18.2% (5.7b remaining)

Error of 11.4b against oracle of 5.8b and baseline of 12.7b

bsearch68.0ms

Steps
ItersRangePoint
8
3.594603974860845e+173
6.302835922400278e+177
6.191224408848943e+177

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
14425
24425

end0.0ms

sample830.0ms

Algorithm
intervals
Results
255.0ms6313×body80valid
122.0ms8000×pre80true
108.0ms513×body1280valid
104.0ms629×body640valid
41.0ms332×body320valid
17.0ms213×body160valid