Details

Time bar (total: 21.3s)

sample35.0ms

Algorithm
intervals
Results
12.0ms213×body80valid
4.0ms256×pre80true
3.0ms13×body1280valid
2.0ms14×body640valid
1.0ms10×body320valid
1.0ms6×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.2b

localize12.0ms

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))
2.1b
(+ (/ (/ (* (+ 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)))

rewrite465.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
43×add-sqr-sqrt add-cube-cbrt
42×fma-def
24×associate-/r/
20×distribute-lft-out
17×add-exp-log add-cbrt-cube
16×flip3-+ flip-+
12×div-inv
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
5×add-log-exp
4×frac-times
3×pow1 expm1-log1p-u flip3-- flip-- log1p-expm1-u
2×frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×+-commutative sum-log
Counts
3 → 159
Calls
3 calls:
91.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
341.0ms
(+ (/ (/ (* (+ 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)))

series572.0ms

Counts
3 → 9
Calls
3 calls:
226.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
268.0ms
(+ (/ (/ (* (+ 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)))

simplify95.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
07011971
137401800
250011782

prune540.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 5.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))
3.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite402.0ms

Algorithm
rewrite-expression-head
Rules
319×times-frac
290×*-un-lft-identity
215×add-sqr-sqrt
140×add-cube-cbrt
82×associate-*r*
42×distribute-lft-out
33×distribute-lft-out-- difference-of-squares
31×associate-/l*
20×add-exp-log add-cbrt-cube
16×associate-/r/
11×flip3-+ flip-+
10×div-inv
7×cbrt-undiv div-exp associate-/r*
6×pow1 add-log-exp
4×expm1-log1p-u associate-*l* log1p-expm1-u
3×div-sub prod-exp cbrt-unprod associate-/l/ unswap-sqr
2×frac-times frac-2neg associate-*l/ clear-num
1×+-commutative flip3-- fma-def associate-*r/ pow-prod-down sum-log *-commutative flip--
Counts
4 → 298
Calls
4 calls:
67.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
106.0ms
(/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))
166.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
47.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

series754.0ms

Counts
4 → 12
Calls
4 calls:
83.0ms
(/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
163.0ms
(/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))
232.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
276.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify67.0ms

Algorithm
egg-herbie
Counts
310 → 310
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010694511
150014265

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)))
3.1b
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
3.2b
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0))
3.6b
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

rewrite309.0ms

Algorithm
rewrite-expression-head
Rules
141×times-frac
121×*-un-lft-identity
98×add-sqr-sqrt
82×associate-*r*
65×add-cube-cbrt
16×distribute-lft-out
14×add-exp-log
13×add-cbrt-cube
12×distribute-lft-out-- difference-of-squares
8×pow1 flip3-+ flip-+
6×log-prod associate-/r/ add-log-exp
4×expm1-log1p-u log-div exp-prod associate-*l* log1p-expm1-u div-inv
3×cbrt-undiv div-exp exp-sum prod-exp cbrt-unprod unswap-sqr
2×frac-times exp-diff associate-*l/ log-pow
1×+-commutative fma-def associate-*r/ rem-log-exp pow-prod-down sum-log *-commutative rem-exp-log
Counts
4 → 160
Calls
4 calls:
46.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)))
166.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
45.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0))
42.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

series1.1s

Counts
4 → 12
Calls
4 calls:
276.0ms
(exp (log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)))
235.0ms
(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta))))
279.0ms
(log (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0))
277.0ms
(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) (fma i 2.0 (+ alpha beta)))) 1.0)

simplify122.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (99.0ms)

IterNodesCost
09072545
148792353
250012345

prune618.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
0.4b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.1b
(* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
6.2b
(+ (* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

rewrite2.2s

Algorithm
rewrite-expression-head
Rules
12417×times-frac
7184×*-un-lft-identity
5671×add-sqr-sqrt
4426×add-cube-cbrt
3461×associate-*r*
3209×sqrt-prod
800×distribute-lft-out
575×distribute-lft-out-- difference-of-squares
450×associate-/r/
422×sqrt-div
239×div-inv
214×flip3-+ flip-+
63×add-exp-log
37×add-cbrt-cube
33×div-exp
21×unswap-sqr
17×cbrt-undiv
14×associate-/r*
13×prod-exp
8×pow1 associate-/l*
7×cbrt-unprod
6×add-log-exp
4×expm1-log1p-u rec-exp 1-exp associate-*l* log1p-expm1-u
3×pow-flip
2×frac-times frac-2neg associate-*l/ clear-num associate-/l/
1×+-commutative flip3-- fma-def sqrt-pow1 pow1/2 div-sub associate-*r/ pow-prod-down sum-log *-commutative flip-- inv-pow
Counts
4 → 3655
Calls
4 calls:
74.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
63.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
1.2s
(* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
270.0ms
(+ (* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

series754.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
121.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
232.0ms
(* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))))))
276.0ms
(+ (* (+ alpha beta) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) (/ (fma i 2.0 (+ alpha beta)) (/ (- beta alpha) (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))))) 1.0)

simplify753.0ms

Algorithm
egg-herbie
Counts
3667 → 3667
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
0500282223

prune10.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.8b

regimes291.0ms

Accuracy

10.4% (7.5b remaining)

Error of 11.5b against oracle of 4.0b and baseline of 12.4b

bsearch90.0ms

Steps
ItersRangePoint
9
2.4649659853731173e+247
8.03398024326001e+253
1.7553714861944655e+248

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05245
15245

end0.0ms

sample815.0ms

Algorithm
intervals
Results
264.0ms6353×body80valid
120.0ms8000×pre80true
105.0ms511×body1280valid
91.0ms572×body640valid
46.0ms375×body320valid
15.0ms189×body160valid