Details

Time bar (total: 14.2s)

sample56.0ms

Algorithm
intervals
Results
16.0ms209×body80valid
10.0ms256×pre80true
6.0ms16×body1280valid
4.0ms13×body640valid
3.0ms13×body320valid
1.0ms5×body160valid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03114
110714
247914
3231514
4500214

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.1b
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
1.1b
(+ (/ (/ (* (+ 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)))

rewrite501.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
87×*-un-lft-identity
46×fma-def
45×add-sqr-sqrt add-cube-cbrt
24×associate-/r/
21×distribute-lft-out
18×add-exp-log add-cbrt-cube
17×flip3-+ flip-+
12×div-inv
11×add-log-exp
10×associate-/l*
9×associate-/l/
7×cbrt-undiv div-exp associate-/r*
4×pow1 expm1-log1p-u frac-times sum-log log1p-expm1-u
3×flip3-- flip--
2×+-commutative frac-2neg associate-*r/ associate-*l/ prod-exp clear-num cbrt-unprod
1×associate-+l+
Counts
4 → 178
Calls
4 calls:
15.0ms
(+ (+ alpha beta) (* 2.0 i))
96.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
352.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
30.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series195.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (+ alpha beta) (* 2.0 i))
74.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
95.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify98.0ms

Algorithm
egg-herbie
Counts
190 → 190
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
07242051
141011860
250011852

prune1.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* 2.0 i))
0.0b
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
0.1b
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
11.2b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
174×times-frac
166×*-un-lft-identity
120×add-sqr-sqrt
82×add-cube-cbrt
26×associate-/l*
23×distribute-lft-out
19×distribute-lft-out-- difference-of-squares
14×associate-/r/
11×add-exp-log add-cbrt-cube
9×add-log-exp
8×flip3-+ flip-+
7×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u fma-def div-exp log1p-expm1-u
3×div-sub sum-log associate-/l/
2×frac-2neg clear-num
1×+-commutative associate-+l+ flip3-- flip-- fma-udef
Counts
4 → 200
Calls
4 calls:
17.0ms
(+ (+ alpha beta) (* 2.0 i))
23.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
98.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series158.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(+ (+ alpha beta) (* 2.0 i))
16.0ms
(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
43.0ms
(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
92.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify96.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
07503192
135682956
250032937

prune2.3s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.1b
(pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)
11.2b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
12.4b
(cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3))

rewrite180.0ms

Algorithm
rewrite-expression-head
Rules
594×*-un-lft-identity
524×times-frac
348×cbrt-prod
330×add-sqr-sqrt
218×add-cube-cbrt
182×unpow-prod-down cube-prod
132×distribute-lft-out
61×associate-/l*
56×distribute-lft-out-- difference-of-squares
30×associate-/r/
15×flip3-+ flip-+ div-inv
9×add-exp-log
8×add-cbrt-cube
7×cube-mult unpow3 sqr-pow
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u add-log-exp
3×cube-div pow-unpow
2×cbrt-undiv cbrt-div div-exp pow-exp rem-cube-cbrt
1×pow-to-exp pow-pow frac-2neg pow1/3 clear-num rem-cbrt-cube fma-udef associate-/l/
Counts
4 → 480
Calls
4 calls:
115.0ms
(/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
12.0ms
(pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
14.0ms
(cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3))

series205.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
51.0ms
(pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)
91.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3)) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
17.0ms
(cbrt (pow (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) 3))

simplify152.0ms

Algorithm
egg-herbie
Counts
492 → 492
Iterations

Useful iterations: 2 (75.0ms)

IterNodesCost
08578112
138057232
250017204

prune2.8s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
5.3b
(cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
11.2b
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) (/ (+ (+ (fma 2.0 i beta) alpha) 2.0) (cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))))) 1.0)
13.2b
(cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
246×*-un-lft-identity
148×times-frac
122×add-sqr-sqrt
62×add-cube-cbrt
48×swap-sqr
43×distribute-lft-out
36×distribute-lft-out--
27×cbrt-prod
26×associate-*r* associate-*l*
24×difference-of-squares
16×add-exp-log add-cbrt-cube
11×pow1
10×associate-/r/
5×flip3-+ flip-+ div-inv
4×cbrt-undiv expm1-log1p-u cbrt-div div-exp prod-exp cbrt-unprod log1p-expm1-u add-log-exp unswap-sqr
2×frac-times pow1/3 associate-*r/ associate-*l/
1×pow2 pow-plus pow-prod-down pow-sqr *-commutative pow-prod-up fma-udef
Counts
4 → 191
Calls
4 calls:
52.0ms
(* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
5.0ms
(cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
0.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) (/ (+ (+ (fma 2.0 i beta) alpha) 2.0) (cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))))) 1.0)
12.0ms
(cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))

series376.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
77.0ms
(cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))
92.0ms
(fma (/ (/ (+ alpha beta) 1) 1) (/ (cbrt (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))) (/ (+ (+ (fma 2.0 i beta) alpha) 2.0) (cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)))))) 1.0)
165.0ms
(cbrt (* (/ (- beta alpha) (+ (fma 2.0 i beta) alpha)) (/ (- beta alpha) (+ (fma 2.0 i beta) alpha))))

simplify89.0ms

Algorithm
egg-herbie
Counts
203 → 203
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06882683
130712448
250012316

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

regimes885.0ms

Accuracy

14.5% (5.5b remaining)

Error of 11.2b against oracle of 5.6b and baseline of 12.1b

bsearch21.0ms

Steps
ItersRangePoint
4
8.790873633702001e+153
1.2605266572077815e+154
1.248606679275357e+154

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04535
14535

end0.0ms

sample1.5s

Algorithm
intervals
Results
500.0ms6403×body80valid
317.0ms8000×pre80true
190.0ms471×body1280valid
187.0ms582×body640valid
83.0ms352×body320valid
30.0ms192×body160valid