Details

Time bar (total: 11.1s)

sample38.0ms

Algorithm
intervals
Results
8.0ms207×body80valid
6.0ms18×body640valid
4.0ms256×pre80true
3.0ms17×body1280valid
1.0ms7×body320valid
1.0ms7×body160valid

simplify54.0ms

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: 26.1b

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))
1.6b
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
22.6b
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite852.0ms

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:
173.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
618.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
54.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series547.0ms

Counts
3 → 9
Calls
3 calls:
217.0ms
(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
260.0ms
(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
69.0ms
(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify97.0ms

Algorithm
egg-herbie
Counts
168 → 168
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
07011971
137401800
250011782

prune518.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize15.0ms

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)) 2.0))
0.1b
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
0.3b
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
1.6b
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

rewrite1.1s

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:
168.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
29.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
12.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
748.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

series632.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
73.0ms
(/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha)))
70.0ms
(/ (fma i 2.0 (+ alpha beta)) (- beta alpha))
267.0ms
(+ (/ (/ (+ alpha beta) (/ (fma i 2.0 (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)

simplify152.0ms

Algorithm
egg-herbie
Counts
1025 → 1025
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0176912717
1500112368

prune2.6s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
2.1b
(+ (* (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha)))) 1.0)

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow1/3
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 53
Calls
4 calls:
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
148.0ms
(+ (* (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha)))) 1.0)

series961.0ms

Counts
4 → 12
Calls
4 calls:
222.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
226.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
217.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
296.0ms
(+ (* (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha)))) 1.0)

simplify37.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0251872
1851792
25002770

prune349.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
0.8b
(cbrt (fma i 2.0 (+ alpha beta)))
2.1b
(fma (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha))) 1.0)

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
4.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
1.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
0.0ms
(fma (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha))) 1.0)

series1.4s

Counts
4 → 12
Calls
4 calls:
228.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
231.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
225.0ms
(cbrt (fma i 2.0 (+ alpha beta)))
718.0ms
(fma (/ (cbrt (+ alpha beta)) (/ (* (cbrt (fma i 2.0 (+ alpha beta))) (cbrt (fma i 2.0 (+ alpha beta)))) (cbrt (+ alpha beta)))) (/ (/ (cbrt (+ alpha beta)) (+ alpha (+ beta (fma i 2.0 2.0)))) (/ (cbrt (fma i 2.0 (+ alpha beta))) (- beta alpha))) 1.0)

simplify76.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0216669
1638594
22951569
35001557

prune372.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

regimes223.0ms

Accuracy

0% (6.7b remaining)

Error of 12.5b against oracle of 5.8b and baseline of 12.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02113
12113

end0.0ms

sample866.0ms

Algorithm
intervals
Results
244.0ms6337×body80valid
123.0ms8000×pre80true
102.0ms511×body1280valid
98.0ms595×body640valid
41.0ms365×body320valid
15.0ms192×body160valid