Details

Time bar (total: 13.2s)

sample28.0ms

Algorithm
intervals
Results
9.0ms256×body80valid
7.0ms256×pre80true

simplify82.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (+ alpha beta) (* beta alpha))
0.0b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
804×times-frac
587×*-un-lft-identity
341×add-sqr-sqrt add-cube-cbrt
123×distribute-lft-out
82×associate-/l*
54×associate-/r/
29×flip3-+ flip-+
27×div-inv
20×add-exp-log add-cbrt-cube
10×cbrt-undiv div-exp associate-/r*
9×add-log-exp
4×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l/
3×frac-2neg clear-num sum-log
1×+-commutative associate-+l+
Counts
4 → 475
Calls
4 calls:
58.0ms
(+ (+ alpha beta) (* beta alpha))
347.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
505.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
300.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series354.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(+ (+ alpha beta) (* beta alpha))
129.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
140.0ms
(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
72.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify140.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0153413079
1500112129

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.6b
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.6b
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.9b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
756×times-frac
594×*-un-lft-identity
419×sqrt-prod
372×add-sqr-sqrt add-cube-cbrt
111×distribute-lft-out
61×associate-/l*
40×sqrt-div associate-/r/
26×associate-/r*
24×add-exp-log
21×flip3-+ flip-+
20×div-inv
18×add-cbrt-cube
12×div-exp
8×cbrt-undiv
6×pow1
4×expm1-log1p-u frac-2neg clear-num log1p-expm1-u associate-/l/ add-log-exp
3×pow-flip
2×rec-exp 1-exp
1×sqrt-pow1 pow1/2 inv-pow
Counts
4 → 587
Calls
4 calls:
38.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
187.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
445.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
292.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

series410.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
94.0ms
(/ (/ 1 (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
157.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
93.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))

simplify143.0ms

Algorithm
egg-herbie
Counts
599 → 599
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
0136913739
1500112934

prune1.4s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
0.0b
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
0.5b
(/ (/ 1 1) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite897.0ms

Algorithm
rewrite-expression-head
Rules
389×*-un-lft-identity
338×times-frac
159×add-sqr-sqrt
150×add-cube-cbrt
136×distribute-lft-out
114×add-exp-log
85×associate-*l*
72×div-exp
52×add-cbrt-cube
25×cbrt-undiv
24×prod-exp
22×associate-/l*
20×1-exp associate-/r*
17×div-inv
9×cbrt-unprod
8×rec-exp
6×pow1
5×associate-/l/
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×flip3-+ associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative
Counts
4 → 343
Calls
4 calls:
179.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
328.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
97.0ms
(/ (/ 1 1) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
267.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series563.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
214.0ms
(* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta)))
153.0ms
(/ (/ 1 1) (* (/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))) (fma 1.0 2.0 (+ alpha beta))))
70.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify81.0ms

Algorithm
egg-herbie
Counts
355 → 355
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
011456197
150015584

prune808.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
0.6b
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
0.6b
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
2.4b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
690×times-frac
502×*-un-lft-identity
425×add-sqr-sqrt
294×add-cube-cbrt
222×sqrt-prod
132×associate-*l*
99×distribute-lft-out
85×associate-*r*
75×add-exp-log
49×add-cbrt-cube
44×associate-/r/
39×div-exp
30×unswap-sqr
25×associate-/l*
23×cbrt-undiv flip3-+ flip-+ div-inv
17×associate-/r*
15×prod-exp
12×sqrt-div
9×cbrt-unprod
8×pow1
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u add-log-exp
3×pow-flip frac-2neg clear-num associate-/l/
1×frac-times sqrt-pow1 pow1/2 associate-*r/ pow-prod-down associate-*l/ *-commutative inv-pow
Counts
4 → 545
Calls
4 calls:
1.1s
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
443.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
129.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
295.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series475.0ms

Counts
4 → 12
Calls
4 calls:
158.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (fma 1.0 2.0 (+ alpha beta))))
179.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
61.0ms
(/ 1 (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))
78.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify161.0ms

Algorithm
egg-herbie
Counts
557 → 557
Iterations

Useful iterations: 1 (40.0ms)

IterNodesCost
0197014033
1500213254

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes73.0ms

Accuracy

64.7% (1.4b remaining)

Error of 1.4b against oracle of 0.1b and baseline of 3.9b

bsearch48.0ms

Steps
ItersRangePoint
7
2.1826540956841364e+159
4.007606716386316e+161
2.234411931849944e+159

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04125
14125

end0.0ms

sample564.0ms

Algorithm
intervals
Results
276.0ms8000×body80valid
100.0ms8000×pre80true