Details

Time bar (total: 6.3s)

sample27.0ms

Algorithm
intervals
Results
11.0ms256×body80valid
4.0ms256×pre80true

simplify83.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 2 (6.0ms)

IterNodesCost
03317
112215
259813
3447513
4500113

prune8.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 3.8b

Counts
2 → 2

localize12.0ms

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))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite120.0ms

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:
6.0ms
(+ (+ alpha beta) (* beta alpha))
20.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
40.0ms
(/ (/ (/ (+ (+ (+ 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))
14.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series377.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (+ alpha beta) (* beta alpha))
137.0ms
(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))
148.0ms
(/ (/ (/ (+ (+ (+ 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))
77.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify147.0ms

Algorithm
egg-herbie
Counts
487 → 487
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0153413079
1500112129

prune1.0s

Filtered
487 candidates to 297 candidates (61.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New4816487
Fresh101
Picked101
Done000
Total4836489

Merged error: 1.5b

Counts
489 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
0.0b
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
0.1b
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
3.6b
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
205×times-frac
134×add-exp-log
131×*-un-lft-identity
123×add-sqr-sqrt
104×add-cube-cbrt
82×div-exp
52×add-cbrt-cube
44×associate-*r*
30×prod-exp
25×cbrt-undiv
24×1-exp
20×associate-/r*
16×associate-/r/ div-inv
13×associate-/l*
12×rec-exp
11×flip3-+ flip-+ distribute-lft-out
9×cbrt-unprod
7×pow1 associate-/l/ unswap-sqr
4×expm1-log1p-u frac-times associate-*l* associate-*l/ log1p-expm1-u add-log-exp
3×frac-2neg clear-num
2×associate-*r/ un-div-inv
1×pow-flip pow-prod-down *-commutative inv-pow
Counts
4 → 289
Calls
4 calls:
7.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
22.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
31.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
28.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

series463.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))
159.0ms
(/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0)))
174.0ms
(/ (/ (* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
84.0ms
(* (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (/ 1 (/ (fma 1.0 2.0 (+ alpha beta)) 1)))

simplify71.0ms

Algorithm
egg-herbie
Counts
301 → 301
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012134435
150013747

prune611.0ms

Filtered
301 candidates to 185 candidates (61.5%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New3010301
Fresh055
Picked011
Done000
Total3016307

Merged error: 1.5b

Counts
307 → 6

localize19.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
0.7b
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
3.6b
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
30×sqrt-prod
28×sqrt-div
22×*-un-lft-identity
14×pow1 add-cube-cbrt flip3-+ associate-*l* flip-+
12×associate-*r*
8×add-exp-log frac-times add-cbrt-cube unswap-sqr
6×sqrt-pow1 pow1/2 pow-prod-down
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u distribute-lft-out add-log-exp
2×rem-sqrt-square sqrt-unprod prod-exp *-commutative cbrt-unprod hypot-def
Counts
4 → 120
Calls
4 calls:
16.0ms
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
21.0ms
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
7.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

series227.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
66.0ms
(* (sqrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (sqrt (+ (+ alpha beta) (* 2.0 1.0))))
52.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
47.0ms
(sqrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03741568
114301508
250011494

prune496.0ms

Filtered
132 candidates to 98 candidates (74.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1320132
Fresh044
Picked011
Done011
Total1326138

Merged error: 1.5b

Counts
138 → 6

localize17.0ms

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)))
1.0b
(/ 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))))
3.6b
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
377×*-un-lft-identity
310×times-frac
147×add-sqr-sqrt
138×add-cube-cbrt
136×distribute-lft-out
85×associate-*l*
54×add-exp-log
34×add-cbrt-cube
24×div-exp
20×associate-/r*
15×div-inv
14×cbrt-undiv
12×prod-exp associate-/l*
9×pow1
6×cbrt-unprod
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u associate-/l/ add-log-exp
3×frac-2neg associate-*r* clear-num associate-/r/ unswap-sqr
2×pow-flip flip3-+ pow-prod-down associate-*l/ flip-+ fma-udef
1×distribute-rgt-in distribute-lft-in *-commutative inv-pow
Counts
4 → 305
Calls
4 calls:
19.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
28.0ms
(* (/ (+ 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)))
20.0ms
(/ 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))))
12.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

series621.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ beta (+ alpha (fma 1.0 2.0 1.0))) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta))))
240.0ms
(* (/ (+ 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)))
160.0ms
(/ 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))))
84.0ms
(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (fma 1.0 2.0 (+ alpha beta)))

simplify145.0ms

Algorithm
egg-herbie
Counts
317 → 317
Iterations

Useful iterations: 2 (94.0ms)

IterNodesCost
08925409
144414944
250014942

prune646.0ms

Filtered
317 candidates to 179 candidates (56.5%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New3161317
Fresh123
Picked011
Done022
Total3176323

Merged error: 0.4b

Counts
323 → 6

regimes69.0ms

Accuracy

71.4% (1.1b remaining)

Error of 1.2b against oracle of 0.1b and baseline of 3.9b

bsearch60.0ms

Steps
ItersRangePoint
7
4.0917562849863095e+159
2.5534508082457815e+161
3.298192609819446e+160

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04126
14326
24326

end0.0ms

sample664.0ms

Algorithm
intervals
Results
370.0ms8000×body80valid
138.0ms8000×pre80true