Details

Time bar (total: 4.5s)

sample77.0ms

Algorithm
intervals
Results
37.0ms108×body1280valid
15.0ms76×body640valid
8.0ms257×body80overflowed
5.0ms39×body320valid
2.0ms19×body160valid
1.0ms14×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (43.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017

prune7.0ms

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: 0.3b

Counts
2 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.3b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube
3×associate-/r* associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv expm1-udef
Counts
2 → 40
Calls
2 calls:
1.0ms
(fma 1 1 (exp (+ x x)))
3.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series95.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(fma 1 1 (exp (+ x x)))
73.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify75.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (69.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune107.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New42446
Fresh011
Picked101
Done000
Total43548

Merged error: 0.2b

Counts
48 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(exp (log1p (exp (* 2 x))))
0.3b
(log1p (exp (* 2 x)))
0.3b
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
5×add-cbrt-cube
4×add-exp-log expm1-log1p-u add-log-exp
3×pow1 exp-prod associate-/r* log1p-expm1-u associate-/l*
2×log1p-udef rem-exp-log
1×cbrt-undiv frac-2neg div-sub log1p-expm1 div-exp clear-num div-inv expm1-udef
Counts
3 → 55
Calls
3 calls:
2.0ms
(exp (log1p (exp (* 2 x))))
1.0ms
(log1p (exp (* 2 x)))
4.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

series274.0ms

Counts
3 → 9
Calls
3 calls:
78.0ms
(exp (log1p (exp (* 2 x))))
51.0ms
(log1p (exp (* 2 x)))
145.0ms
(/ (expm1 (+ x x)) (exp (log1p (exp (* 2 x)))))

simplify67.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0182523
1556477
22509465
35001451

prune140.0ms

Filtered
64 candidates to 50 candidates (78.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New63164
Fresh134
Picked011
Done000
Total64569

Merged error: 0.2b

Counts
69 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.0b
(hypot 1 (exp x))
0.6b
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
0.7b
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
150×times-frac
89×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
42×sqrt-prod
16×associate-/l*
11×add-exp-log add-cbrt-cube
9×associate-/r* div-inv
4×pow1 cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u add-log-exp
3×div-sub
2×frac-2neg clear-num expm1-udef
1×hypot-udef fma-udef associate-/l/
Counts
4 → 165
Calls
4 calls:
1.0ms
(fma 1 1 (exp (+ x x)))
1.0ms
(hypot 1 (exp x))
12.0ms
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
3.0ms
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

series454.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(fma 1 1 (exp (+ x x)))
59.0ms
(hypot 1 (exp x))
250.0ms
(/ (/ (expm1 (* 2 x)) (hypot 1 (exp x))) (sqrt (fma 1 1 (exp (+ x x)))))
124.0ms
(/ (expm1 (* 2 x)) (hypot 1 (exp x)))

simplify76.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
07112850
129502529
250012340

prune408.0ms

Filtered
177 candidates to 119 candidates (67.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1770177
Fresh033
Picked011
Done011
Total1775182

Merged error: 0.2b

Counts
182 → 5

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
0.0b
(- x (* 1/3 (pow x 3)))
0.1b
(* 1/3 (pow x 3))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
12×associate-*r*
9×add-cube-cbrt *-un-lft-identity
8×add-exp-log
5×add-cbrt-cube add-log-exp
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 expm1-log1p-u fma-neg associate-*l* prod-diff prod-exp log1p-expm1-u
2×sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod fma-udef
Counts
3 → 63
Calls
3 calls:
1.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
3.0ms
(- x (* 1/3 (pow x 3)))
6.0ms
(* 1/3 (pow x 3))

series172.0ms

Counts
3 → 9
Calls
3 calls:
56.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
80.0ms
(- x (* 1/3 (pow x 3)))
36.0ms
(* 1/3 (pow x 3))

simplify37.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25002292

prune131.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New72072
Fresh022
Picked011
Done022
Total72577

Merged error: 0.2b

Counts
77 → 5

regimes45.0ms

Accuracy

0% (0.1b remaining)

Error of 0.7b against oracle of 0.6b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0157
1177
2177

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.0s3266×body1280valid
476.0ms2442×body640valid
239.0ms7546×body80overflowed
152.0ms1232×body320valid
50.0ms620×body160valid
18.0ms440×body80valid