Details

Time bar (total: 3.8s)

sample74.0ms

Algorithm
intervals
Results
32.0ms97×body1280valid
17.0ms78×body640valid
7.0ms234×body80overflowed
6.0ms45×body320valid
1.0ms17×body160valid
1.0ms19×body80valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (43.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750017

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.5b

Counts
2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.5b
(/ (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))))

series93.0ms

Counts
2 → 6
Calls
2 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
71.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify76.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (70.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune106.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New43346
Fresh000
Picked101
Done000
Total44347

Merged error: 0.5b

Counts
47 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (+ (exp (* 2 x)) 1))
0.0b
(+ (exp (* 2 x)) 1)
0.5b
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
29×add-sqr-sqrt
26×times-frac
22×add-cube-cbrt
18×associate-*r*
16×add-exp-log
10×add-cbrt-cube
8×distribute-lft-out
6×pow1
5×add-log-exp
4×div-exp prod-exp associate-/r* associate-/r/
3×expm1-log1p-u fma-def flip3-+ associate-*l* flip-+ log1p-expm1-u associate-/l* unswap-sqr
2×cbrt-undiv rec-exp 1-exp cbrt-unprod div-inv
1×+-commutative pow-flip frac-2neg associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
3 → 99
Calls
3 calls:
6.0ms
(/ 1 (+ (exp (* 2 x)) 1))
4.0ms
(+ (exp (* 2 x)) 1)
10.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series85.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(/ 1 (+ (exp (* 2 x)) 1))
10.0ms
(+ (exp (* 2 x)) 1)
56.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify49.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0320771
11601634
25001594

prune160.0ms

Filtered
108 candidates to 65 candidates (60.2%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1080108
Fresh022
Picked011
Done000
Total1083111

Merged error: 0.5b

Counts
111 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
0.4b
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
0.5b
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
53×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
16×add-exp-log associate-/r*
10×add-cbrt-cube
8×div-exp
6×div-inv associate-/l*
4×pow1 cbrt-undiv
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×rec-exp frac-2neg 1-exp clear-num
1×pow-flip associate-/r/ fma-udef inv-pow
Counts
3 → 117
Calls
3 calls:
1.0ms
(fma 1 1 (exp (+ x x)))
6.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
3.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

series165.0ms

Counts
3 → 9
Calls
3 calls:
21.0ms
(fma 1 1 (exp (+ x x)))
71.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))
72.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
126 → 126
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03871449
117421257
250011169

prune190.0ms

Filtered
126 candidates to 75 candidates (59.5%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1260126
Fresh011
Picked011
Done011
Total1263129

Merged error: 0.5b

Counts
129 → 3

localize9.0ms

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))

series177.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
82.0ms
(- x (* 1/3 (pow x 3)))
42.0ms
(* 1/3 (pow x 3))

simplify36.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25002292

prune132.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New70272
Fresh000
Picked011
Done022
Total70575

Merged error: 0.5b

Counts
75 → 5

regimes24.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0177
1197
2197

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s3263×body1280valid
499.0ms2430×body640valid
234.0ms7416×body80overflowed
157.0ms1226×body320valid
54.0ms645×body160valid
18.0ms436×body80valid