Details

Time bar (total: 4.9s)

sample107.0ms

Algorithm
intervals
Results
43.0ms237×body10240exit
32.0ms105×body1280valid
15.0ms80×body640valid
4.0ms33×body320valid
2.0ms27×body160valid
0.0ms11×body80valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 7 (47.0ms)

IterNodesCost
0159
1249
2329
3449
4639
51799
611849
750027

prune7.0ms

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: 0.3b

Counts
2 → 1

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite6.0ms

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)))
4.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series100.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(fma 1 1 (exp (+ x x)))
72.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify78.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (72.0ms)

IterNodesCost
0149395
1506351
22431344
35001343

prune97.0ms

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: 0.2b

Counts
47 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
24×add-cube-cbrt
18×associate-*r*
16×add-exp-log
10×associate-*r/ add-cbrt-cube
9×distribute-lft-out
8×associate-/r*
7×associate-/l*
6×pow1
5×add-log-exp
4×fma-def div-exp prod-exp associate-/r/
3×expm1-log1p-u flip3-+ associate-*l* clear-num un-div-inv flip-+ log1p-expm1-u unswap-sqr
2×cbrt-undiv rec-exp frac-2neg 1-exp *-commutative cbrt-unprod div-inv
1×+-commutative pow-flip pow-prod-down sum-log exp-lft-sqr inv-pow
Counts
3 → 111
Calls
3 calls:
7.0ms
(+ (exp (* 2 x)) 1)
9.0ms
(/ 1 (+ (exp (* 2 x)) 1))
17.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

series87.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(+ (exp (* 2 x)) 1)
19.0ms
(/ 1 (+ (exp (* 2 x)) 1))
57.0ms
(* (expm1 (+ x x)) (/ 1 (+ (exp (* 2 x)) 1)))

simplify47.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0325811
11623668
25001639

prune179.0ms

Filtered
120 candidates to 72 candidates (60.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1200120
Fresh022
Picked011
Done000
Total1203123

Merged error: 0.2b

Counts
123 → 3

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
0.0b
(fma 1 1 (exp (+ x x)))
0.2b
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
84×times-frac
56×*-un-lft-identity
55×add-sqr-sqrt add-cube-cbrt
19×associate-/r*
16×add-exp-log
10×add-cbrt-cube associate-/l*
9×associate-/r/
8×div-exp
6×div-inv
4×pow1 cbrt-undiv clear-num
3×expm1-log1p-u frac-2neg log1p-expm1-u add-log-exp
2×rec-exp 1-exp remove-double-div
1×pow-flip fma-udef inv-pow
Counts
3 → 127
Calls
3 calls:
3.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
1.0ms
(fma 1 1 (exp (+ x x)))
8.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

series168.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x)))
22.0ms
(fma 1 1 (exp (+ x x)))
72.0ms
(/ 1 (/ (fma 1 1 (exp (+ x x))) (expm1 (+ x x))))

simplify56.0ms

Algorithm
egg-herbie
Counts
136 → 136
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
03921493
117601297
250021206

prune203.0ms

Filtered
136 candidates to 82 candidates (60.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1360136
Fresh011
Picked011
Done011
Total1363139

Merged error: 0.2b

Counts
139 → 3

localize13.0ms

Local error

Found 3 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
68×add-sqr-sqrt
57×prod-diff
43×*-un-lft-identity
38×add-cube-cbrt
33×associate-*r*
17×unpow-prod-down
15×unswap-sqr
13×associate-*l*
9×sqr-pow
8×add-exp-log
5×pow1 unpow3 add-cbrt-cube add-log-exp
4×*-commutative difference-of-squares
3×expm1-log1p-u fma-neg prod-exp log1p-expm1-u
2×distribute-lft-out--
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- diff-log pow-prod-down pow-exp flip-- cbrt-unprod fma-udef
Counts
3 → 120
Calls
3 calls:
11.0ms
(- x (* 1/3 (pow x 3)))
1.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
7.0ms
(* 1/3 (pow x 3))

series181.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(- x (* 1/3 (pow x 3)))
60.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
39.0ms
(* 1/3 (pow x 3))

simplify74.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05031421
11788747
25002747

prune146.0ms

Filtered
129 candidates to 53 candidates (41.1%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New1272129
Fresh000
Picked101
Done022
Total1284132

Merged error: 0.2b

Counts
132 → 4

regimes20.0ms

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

sample3.2s

Algorithm
intervals
Results
1.3s7424×body10240exit
983.0ms3236×body1280valid
464.0ms2462×body640valid
143.0ms1229×body320valid
51.0ms658×body160valid
15.0ms415×body80valid