Details

Time bar (total: 5.1s)

sample100.0ms

Algorithm
intervals
Results
38.0ms243×body10240exit
32.0ms101×body1280valid
14.0ms80×body640valid
4.0ms40×body320valid
1.0ms19×body160valid
1.0ms16×body80valid

simplify44.0ms

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)

Merged error: 1.5b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 1 1 (exp (+ x x)))
1.5b
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

rewrite4.0ms

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:
0.0ms
(fma 1 1 (exp (+ x x)))
2.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

series89.0ms

Counts
2 → 6
Calls
2 calls:
20.0ms
(fma 1 1 (exp (+ x x)))
68.0ms
(/ (expm1 (+ x x)) (fma 1 1 (exp (+ x x))))

simplify72.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (67.0ms)

IterNodesCost
0150395
1512351
22464344
35002343

prune113.0ms

Filtered
46 candidates to 39 candidates (84.8%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (exp (* 2 x)) 1)
1.5b
(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
12×add-sqr-sqrt add-cube-cbrt times-frac
5×distribute-lft-out
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×fma-def associate-/l*
2×pow1 expm1-log1p-u flip3-+ associate-/r/ flip-+ log1p-expm1-u
1×cbrt-undiv +-commutative frac-2neg div-sub div-exp clear-num sum-log div-inv expm1-udef
Counts
2 → 53
Calls
2 calls:
4.0ms
(+ (exp (* 2 x)) 1)
7.0ms
(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

series64.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(+ (exp (* 2 x)) 1)
52.0ms
(/ (expm1 (+ x x)) (+ (exp (* 2 x)) 1))

simplify141.0ms

Algorithm
egg-herbie
Counts
59 → 59
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0204470
1862421
24909412
35001411

prune117.0ms

Filtered
59 candidates to 44 candidates (74.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 1.4b

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
1.2b
(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
1.5b
(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
5.8b
(- (* 1 1) (* (exp (* 2 x)) 1))

rewrite129.0ms

Algorithm
rewrite-expression-head
Rules
36×*-un-lft-identity
27×add-sqr-sqrt
25×times-frac
22×add-cube-cbrt
18×associate-*l*
11×add-exp-log add-cbrt-cube add-log-exp
7×distribute-lft-out
6×pow1
5×flip3-+ flip-+
4×expm1-log1p-u associate-/r* associate-/r/ log1p-expm1-u
3×associate-+r+ associate-*r* associate-/l*
2×cbrt-undiv frac-times sub-neg diff-log associate-*r/ div-exp prod-diff prod-exp sum-log cbrt-unprod div-inv unswap-sqr
1×+-commutative distribute-rgt-in associate-+r- flip3-- distribute-rgt-out-- fma-def frac-2neg distribute-lft-in fma-neg div-sub pow-prod-down associate-*l/ clear-num *-commutative flip-- expm1-udef
Counts
4 → 117
Calls
4 calls:
14.0ms
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
90.0ms
(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
17.0ms
(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
5.0ms
(- (* 1 1) (* (exp (* 2 x)) 1))

series267.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1)))
156.0ms
(* (/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1)) (+ (* (exp (* 2 x)) (exp (* 2 x))) (- (* 1 1) (* (exp (* 2 x)) 1))))
62.0ms
(/ (expm1 (+ x x)) (+ (pow (exp (* 2 x)) 3) 1))
16.0ms
(- (* 1 1) (* (exp (* 2 x)) 1))

simplify96.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 2 (79.0ms)

IterNodesCost
06451822
134191592
250011578

prune394.0ms

Filtered
129 candidates to 101 candidates (78.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 1.4b

localize10.0ms

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))

rewrite11.0ms

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:
2.0ms
(- x (* 1/3 (pow x 3)))
0.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
7.0ms
(* 1/3 (pow x 3))

series163.0ms

Counts
3 → 9
Calls
3 calls:
74.0ms
(- x (* 1/3 (pow x 3)))
49.0ms
(fma (pow x 5) 2/15 (- x (* 1/3 (pow x 3))))
39.0ms
(* 1/3 (pow x 3))

simplify35.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0206338
1835292
25001292

prune151.0ms

Filtered
72 candidates to 48 candidates (66.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.4b

regimes21.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02618
13118
23118

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.2s7325×body10240exit
954.0ms3268×body1280valid
445.0ms2486×body640valid
132.0ms1222×body320valid
41.0ms612×body160valid
14.0ms412×body80valid