Details

Time bar (total: 8.2s)

sample95.0ms

Algorithm
intervals
Results
54.0ms152×body10240exit
11.0ms198×body80valid
6.0ms132×body80overflowed
5.0ms29×body320valid
4.0ms16×body640valid
2.0ms17×body160valid

simplify49.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 3 (7.0ms)

IterNodesCost
0219
1529
21139
32408
416258
550018

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ wj (+ wj 1))
0.0b
(/ x (+ wj 1))
0.0b
(/ (/ x (+ wj 1)) (exp wj))
5.4b
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite427.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
175×times-frac
129×add-sqr-sqrt
124×add-cube-cbrt
72×prod-diff
52×distribute-lft-out
24×associate-/l*
20×associate-/r/
13×add-cbrt-cube
11×add-exp-log flip3-+ associate-/r* flip-+ div-inv
9×add-log-exp
5×cbrt-undiv div-exp
4×pow1 expm1-log1p-u fma-neg log1p-expm1-u
3×frac-2neg clear-num
2×diff-log frac-sub distribute-lft-out-- difference-of-squares
1×sub-neg flip3-- associate--l+ sum-log flip-- associate-/l/
Counts
4 → 260
Calls
4 calls:
5.0ms
(/ wj (+ wj 1))
5.0ms
(/ x (+ wj 1))
12.0ms
(/ (/ x (+ wj 1)) (exp wj))
392.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series148.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ wj (+ wj 1))
26.0ms
(/ x (+ wj 1))
41.0ms
(/ (/ x (+ wj 1)) (exp wj))
60.0ms
(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify120.0ms

Algorithm
egg-herbie
Counts
272 → 272
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
010154090
145553249
250013243

prune518.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* 2 (* wj x))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-exp-log add-cbrt-cube
3×associate-*l* pow-prod-down prod-exp cbrt-unprod
2×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
1×expm1-log1p-u associate-*r* *-commutative log1p-expm1-u add-log-exp
Counts
1 → 20
Calls
1 calls:
6.0ms
(* 2 (* wj x))

series20.0ms

Counts
1 → 3
Calls
1 calls:
20.0ms
(* 2 (* wj x))

simplify79.0ms

Algorithm
egg-herbie
Counts
23 → 23
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
08872
132062
2123762
3344862
4500162

prune48.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ wj (+ wj 1))
0.0b
(/ 1 (exp wj))
0.0b
(* (/ x (+ wj 1)) (/ 1 (exp wj)))
5.4b
(- (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj) (/ wj (+ wj 1)))

rewrite174.0ms

Algorithm
rewrite-expression-head
Rules
116×*-un-lft-identity
102×add-sqr-sqrt
86×times-frac
80×add-cube-cbrt
54×prod-diff
23×add-exp-log
20×add-cbrt-cube
18×associate-*l*
16×distribute-lft-out
13×associate-*r*
11×div-exp
10×associate-/r/
9×add-log-exp
8×prod-exp
7×pow1 associate-/r* div-inv
6×cbrt-undiv flip3-+ flip-+ associate-/l* unswap-sqr
4×expm1-log1p-u pow-flip cbrt-unprod log1p-expm1-u
3×rec-exp exp-prod fma-neg 1-exp
2×frac-2neg diff-log clear-num frac-sub difference-of-squares
1×frac-times sub-neg flip3-- associate-*r/ pow-prod-down associate-*l/ associate--l+ sum-log un-div-inv *-commutative flip-- distribute-lft-out-- inv-pow
Counts
4 → 213
Calls
4 calls:
5.0ms
(/ wj (+ wj 1))
3.0ms
(/ 1 (exp wj))
26.0ms
(* (/ x (+ wj 1)) (/ 1 (exp wj)))
131.0ms
(- (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj) (/ wj (+ wj 1)))

series131.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(/ wj (+ wj 1))
8.0ms
(/ 1 (exp wj))
45.0ms
(* (/ x (+ wj 1)) (/ 1 (exp wj)))
56.0ms
(- (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj) (/ wj (+ wj 1)))

simplify121.0ms

Algorithm
egg-herbie
Counts
225 → 225
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
09943262
147632437
250012433

prune412.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(pow (cbrt wj) 3)
0.7b
(pow (cbrt wj) 3)
0.7b
(pow (cbrt wj) 3)
14.9b
(fma (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (* (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj))) (/ (- (pow (cbrt wj) 3)) (+ wj 1)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×cbrt-prod unpow-prod-down cube-prod
9×pow-unpow
7×pow1 add-exp-log
6×pow-pow
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×cube-mult pow-to-exp pow1/3 unpow3 pow-exp rem-cube-cbrt sqr-pow
1×fma-udef
Counts
4 → 106
Calls
4 calls:
2.0ms
(pow (cbrt wj) 3)
2.0ms
(pow (cbrt wj) 3)
2.0ms
(pow (cbrt wj) 3)
0.0ms
(fma (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (* (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj))) (/ (- (pow (cbrt wj) 3)) (+ wj 1)))

series2.8s

Counts
4 → 12
Calls
4 calls:
229.0ms
(pow (cbrt wj) 3)
237.0ms
(pow (cbrt wj) 3)
236.0ms
(pow (cbrt wj) 3)
2.1s
(fma (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (* (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj)) (cbrt (+ (* (/ x (+ wj 1)) (/ 1 (exp wj))) wj))) (/ (- (pow (cbrt wj) 3)) (+ wj 1)))

simplify53.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0308747
11502640
25001622

prune319.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes70.0ms

Accuracy

32.5% (1.2b remaining)

Error of 1.5b against oracle of 0.3b and baseline of 2.1b

bsearch54.0ms

Steps
ItersRangePoint
8
-1.1902930357079885e-07
-1.3081950593114417e-10
-6.177090336660287e-09

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04345
14845
24845

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.3s3891×body10240exit
343.0ms6266×body80valid
184.0ms3849×body80overflowed
133.0ms794×body320valid
126.0ms518×body640valid
57.0ms512×body160valid