Details

Time bar (total: 22.0s)

sample198.0ms

Algorithm
intervals
Results
63.0ms51×body1280valid
44.0ms63×body10240exit
34.0ms313×body80valid
19.0ms44×body640valid
8.0ms25×body320valid
1.0ms8×body160valid

simplify1.3s

Counts
1 → 1
Iterations
IterNodes
done5001
42356
3395
2124
147
019

prune29.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite181.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
77×exp-neg
76×frac-times
58×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
28×flip3-+ flip-+
19×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×exp-prod associate-*r*
4×expm1-log1p-u log1p-expm1-u
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
29.0ms
(* (+ 1.0 eps) x)
14.0ms
(exp (- (* (- 1.0 eps) x)))
82.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
47.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series457.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(* (+ 1.0 eps) x)
55.0ms
(exp (- (* (- 1.0 eps) x)))
75.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
286.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify686.0ms

Counts
183 → 183
Iterations
IterNodes
done5001
11386
0405

prune893.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(fma 0.6666666666666667 (pow x 3) 2.0)
5.4b
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-cube-cbrt add-log-exp
3×fma-neg prod-diff
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log fma-udef log1p-expm1-u
1×sub-neg flip3-- diff-log associate--l+ flip--
Counts
2 → 31
Calls
2 calls:
0.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
9.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

series180.0ms

Counts
2 → 6
Calls
2 calls:
116.0ms
(fma 0.6666666666666667 (pow x 3) 2.0)
64.0ms
(- (fma 0.6666666666666667 (pow x 3) 2.0) (* 1.0 (* x x)))

simplify590.0ms

Counts
37 → 37
Iterations
IterNodes
done5001
2774
1157
055

prune211.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))))
0.0b
(expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0)))
5.4b
(fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×log1p-expm1-u
3×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 fma-udef expm1-udef
Counts
3 → 32
Calls
3 calls:
0.0ms
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))))
1.0ms
(expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0)))
1.0ms
(fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))

series304.0ms

Counts
3 → 9
Calls
3 calls:
178.0ms
(log1p (expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))))
58.0ms
(expm1 (fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0)))
69.0ms
(fma 0.6666666666666667 (pow x 3) (fma (- x) (* x 1.0) 2.0))

simplify1.4s

Counts
41 → 41
Iterations
IterNodes
done5001
32274
2447
1135
068

prune207.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize65.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- eps 1.0))
0.0b
(* x (- eps 1.0))
0.0b
(/ (exp (* x (- eps 1.0))) eps)
2.0b
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

rewrite1.7s

Algorithm
rewrite-expression-head
Rules
215×*-un-lft-identity
184×prod-diff
179×add-sqr-sqrt
166×add-cube-cbrt
136×times-frac
112×exp-sum
78×distribute-rgt-in distribute-lft-in
25×associate-/l*
24×distribute-neg-in
21×distribute-lft-out
13×sub-neg
10×add-cbrt-cube associate-*r*
9×add-exp-log add-log-exp
8×pow1
6×associate-*l*
5×div-inv
4×expm1-log1p-u fma-neg associate-*r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×associate-/r* flip3-- flip--
2×diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod unswap-sqr
1×cbrt-undiv clear-num sum-log frac-2neg flip3-+ div-exp associate--l+ flip-+
Counts
4 → 311
Calls
4 calls:
18.0ms
(* x (- eps 1.0))
18.0ms
(* x (- eps 1.0))
43.0ms
(/ (exp (* x (- eps 1.0))) eps)
1.6s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

series268.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(* x (- eps 1.0))
36.0ms
(* x (- eps 1.0))
41.0ms
(/ (exp (* x (- eps 1.0))) eps)
132.0ms
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

simplify1.9s

Counts
323 → 323
Iterations
IterNodes
done5000
24467
11186
0523

prune1.7s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes114.0ms

Accuracy

59.8% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 1.9b

bsearch263.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
7.830610238325062
1.1764495451543813

simplify12.0ms

Iterations
IterNodes
done47
247
141
033

end0.0ms

sample9.2s

Algorithm
intervals
Results
3.6s1964×body10240exit
2.2s1723×body1280valid
1.6s10200×body80valid
800.0ms1223×body640valid
359.0ms607×body320valid
138.0ms333×body160valid