Details

Time bar (total: 5.3s)

sample110.0ms

Algorithm
intervals
Results
28.0ms66×body10240exit
27.0ms59×body1280valid
19.0ms327×body80valid
9.0ms35×body640valid
7.0ms22×body320valid
1.0ms8×body160valid

simplify58.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (55.0ms)

IterNodesCost
04716
112416
236516
3137616
4500115

prune16.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.6b

Counts
2 → 2

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- 1.0 eps) x)
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
2.6b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
32×flip3-- flip--
30×flip3-+ flip-+
23×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac fma-neg diff-log prod-diff distribute-lft-out
Counts
4 → 183
Calls
4 calls:
7.0ms
(* (- 1.0 eps) x)
13.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
20.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* (- 1.0 eps) x)
50.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
51.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
339.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
195 → 195
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013724120
150013814

prune467.0ms

Filtered
195 candidates to 107 candidates (54.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1932195
Fresh011
Picked101
Done000
Total1943197

Merged error: 0.7b

Counts
197 → 3

localize9.0ms

Local error

Found 1 expressions with local error:

6.6b
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
1×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube fma-udef log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
1.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

series39.0ms

Counts
1 → 3
Calls
1 calls:
39.0ms
(fma (pow x 3) 0.6666666666666667 (- 2.0 (* 1.0 (pow x 2))))

simplify30.0ms

Algorithm
egg-herbie
Counts
13 → 13
Iterations

Useful iterations: 3 (27.0ms)

IterNodesCost
04289
113678
272278
3500275

prune48.0ms

Filtered
13 candidates to 11 candidates (84.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New10313
Fresh022
Picked101
Done000
Total11516

Merged error: 0.7b

Counts
16 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (* 0.6666666666666667 x) 1.0)
0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt *-un-lft-identity prod-diff
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg flip3-- fma-neg diff-log flip-- fma-udef
Counts
2 → 28
Calls
2 calls:
4.0ms
(- (* 0.6666666666666667 x) 1.0)
1.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

series82.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(- (* 0.6666666666666667 x) 1.0)
44.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)

simplify82.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0145173
1510136
22788133
35002129

prune74.0ms

Filtered
34 candidates to 24 candidates (70.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New32234
Fresh224
Picked101
Done000
Total35439

Merged error: 0.7b

Counts
39 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 0.6666666666666667 x) 1.0)
0.0b
(expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
0.0b
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
0.3b
(log1p (expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity log1p-expm1-u
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube
3×prod-diff
1×sub-neg log1p-udef expm1-log1p flip3-- fma-neg diff-log log1p-expm1 flip-- fma-udef expm1-udef
Counts
4 → 50
Calls
4 calls:
4.0ms
(- (* 0.6666666666666667 x) 1.0)
1.0ms
(expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
1.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
1.0ms
(log1p (expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))

series269.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (* 0.6666666666666667 x) 1.0)
50.0ms
(expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0))
41.0ms
(fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)
138.0ms
(log1p (expm1 (fma (pow x 2) (- (* 0.6666666666666667 x) 1.0) 2.0)))

simplify107.0ms

Algorithm
egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 3 (100.0ms)

IterNodesCost
0202349
1696290
23560285
35002282

prune132.0ms

Filtered
62 candidates to 43 candidates (69.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New60262
Fresh033
Picked101
Done000
Total61566

Merged error: 0.7b

Counts
66 → 5

regimes83.0ms

Accuracy

96% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.5b

bsearch122.0ms

Steps
ItersRangePoint
8
0.011261476250181132
4.265898263168925
2.5494520086503014

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04224
14824
24824

end0.0ms

sample2.9s

Algorithm
intervals
Results
784.0ms1905×body10240exit
731.0ms1672×body1280valid
566.0ms10060×body80valid
334.0ms1288×body640valid
112.0ms648×body320valid
38.0ms338×body160valid