Details

Time bar (total: 3.5s)

sample45.0ms

Algorithm
intervals
Results
17.0ms69×body1280valid
9.0ms54×body640valid
4.0ms87×body80valid
3.0ms76×body80overflowed
3.0ms23×body320valid
2.0ms23×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
074
184
284

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize7.0ms

Local error

Found 2 expressions with local error:

0.5b
(/ (exp x) (- (exp x) 1.0))
5.6b
(- (exp x) 1.0)

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
29×add-sqr-sqrt *-un-lft-identity
19×add-cube-cbrt
15×times-frac
9×prod-diff
5×associate-/r* distribute-lft-out-- difference-of-squares
4×add-cbrt-cube add-log-exp
3×add-exp-log fma-neg associate-/l*
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u
1×cbrt-undiv sub-neg frac-2neg diff-log div-exp clear-num div-inv
Counts
2 → 67
Calls
2 calls:
8.0ms
(/ (exp x) (- (exp x) 1.0))
5.0ms
(- (exp x) 1.0)

series43.0ms

Counts
2 → 6
Calls
2 calls:
27.0ms
(/ (exp x) (- (exp x) 1.0))
15.0ms
(- (exp x) 1.0)

simplify190.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (183.0ms)

IterNodesCost
0237520
1786429
24651416
35001404

prune154.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (fma 1/12 x (/ 1 x)) 1/2)
0.1b
(fma 1/12 x (/ 1 x))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt add-cube-cbrt fma-def
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube fma-udef log1p-expm1-u
1×+-commutative associate-+l+ flip3-+ sum-log flip-+ distribute-lft-out
Counts
2 → 28
Calls
2 calls:
3.0ms
(+ (fma 1/12 x (/ 1 x)) 1/2)
0.0ms
(fma 1/12 x (/ 1 x))

series65.0ms

Counts
2 → 6
Calls
2 calls:
16.0ms
(+ (fma 1/12 x (/ 1 x)) 1/2)
50.0ms
(fma 1/12 x (/ 1 x))

simplify38.0ms

Algorithm
egg-herbie
Counts
34 → 34
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
090126
1306119
21283117
35001116

prune67.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b
(/ 1.0 (exp x))
5.6b
(- 1 (/ 1.0 (exp x)))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
99×add-sqr-sqrt
79×*-un-lft-identity
70×times-frac
59×add-cube-cbrt
39×prod-diff
20×difference-of-squares
11×associate-/r*
8×add-exp-log
7×add-cbrt-cube
6×associate-/l*
5×div-inv distribute-lft-out-- add-log-exp
4×pow1
3×expm1-log1p-u fma-neg div-exp log1p-expm1-u
2×cbrt-undiv flip3-- frac-2neg clear-num associate-/r/ flip--
1×sub-neg rec-exp pow-flip diff-log 1-exp inv-pow
Counts
3 → 145
Calls
3 calls:
17.0ms
(/ 1 (- 1 (/ 1.0 (exp x))))
3.0ms
(/ 1.0 (exp x))
13.0ms
(- 1 (/ 1.0 (exp x)))

series106.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(/ 1 (- 1 (/ 1.0 (exp x))))
18.0ms
(/ 1.0 (exp x))
37.0ms
(- 1 (/ 1.0 (exp x)))

simplify62.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05521839
122981281
250011188

prune186.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 1 (+ 1 (sqrt (/ 1.0 (exp x))))) (- 1 (sqrt (/ 1.0 (exp x)))))
0.0b
(/ 1.0 (exp x))
0.0b
(/ 1.0 (exp x))
5.6b
(- 1 (sqrt (/ 1.0 (exp x))))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
503×add-sqr-sqrt
502×times-frac
437×*-un-lft-identity
191×add-cube-cbrt
190×sqrt-prod
138×difference-of-squares
72×distribute-lft-out
48×prod-diff
46×distribute-lft-out--
27×associate-/l*
26×associate-/r/
18×div-inv
17×associate-/r*
15×add-exp-log
13×add-cbrt-cube
12×flip3-+ flip-+
8×div-exp
6×add-log-exp
5×cbrt-undiv
4×pow1 expm1-log1p-u log1p-expm1-u
3×frac-2neg fma-neg clear-num
2×flip3-- flip--
1×sub-neg rec-exp diff-log 1-exp associate-/l/
Counts
4 → 415
Calls
4 calls:
54.0ms
(/ (/ 1 (+ 1 (sqrt (/ 1.0 (exp x))))) (- 1 (sqrt (/ 1.0 (exp x)))))
3.0ms
(/ 1.0 (exp x))
3.0ms
(/ 1.0 (exp x))
14.0ms
(- 1 (sqrt (/ 1.0 (exp x))))

series395.0ms

Counts
4 → 12
Calls
4 calls:
294.0ms
(/ (/ 1 (+ 1 (sqrt (/ 1.0 (exp x))))) (- 1 (sqrt (/ 1.0 (exp x)))))
13.0ms
(/ 1.0 (exp x))
13.0ms
(/ 1.0 (exp x))
74.0ms
(- 1 (sqrt (/ 1.0 (exp x))))

simplify89.0ms

Algorithm
egg-herbie
Counts
427 → 427
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
014028183
150016677

prune518.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes44.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 21.2b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02815
12815

end0.0ms

sample1.3s

Algorithm
intervals
Results
546.0ms2248×body1280valid
284.0ms1642×body640valid
120.0ms2830×body80valid
102.0ms854×body320valid
99.0ms2456×body80overflowed
35.0ms427×body160valid