Details

Time bar (total: 1.8s)

analyze3.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
62.5%25%12.5%4
68.7%12.5%18.8%5
71.8%6.2%21.9%6
73.4%3.1%23.5%7
74.2%1.6%24.3%8
74.6%0.8%24.6%9
75%0.4%24.6%10
75.1%0.2%24.7%11
75.1%0.1%24.8%12
75.1%0%24.8%13
75.2%0%24.8%14

sample33.0ms

Algorithm
intervals
Results
15.0ms79×body1280valid
7.0ms49×body640valid
4.0ms100×body80valid
1.0ms17×body320valid
1.0ms11×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
086
186

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.5b

Counts
2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
2.5b
(- (exp x) 1.0)

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt *-un-lft-identity
15×times-frac
12×add-cube-cbrt
5×associate-/l* distribute-lft-out-- difference-of-squares
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r*
2×pow1 flip3-- flip-- associate-/l/
1×cbrt-undiv sub-neg frac-2neg diff-log div-sub div-exp clear-num div-inv
Counts
2 → 51
Calls
2 calls:
6.0ms
(/ (- (exp x) 1.0) x)
4.0ms
(- (exp x) 1.0)

series6.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(/ (- (exp x) 1.0) x)
2.0ms
(- (exp x) 1.0)

simplify56.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
05003536

prune74.0ms

Filtered
43 candidates to 57 candidates (-32.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New53457
Fresh000
Picked101
Done000
Total54458

Merged error: 0.0b

Counts
58 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (* x (+ 1/2 (* x 1/6))))
0.1b
(* x (+ 1/2 (* x 1/6)))
0.3b
(* x 1/6)
3.1b
(/ (+ x (* x (* x (+ 1/2 (* x 1/6))))) x)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
15×add-exp-log add-cbrt-cube
13×pow1
9×times-frac associate-*l*
7×associate-*r*
6×associate-*r/
5×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×flip3-+ associate-/r* *-commutative flip-+ associate-/l*
2×associate-/l/ unswap-sqr
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 93
Calls
4 calls:
6.0ms
(* x (* x (+ 1/2 (* x 1/6))))
5.0ms
(* x (+ 1/2 (* x 1/6)))
3.0ms
(* x 1/6)
5.0ms
(/ (+ x (* x (* x (+ 1/2 (* x 1/6))))) x)

series18.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* x (* x (+ 1/2 (* x 1/6))))
5.0ms
(* x (+ 1/2 (* x 1/6)))
2.0ms
(* x 1/6)
5.0ms
(/ (+ x (* x (* x (+ 1/2 (* x 1/6))))) x)

simplify64.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049401102
149401102

prune104.0ms

Filtered
69 candidates to 105 candidates (-52.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1050105
Fresh033
Picked011
Done000
Total1054109

Merged error: 0.0b

Counts
109 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (+ (exp x) 1.0))
0.0b
(* (exp x) (exp x))
0.0b
(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
2.5b
(- (* (exp x) (exp x)) (* 1.0 1.0))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×add-cube-cbrt exp-prod
13×pow1 add-cbrt-cube
11×add-exp-log
7×associate-*r*
6×associate-*l* add-log-exp
5×pow-prod-down
4×times-frac associate-*r/ pow-sqr pow-prod-up associate-/l*
3×swap-sqr prod-exp cbrt-unprod difference-of-squares
2×cbrt-undiv flip3-- flip3-+ div-exp associate-/r/ *-commutative flip-- flip-+ associate-/l/ unswap-sqr
1×pow2 distribute-rgt-in sub-neg frac-2neg distribute-lft-in pow-plus diff-log div-sub clear-num associate-/r* div-inv distribute-lft-out
Counts
4 → 97
Calls
4 calls:
7.0ms
(* x (+ (exp x) 1.0))
8.0ms
(* (exp x) (exp x))
12.0ms
(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
6.0ms
(- (* (exp x) (exp x)) (* 1.0 1.0))

series25.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* x (+ (exp x) 1.0))
3.0ms
(* (exp x) (exp x))
14.0ms
(/ (- (* (exp x) (exp x)) (* 1.0 1.0)) (* x (+ (exp x) 1.0)))
4.0ms
(- (* (exp x) (exp x)) (* 1.0 1.0))

simplify82.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 0 (73.0ms)

IterNodesCost
04950914
14950914

prune115.0ms

Filtered
76 candidates to 109 candidates (-43.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1081109
Fresh022
Picked101
Done011
Total1094113

Merged error: 0.0b

Counts
113 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp x) 1.0)
0.0b
(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
0.0b
(pow (exp x) 2)
2.5b
(- (pow (exp x) 2) (* 1.0 1.0))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
32×add-sqr-sqrt
28×times-frac
24×difference-of-squares
20×add-cube-cbrt
9×unpow-prod-down distribute-lft-out
8×add-log-exp
7×associate-/l* unpow2 sqr-pow
6×add-exp-log add-cbrt-cube
5×pow1
4×pow-pow associate-/r*
3×pow-unpow exp-prod
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative pow-to-exp sub-neg frac-2neg diff-log div-sub div-exp pow-exp clear-num sum-log div-inv
Counts
4 → 104
Calls
4 calls:
4.0ms
(+ (exp x) 1.0)
10.0ms
(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0ms
(pow (exp x) 2)
5.0ms
(- (pow (exp x) 2) (* 1.0 1.0))

series18.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(+ (exp x) 1.0)
9.0ms
(/ (- (pow (exp x) 2) (* 1.0 1.0)) (+ (exp x) 1.0))
3.0ms
(pow (exp x) 2)
4.0ms
(- (pow (exp x) 2) (* 1.0 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
050181316

prune126.0ms

Filtered
78 candidates to 116 candidates (-48.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1151116
Fresh112
Picked101
Done011
Total1173120

Merged error: 0.0b

Counts
120 → 3

regimes33.0ms

Accuracy

98.8% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.7b

bsearch21.0ms

Steps
ItersRangePoint
10
-0.000787588323402845
-4.795285847932189e-14
-0.00011068363192155683

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02732
12732

end0.0ms

analyze3.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
0%100%0%2
25%75%0%3
62.5%25%12.5%4
68.7%12.5%18.8%5
71.8%6.2%21.9%6
73.4%3.1%23.5%7
74.2%1.6%24.3%8
74.6%0.8%24.6%9
75%0.4%24.6%10
75.1%0.2%24.7%11
75.1%0.1%24.8%12
75.1%0%24.8%13
75.2%0%24.8%14

sample880.0ms

Algorithm
intervals
Results
422.0ms2271×body1280valid
194.0ms1617×body640valid
75.0ms2868×body80valid
65.0ms824×body320valid
22.0ms420×body160valid

Profiling

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