Details

Time bar (total: 2.0s)

analyze4.0ms (0.2%)

Algorithm
1×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

sample30.0ms (1.5%)

Algorithm
1×intervals
Results
13.0ms67×body1280valid
5.0ms40×body640valid
3.0ms109×body80valid
2.0ms21×body320valid
1.0ms19×body160valid

simplify11.0ms (0.6%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (9.0ms)

IterNodesCost
02286
12286

prune5.0ms (0.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 35.5b

Counts
2 → 1

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b
(/ (- (exp x) 1.0) x)
5.8b
(- (exp x) 1.0)

rewrite12.0ms (0.6%)

Algorithm
1×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 (0.3%)

Counts
2 → 6
Calls

2 calls:

4.0ms
(/ (- (exp x) 1.0) x)
2.0ms
(- (exp x) 1.0)

simplify46.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04909534
14909534

prune99.0ms (5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New52557
Fresh000
Picked101
Done000
Total53558

Merged error: 0.2b

Counts
58 → 5

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (* x (+ 1/2 (* x 1/6))))
0.0b
(* x (+ 1/2 (* x 1/6)))
0.4b
(* x 1/6)

rewrite16.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
11×add-sqr-sqrt
7×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
5×add-log-exp
2×distribute-rgt-in associate-+r+ distribute-lft-in flip3-+ associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
1×+-commutative sum-log
Counts
3 → 53
Calls

3 calls:

7.0ms
(* x (+ 1/2 (* x 1/6)))
4.0ms
(* x 1/6)
3.0ms
(+ 1 (* x (+ 1/2 (* x 1/6))))

series11.0ms (0.5%)

Counts
3 → 9
Calls

3 calls:

6.0ms
(* x (+ 1/2 (* x 1/6)))
3.0ms
(+ 1 (* x (+ 1/2 (* x 1/6))))
2.0ms
(* x 1/6)

simplify52.0ms (2.6%)

Algorithm
1×egg-herbie
Counts
62 → 62
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04963483
14963483

prune93.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New61162
Fresh044
Picked011
Done000
Total61667

Merged error: 0.2b

Counts
67 → 6

localize14.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.4b
(* x 1/6)
14.7b
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
14.7b
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
14.7b
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))

rewrite13.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
11×add-sqr-sqrt
9×cbrt-prod add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log cbrt-div add-cbrt-cube
4×add-log-exp
3×flip3-+ pow1/3 associate-*r* associate-*l* flip-+
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 57
Calls

4 calls:

4.0ms
(* x 1/6)
3.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
3.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
2.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))

series23.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

7.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
7.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
7.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
2.0ms
(* x 1/6)

simplify30.0ms (1.5%)

Algorithm
1×egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
04958928
14958928

prune210.0ms (10.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New68169
Fresh044
Picked101
Done011
Total69675

Merged error: 0.2b

Counts
75 → 6

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.4b
(* x 1/6)
0.4b
(* x 1/36)
14.7b
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
14.7b
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))

rewrite13.0ms (0.7%)

Algorithm
1×rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×cbrt-prod associate-*r* associate-*l*
4×cbrt-div add-log-exp
2×flip3-+ pow1/3 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ unswap-sqr
Counts
4 → 62
Calls

4 calls:

3.0ms
(* x 1/6)
3.0ms
(* x 1/36)
3.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
2.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))

series18.0ms (0.9%)

Counts
4 → 12
Calls

4 calls:

7.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
7.0ms
(cbrt (+ 1 (* x (+ (* x 1/6) 1/2))))
2.0ms
(* x 1/36)
2.0ms
(* x 1/6)

simplify46.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05083721

prune202.0ms (10.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New73174
Fresh044
Picked101
Done011
Total74680

Merged error: 0.1b

Counts
80 → 6

regimes43.0ms (2.2%)

Accuracy

Total 0.2b remaining (75.7%)

Threshold costs 0.2b (75.7%)

bsearch7.0ms (0.3%)

Steps
ItersRangePoint
5
-0.0003268625709671245
-8.946218564378357e-05
-0.00013902426818612792

simplify1.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03121
13121

end0.0ms (0%)

sample933.0ms (47.6%)

Algorithm
1×intervals
Results
440.0ms2247×body1280valid
214.0ms1688×body640valid
70.0ms808×body320valid
67.0ms2815×body80valid
24.0ms442×body160valid

Profiling

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