Details

Time bar (total: 4.5s)

sample85.0ms

Algorithm
intervals
Results
36.0ms79×body1280valid
16.0ms33×body2560valid
15.0ms53×body640valid
5.0ms31×body320valid
2.0ms52×body80valid
1.0ms8×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 55.1b

Counts
2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* x x) 1.0)
0.5b
(+ x (sqrt (+ (* x x) 1.0)))
1.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
15.7b
(sqrt (+ (* x x) 1.0))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-log-exp
7×add-sqr-sqrt
6×pow1 add-cube-cbrt
5×add-exp-log
4×log-prod flip3-+ add-cbrt-cube flip-+
3×sqrt-prod
2×+-commutative log-div sqrt-div sum-log distribute-lft-out
1×rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp log-pow
Counts
4 → 53
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
5.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series21.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(+ x (sqrt (+ (* x x) 1.0)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0333450
11163414
25001398

prune135.0ms

Filtered
65 candidates to 53 candidates (18.5%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New59665
Fresh000
Picked101
Done000
Total60666

Merged error: 0.0b

Counts
66 → 6

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
0.1b
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
182×add-sqr-sqrt
140×unpow-prod-down cube-prod
118×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×add-exp-log unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 286
Calls
2 calls:
12.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
52.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series32.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
20.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify113.0ms

Algorithm
egg-herbie
Counts
292 → 292
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
08542083
146421650
250021650

prune393.0ms

Filtered
292 candidates to 111 candidates (62.0%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New2911292
Fresh055
Picked011
Done000
Total2917298

Merged error: 0.0b

Counts
298 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (neg 0.0625) (pow x 5))
0.4b
(/ 0.125 (pow x 3))
14.8b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
17.7b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
126×times-frac
110×*-un-lft-identity
102×add-sqr-sqrt
76×add-cube-cbrt
47×unpow-prod-down
26×distribute-rgt-neg-in
24×distribute-lft-neg-in
19×associate-/r*
17×sqr-pow
15×add-exp-log
14×cube-prod distribute-lft-out--
13×associate-/l*
12×log-prod
10×difference-of-squares
9×add-log-exp
8×neg-mul-1 frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×cube-mult flip3-- unpow3 flip--
3×diff-log associate--r+
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num div-inv associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 223
Calls
4 calls:
6.0ms
(/ (neg 0.0625) (pow x 5))
5.0ms
(/ 0.125 (pow x 3))
70.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
72.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

series28.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ (neg 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
10.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5)))))
10.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (neg 0.0625) (pow x 5))))

simplify104.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08371963
137941884
250021876

prune437.0ms

Filtered
235 candidates to 152 candidates (35.3%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New2350235
Fresh055
Picked011
Done011
Total2357242

Merged error: 0.0b

Counts
242 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
0.8b
(- x (sqrt (+ (* x x) 1.0)))
1.9b
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
15.7b
(sqrt (+ (* x x) 1.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
105×add-sqr-sqrt
80×*-un-lft-identity
60×times-frac
37×difference-of-squares
36×log-prod
30×add-cube-cbrt
25×distribute-lft-out--
15×sqrt-prod
9×add-exp-log
6×pow1 associate-/r* add-cbrt-cube add-log-exp
5×associate-/l*
4×flip3-- associate-/r/ flip--
2×sqrt-div div-exp rem-log-exp div-inv associate-/l/
1×cbrt-undiv sub-neg rem-sqrt-square log-div frac-2neg sqrt-pow1 flip3-+ sub0-neg pow1/2 diff-log div-sub distribute-frac-neg clear-num log-pow flip-+
Counts
4 → 136
Calls
4 calls:
10.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
6.0ms
(- x (sqrt (+ (* x x) 1.0)))
11.0ms
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
4.0ms
(sqrt (+ (* x x) 1.0))

series26.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
5.0ms
(- x (sqrt (+ (* x x) 1.0)))
11.0ms
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify86.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06271716
123681646
250011641

prune226.0ms

Filtered
148 candidates to 100 candidates (32.4%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1471148
Fresh134
Picked101
Done022
Total1496155

Merged error: 0.0b

Counts
155 → 6

regimes54.0ms

Accuracy

99.4% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 32.2b

bsearch18.0ms

Steps
ItersRangePoint
3
0.8654901203590915
1.132733130973407
0.9031544538205186
7
-1.3201891031641613
-0.005305593335282472
-1.0402765450235887

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04127
14127

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s2491×body1280valid
463.0ms1699×body640valid
352.0ms1077×body2560valid
138.0ms848×body320valid
61.0ms1472×body80valid
40.0ms413×body160valid

Profiling

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