Details

Time bar (total: 3.7s)

sample93.0ms

Algorithm
intervals
Results
46.0ms80×body1280valid
16.0ms44×body640valid
12.0ms32×body2560valid
5.0ms23×body320valid
3.0ms66×body80valid
1.0ms11×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
099
199

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 54.4b

Counts
2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b
(+ x (sqrt (+ (* x x) 1.0)))
2.6b
(log (+ x (sqrt (+ (* x x) 1.0))))
18.0b
(sqrt (+ (* x x) 1.0))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
6×add-sqr-sqrt
5×pow1 add-cube-cbrt add-log-exp
4×add-exp-log log-prod
3×flip3-+ sqrt-prod add-cbrt-cube flip-+
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow
Counts
3 → 42
Calls
3 calls:
6.0ms
(+ x (sqrt (+ (* x x) 1.0)))
6.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series17.0ms

Counts
3 → 9
Calls
3 calls:
4.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
05075600

prune113.0ms

Filtered
42 candidates to 51 candidates (-21.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New46551
Fresh000
Picked101
Done000
Total47552

Merged error: 0.0b

Counts
52 → 5

localize9.0ms

Local error

Found 1 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
50×associate-*l*
48×add-sqr-sqrt
40×times-frac
29×add-cube-cbrt *-un-lft-identity
25×unpow-prod-down cube-prod
20×sqrt-prod
9×add-exp-log
8×unswap-sqr
4×prod-exp
3×associate-*r* add-cbrt-cube
2×pow-exp div-inv sqr-pow
1×pow1 cube-div cube-mult pow-to-exp unpow3 div-exp associate-*l/ *-commutative cbrt-unprod add-log-exp
Counts
1 → 75
Calls
1 calls:
13.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

series15.0ms

Counts
1 → 3
Calls
1 calls:
15.0ms
(* (pow (/ x (sqrt 1.0)) 3) -1/6)

simplify39.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
04973758
14973758

prune126.0ms

Filtered
40 candidates to 78 candidates (-95.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh044
Picked011
Done000
Total78583

Merged error: 0.0b

Counts
83 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 0.0625 (pow x 5))
0.3b
(/ 0.125 (pow x 3))
11.4b
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
19.6b
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
71×times-frac
68×*-un-lft-identity
46×add-cube-cbrt
26×unpow-prod-down
19×associate-/r*
15×add-exp-log
14×cube-prod
11×log-prod
10×difference-of-squares sqr-pow
9×add-log-exp
8×add-cbrt-cube
6×div-exp frac-sub associate-/l* distribute-lft-out--
5×pow1 log-div
4×cube-mult unpow3 distribute-lft-out
2×cbrt-undiv pow-to-exp flip3-- frac-2neg flip3-+ diff-log frac-add pow-exp clear-num flip-- flip-+ div-inv
1×sub-neg rem-log-exp sum-log log-pow associate--r+
Counts
4 → 160
Calls
4 calls:
8.0ms
(/ 0.0625 (pow x 5))
9.0ms
(/ 0.125 (pow x 3))
44.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
35.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(/ 0.0625 (pow x 5))
3.0ms
(/ 0.125 (pow x 3))
10.0ms
(log (- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5)))))
5.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.5 x) (/ 0.0625 (pow x 5))))

simplify55.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
053612503

prune292.0ms

Filtered
110 candidates to 172 candidates (-56.4%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1720172
Fresh033
Picked011
Done011
Total1725177

Merged error: 0.0b

Counts
177 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
0.3b
(/ 0.125 (pow x 3))
10.5b
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
51×times-frac
44×*-un-lft-identity
29×add-cube-cbrt
14×unpow-prod-down cube-prod
12×associate-/r*
10×difference-of-squares
9×add-exp-log
6×log-prod sqr-pow
5×add-cbrt-cube distribute-lft-out add-log-exp
4×pow1 cube-mult unpow3
3×div-exp associate-/l* distribute-lft-out--
2×log-div
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg flip3-+ diff-log rem-log-exp pow-exp clear-num log-pow frac-sub flip-- flip-+ div-inv
Counts
3 → 107
Calls
3 calls:
29.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
5.0ms
(/ 0.125 (pow x 3))
32.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

series19.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(- (/ 0.5 x) (/ 0.125 (pow x 3)))
3.0ms
(/ 0.125 (pow x 3))
9.0ms
(log (+ x (+ x (- (/ 0.5 x) (/ 0.125 (pow x 3))))))

simplify30.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
057231435

prune142.0ms

Filtered
70 candidates to 116 candidates (-65.7%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New1160116
Fresh022
Picked011
Done022
Total1165121

Merged error: 0.0b

Counts
121 → 5

regimes165.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 31.4b

bsearch30.0ms

Steps
ItersRangePoint
10
0.01683730658649282
12785707414306.22
0.8957535344777527
8
-12322.514085840688
-0.2101619750885166
-0.9995529792995811

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
09455
19455

end0.0ms

sample2.2s

Algorithm
intervals
Results
1.1s2353×body1280valid
450.0ms1588×body640valid
265.0ms780×body2560valid
128.0ms766×body320valid
87.0ms2102×body80valid
40.0ms411×body160valid

Profiling

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