Details

Time bar (total: 1.6s)

sample15.0ms

Algorithm
intervals
Results
8.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
063
163

prune2.0ms

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: 16.4b

Counts
2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (* x x) 1.0)
16.4b
(/ x (+ (* x x) 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 40
Calls
2 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(/ x (+ (* x x) 1.0))

series9.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(+ (* x x) 1.0)
5.0ms
(/ x (+ (* x x) 1.0))

simplify110.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0194267
1717245
23039242
35002242

prune71.0ms

Filtered
46 candidates to 37 candidates (19.6%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New42446
Fresh000
Picked011
Done000
Total42547

Merged error: 0b

Counts
47 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (sqrt (+ (* x x) 1.0)))
0.0b
(/ x (sqrt (+ (* x x) 1.0)))
16.4b
(sqrt (+ (* x x) 1.0))
16.4b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
36×add-cube-cbrt *-un-lft-identity times-frac
30×sqrt-prod
12×associate-/r*
10×add-exp-log
8×pow1 sqrt-div add-cbrt-cube
6×associate-/l*
4×flip3-+ associate-/r/ flip-+ add-log-exp
3×pow-flip sqrt-pow1 pow1/2 div-exp
2×cbrt-undiv rem-sqrt-square frac-2neg clear-num div-inv
1×rec-exp 1-exp inv-pow
Counts
4 → 118
Calls
4 calls:
6.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
6.0ms
(/ x (sqrt (+ (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
5.0ms
(sqrt (+ (* x x) 1.0))

series19.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1 (sqrt (+ (* x x) 1.0)))
7.0ms
(/ x (sqrt (+ (* x x) 1.0)))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

simplify46.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0388966
11519889
25001850

prune176.0ms

Filtered
130 candidates to 84 candidates (35.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1291130
Fresh213
Picked101
Done011
Total1323135

Merged error: 0b

Counts
135 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (sqrt (+ (* x x) 1.0))) (sqrt (sqrt (+ (* x x) 1.0))))
16.4b
(sqrt (+ (* x x) 1.0))
16.4b
(sqrt (+ (* x x) 1.0))
16.4b
(sqrt (+ (* x x) 1.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
75×sqrt-prod
52×add-sqr-sqrt
35×sqrt-pow1
30×pow1 sqrt-div
19×add-cube-cbrt *-un-lft-identity pow1/2
15×swap-sqr
9×flip3-+ associate-*r* associate-*l* pow-prod-up flip-+ unswap-sqr
6×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times add-log-exp
3×rem-sqrt-square
2×associate-*r/ associate-*l/
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 128
Calls
4 calls:
16.0ms
(* (sqrt (sqrt (+ (* x x) 1.0))) (sqrt (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))
4.0ms
(sqrt (+ (* x x) 1.0))

series15.0ms

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

simplify47.0ms

Algorithm
egg-herbie
Counts
140 → 140
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0255894
11060840
25002816

prune211.0ms

Filtered
140 candidates to 79 candidates (43.6%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1400140
Fresh011
Picked011
Done011
Total1403143

Merged error: 0b

Counts
143 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
0.1b
(/ 1 (pow x 5))
0.4b
(/ 1.0 (pow x 3))
20.0b
(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
59×times-frac
52×add-sqr-sqrt
49×*-un-lft-identity
45×add-cube-cbrt
24×unpow-prod-down
19×associate-/r*
18×add-exp-log
12×cube-prod
11×add-log-exp
9×div-exp
8×frac-sub add-cbrt-cube sqr-pow
6×associate-/l*
4×pow1 cube-mult pow-to-exp diff-log unpow3 pow-exp div-inv
3×sub-neg rec-exp flip3-- 1-exp flip-- distribute-lft-out-- difference-of-squares
2×cbrt-undiv frac-2neg associate-*r/ clear-num un-div-inv associate--r+
1×pow-flip inv-pow associate--r-
Counts
4 → 158
Calls
4 calls:
16.0ms
(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
4.0ms
(/ 1 (pow x 5))
5.0ms
(/ 1.0 (pow x 3))
12.0ms
(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(- (/ 1 x) (- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5)))))
4.0ms
(/ 1 (pow x 5))
4.0ms
(/ 1.0 (pow x 3))
11.0ms
(- (/ 1.0 (pow x 3)) (* 1.0 (/ 1 (pow x 5))))

simplify83.0ms

Algorithm
egg-herbie
Counts
170 → 170
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
05291077
12934970
25001965

prune205.0ms

Filtered
170 candidates to 89 candidates (47.6%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1700170
Fresh000
Picked011
Done022
Total1703173

Merged error: 0b

Counts
173 → 3

regimes72.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 15.2b

bsearch25.0ms

Steps
ItersRangePoint
9
1.132733130973407
94732.78899832016
415.65688547362504
7
-973.9244444074952
-49.08804872927817
-406.6112335613523

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03523
13523

end0.0ms

sample308.0ms

Algorithm
intervals
Results
174.0ms8000×body80valid

Profiling

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