Details

Time bar (total: 5.6s)

sample62.0ms

Algorithm
intervals
Results
30.0ms77×body1280valid
12.0ms55×body640valid
6.0ms24×body2560valid
3.0ms25×body320valid
2.0ms61×body80valid
1.0ms14×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
095
195

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 54.3b

localize6.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
3.4b
(log (+ x (sqrt (+ (* x x) 1.0))))
14.3b
(sqrt (+ (* x x) 1.0))

rewrite24.0ms

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:
11.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series265.0ms

Counts
3 → 9
Calls
3 calls:
58.0ms
(+ x (sqrt (+ (* x x) 1.0)))
165.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
42.0ms
(sqrt (+ (* x x) 1.0))

simplify181.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 3 (174.0ms)

IterNodesCost
0309393
11027364
24764348
35002347

prune148.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 1 expressions with local error:

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

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
181×add-sqr-sqrt
140×unpow-prod-down cube-prod
117×add-cube-cbrt *-un-lft-identity
80×sqrt-prod
40×sqr-pow
30×cube-mult unpow3
25×unswap-sqr
24×add-exp-log
10×prod-exp
9×div-exp
6×pow-to-exp pow-exp add-cbrt-cube
3×pow1 associate-*l*
2×cbrt-unprod
1×cbrt-undiv associate-*r/ pow-prod-down *-commutative div-inv add-log-exp
Counts
1 → 270
Calls
1 calls:
69.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series138.0ms

Counts
1 → 3
Calls
1 calls:
138.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify89.0ms

Algorithm
egg-herbie
Counts
273 → 273
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07251757
138321368
250021368

prune367.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- 0.0625) (pow x 5))
0.2b
(/ 0.125 (pow x 3))
10.2b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
19.0b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite369.0ms

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
(/ (- 0.0625) (pow x 5))
4.0ms
(/ 0.125 (pow x 3))
167.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
183.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(/ (- 0.0625) (pow x 5))
36.0ms
(/ 0.125 (pow x 3))
181.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
58.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify99.0ms

Algorithm
egg-herbie
Counts
235 → 235
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
08402002
138201923
250011915

prune559.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
0.3b
(- x (sqrt (+ (* x x) 1.0)))
3.4b
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
14.3b
(sqrt (+ (* x x) 1.0))

rewrite51.0ms

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:
22.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
8.0ms
(- 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))

series482.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0))))
65.0ms
(- x (sqrt (+ (* x x) 1.0)))
262.0ms
(log (/ (- 0 1.0) (- x (sqrt (+ (* x x) 1.0)))))
48.0ms
(sqrt (+ (* x x) 1.0))

simplify78.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
06271716
123681646
250011641

prune287.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 32.5b

bsearch83.0ms

Steps
ItersRangePoint
9
0.004380743253548005
488.5072251079851
0.888575674591003
9
-3.9934486818618
-6.3299436832828755e-06
-1.013888797647559

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05129
15129

end0.0ms

sample1.8s

Algorithm
intervals
Results
937.0ms2312×body1280valid
355.0ms1527×body640valid
218.0ms809×body2560valid
111.0ms829×body320valid
68.0ms2130×body80valid
30.0ms393×body160valid