Details

Time bar (total: 12.5s)

sample72.0ms

Algorithm
intervals
Results
39.0ms90×body1280valid
13.0ms54×body640valid
6.0ms22×body2560valid
3.0ms24×body320valid
2.0ms54×body80valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.2b
(+ x (sqrt (+ (* x x) 1.0)))
3.0b
(log (+ x (sqrt (+ (* x x) 1.0))))
11.9b
(sqrt (+ (* x x) 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×add-sqr-sqrt
6×add-cube-cbrt
5×pow1 add-log-exp
4×add-exp-log log-prod
3×expm1-log1p-u fma-def flip3-+ sqrt-prod add-cbrt-cube flip-+ log1p-expm1-u
2×log-div sqrt-div distribute-lft-out
1×+-commutative rem-sqrt-square sqrt-pow1 pow1/2 rem-log-exp sum-log log-pow hypot-def
Counts
3 → 52
Calls
3 calls:
9.0ms
(+ x (sqrt (+ (* x x) 1.0)))
8.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms
(sqrt (+ (* x x) 1.0))

series290.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(+ x (sqrt (+ (* x x) 1.0)))
168.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
65.0ms
(sqrt (+ (* x x) 1.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0331422
11127385
25002366

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

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)))

rewrite232.0ms

Algorithm
rewrite-expression-head
Rules
240×times-frac
220×associate-*r*
184×add-sqr-sqrt
140×unpow-prod-down cube-prod
126×*-un-lft-identity
120×add-cube-cbrt
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×pow1 pow-to-exp pow-exp add-log-exp
5×fma-neg prod-diff
4×distribute-lft-out
3×associate-*r/ associate-*l*
2×expm1-log1p-u diff-log log-pow frac-sub cbrt-unprod log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 300
Calls
2 calls:
138.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
74.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series283.0ms

Counts
2 → 6
Calls
2 calls:
150.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
133.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify116.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (93.0ms)

IterNodesCost
08882345
148131909
250011888

prune437.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.2b
(+ x (hypot x (sqrt 1.0)))
3.0b
(log (+ x (hypot x (sqrt 1.0))))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
9×*-un-lft-identity
5×add-sqr-sqrt add-cube-cbrt add-log-exp
4×pow1 add-exp-log log-prod
3×expm1-log1p-u fma-def add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ flip-+ distribute-lft-out
1×+-commutative hypot-udef rem-log-exp sum-log log-pow
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
2.0ms
(+ x (hypot x (sqrt 1.0)))
2.0ms
(log (+ x (hypot x (sqrt 1.0))))

series493.0ms

Counts
3 → 9
Calls
3 calls:
100.0ms
(hypot x (sqrt 1.0))
124.0ms
(+ x (hypot x (sqrt 1.0)))
269.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify89.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (84.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune135.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 0.125 (pow x 3))
0.3b
(/ (- 0.0625) (pow x 5))
16.0b
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
23.9b
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

rewrite822.0ms

Algorithm
rewrite-expression-head
Rules
2802×times-frac
2496×add-sqr-sqrt
1944×*-un-lft-identity
1522×prod-diff
1510×add-cube-cbrt
965×associate--r+
652×unpow-prod-down
339×distribute-rgt-neg-in
330×difference-of-squares
297×distribute-lft-neg-in
272×sqr-pow
149×cube-prod
134×distribute-lft-out--
104×div-inv
99×neg-mul-1
49×cube-mult unpow3
40×fma-neg
19×associate-/r*
15×add-exp-log
13×associate-/l*
12×log-prod
9×add-log-exp
8×frac-sub add-cbrt-cube
6×div-exp
5×pow1 log-div
4×expm1-log1p-u flip3-- flip-- log1p-expm1-u
3×diff-log
2×cbrt-undiv neg-sub0 pow-to-exp sub-neg frac-2neg div-sub pow-exp clear-num associate--r-
1×distribute-frac-neg rem-log-exp log-pow
Counts
4 → 1793
Calls
4 calls:
4.0ms
(/ 0.125 (pow x 3))
6.0ms
(/ (- 0.0625) (pow x 5))
250.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
342.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

series337.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(/ 0.125 (pow x 3))
54.0ms
(/ (- 0.0625) (pow x 5))
183.0ms
(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
59.0ms
(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))

simplify423.0ms

Algorithm
egg-herbie
Counts
1805 → 1805
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500248078

prune6.4s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

regimes30.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.9b

bsearch91.0ms

Steps
ItersRangePoint
10
2.30341956868392e-10
214.50772926448735
0.0009283479637735851
9
-1898619.482837422
-0.12347723982223391
-1.0248436231258424

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05272
15672
25672

end0.0ms

sample1.9s

Algorithm
intervals
Results
969.0ms2335×body1280valid
363.0ms1537×body640valid
216.0ms773×body2560valid
119.0ms838×body320valid
72.0ms2100×body80valid
34.0ms417×body160valid