Details

Time bar (total: 6.2s)

sample83.0ms

Algorithm
intervals
Results
36.0ms70×body1280valid
20.0ms64×body640valid
9.0ms24×body2560valid
4.0ms69×body80valid
4.0ms19×body320valid
1.0ms10×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0105
1105

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 52.6b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.2b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite23.0ms

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))))
5.0ms
(sqrt (+ (* x x) 1.0))

series269.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
164.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
45.0ms
(sqrt (+ (* x x) 1.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0331422
11127385
25002366

prune181.0ms

Pruning

5 alts after pruning (5 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)))

rewrite229.0ms

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:
136.0ms
(- (+ (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)))

series294.0ms

Counts
2 → 6
Calls
2 calls:
154.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
140.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify115.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08882291
147681819
250011795

prune446.0ms

Pruning

5 alts after pruning (4 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))
0.5b
(+ x (hypot x (sqrt 1.0)))
2.2b
(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))))

series503.0ms

Counts
3 → 9
Calls
3 calls:
95.0ms
(hypot x (sqrt 1.0))
124.0ms
(+ x (hypot x (sqrt 1.0)))
283.0ms
(log (+ x (hypot x (sqrt 1.0))))

simplify88.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (83.0ms)

IterNodesCost
0268349
1886321
23696305
35001303

prune141.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
0.5b
(+ x (hypot x (sqrt 1.0)))
0.5b
(+ x (hypot x (sqrt 1.0)))
2.2b
(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
35×pow1
32×*-un-lft-identity
26×add-sqr-sqrt sqrt-prod
24×sqrt-div
16×sqrt-pow1 pow1/2
14×add-cube-cbrt flip3-+ log-pow flip-+
11×swap-sqr
10×pow-prod-up
9×add-exp-log
8×frac-times log-div distribute-lft-out add-log-exp
7×associate-*r* associate-*l*
6×fma-def pow-prod-down pow-sqr add-cbrt-cube
4×expm1-log1p-u associate-*r/ associate-*l/ log1p-expm1-u unswap-sqr
2×+-commutative pow2 pow-plus rem-log-exp prod-exp sum-log
1×log-prod sqrt-unprod rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 132
Calls
4 calls:
20.0ms
(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
2.0ms
(+ x (hypot x (sqrt 1.0)))
2.0ms
(+ x (hypot x (sqrt 1.0)))
10.0ms
(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

series675.0ms

Counts
4 → 12
Calls
4 calls:
134.0ms
(* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0)))))
125.0ms
(+ x (hypot x (sqrt 1.0)))
131.0ms
(+ x (hypot x (sqrt 1.0)))
285.0ms
(log (* (sqrt (+ x (hypot x (sqrt 1.0)))) (sqrt (+ x (hypot x (sqrt 1.0))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03551184
113441050
250021012

prune302.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 31.9b

bsearch74.0ms

Steps
ItersRangePoint
6
0.00011468519908208964
0.0012055448239290207
0.0009758525496694311
9
-1078.7327260164275
-0.0019174381104543623
-1.0051038436432536

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03924
13924

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.2s2327×body1280valid
524.0ms1585×body640valid
292.0ms780×body2560valid
163.0ms766×body320valid
145.0ms2124×body80valid
57.0ms418×body160valid