Details

Time bar (total: 6.7s)

sample64.0ms

Algorithm
intervals
Results
30.0ms72×body1280valid
12.0ms45×body640valid
5.0ms20×body2560valid
5.0ms37×body320valid
2.0ms69×body80valid
1.0ms13×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: 53.6b

localize6.0ms

Local error

Found 3 expressions with local error:

1.2b
(+ x (sqrt (+ (* x x) 1.0)))
3.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
13.8b
(sqrt (+ (* x x) 1.0))

rewrite46.0ms

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:
19.0ms
(+ x (sqrt (+ (* x x) 1.0)))
16.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
9.0ms
(sqrt (+ (* x x) 1.0))

series247.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ x (sqrt (+ (* x x) 1.0)))
155.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
39.0ms
(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

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)))

rewrite301.0ms

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:
190.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
86.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series274.0ms

Counts
2 → 6
Calls
2 calls:
148.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
126.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify116.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
08882291
147681819
250011795

prune479.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/6 (pow x 3))
0.1b
(/ x (/ 1.0 x))
11.8b
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
13.6b
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
78×times-frac
59×add-sqr-sqrt
52×add-cube-cbrt *-un-lft-identity
24×add-exp-log
16×add-cbrt-cube
14×associate-/r*
12×associate-*r*
7×div-exp
6×prod-exp div-inv associate-/l*
5×cbrt-undiv
4×pow1 expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u add-log-exp unswap-sqr
3×associate-*l* associate-/r/
2×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num cbrt-unprod sqr-pow
1×cube-mult flip3-- unpow3 *-commutative flip-- fma-udef
Counts
4 → 142
Calls
4 calls:
12.0ms
(* 1/6 (pow x 3))
8.0ms
(/ x (/ 1.0 x))
0.0ms
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
32.0ms
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

series616.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* 1/6 (pow x 3))
22.0ms
(/ x (/ 1.0 x))
160.0ms
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
399.0ms
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ x (/ 1.0 x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

simplify107.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07121991
137781704
250021697

prune567.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 1/6 (pow x 3))
0.4b
(/ 1 (/ (/ 1.0 x) x))
11.8b
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
13.6b
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
396×times-frac
201×add-sqr-sqrt
194×add-cube-cbrt *-un-lft-identity
44×associate-/r*
40×add-exp-log
20×add-cbrt-cube
19×div-exp
18×div-inv
12×associate-*r*
8×cbrt-undiv
6×prod-exp associate-/l*
5×pow1
4×expm1-log1p-u unpow-prod-down cube-prod log1p-expm1-u add-log-exp unswap-sqr
3×rec-exp 1-exp associate-*l* associate-/r/
2×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num cbrt-unprod sqr-pow
1×cube-mult flip3-- pow-flip unpow3 *-commutative flip-- fma-udef inv-pow
Counts
4 → 272
Calls
4 calls:
15.0ms
(* 1/6 (pow x 3))
19.0ms
(/ 1 (/ (/ 1.0 x) x))
0.0ms
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
29.0ms
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

series622.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* 1/6 (pow x 3))
28.0ms
(/ 1 (/ (/ 1.0 x) x))
155.0ms
(fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3)))))
405.0ms
(/ (fma (* (fma (log (sqrt 1.0)) (log (sqrt 1.0)) (- (/ 1 (/ (/ 1.0 x) x)))) 1.0) (sqrt 1.0) (- (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (pow x 3))))) (* (- (log (sqrt 1.0)) (/ x (sqrt 1.0))) (pow (sqrt 1.0) 3)))

simplify66.0ms

Algorithm
egg-herbie
Counts
284 → 284
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013423472
150012604

prune731.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

regimes37.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch76.0ms

Steps
ItersRangePoint
10
1.6041137143851903e-12
1.537653969837454
0.0010068077002032643
9
-11413.0783357711
-0.00024241826916865248
-1.0196250072526523

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04425
14625
24625

end0.0ms

sample1.9s

Algorithm
intervals
Results
969.0ms2347×body1280valid
368.0ms1520×body640valid
219.0ms774×body2560valid
119.0ms845×body320valid
66.0ms2136×body80valid
36.0ms378×body160valid