Details

Time bar (total: 6.0s)

sample68.0ms

Algorithm
intervals
Results
32.0ms74×body1280valid
14.0ms55×body640valid
8.0ms28×body2560valid
3.0ms22×body320valid
2.0ms66×body80valid
1.0ms11×body160valid

simplify4.0ms

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: 55.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.5b
(+ x (sqrt (+ (* x x) 1.0)))
2.9b
(log (+ x (sqrt (+ (* x x) 1.0))))
17.1b
(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)))
9.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
5.0ms
(sqrt (+ (* x x) 1.0))

series278.0ms

Counts
3 → 9
Calls
3 calls:
60.0ms
(+ x (sqrt (+ (* x x) 1.0)))
171.0ms
(log (+ x (sqrt (+ (* x x) 1.0))))
47.0ms
(sqrt (+ (* x x) 1.0))

simplify34.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0331422
11127385
25002366

prune182.0ms

Pruning

5 alts after pruning (5 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)))

rewrite240.0ms

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:
144.0ms
(- (+ (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)))

series300.0ms

Counts
2 → 6
Calls
2 calls:
159.0ms
(- (+ (log (sqrt 1.0)) (/ x (sqrt 1.0))) (* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3))))
141.0ms
(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify119.0ms

Algorithm
egg-herbie
Counts
306 → 306
Iterations

Useful iterations: 2 (95.0ms)

IterNodesCost
08882291
147681819
250011795

prune470.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(hypot x (sqrt 1.0))
0.5b
(+ (hypot x (sqrt 1.0)) x)
2.9b
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
7×add-exp-log
6×pow1 *-un-lft-identity
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt
3×expm1-log1p-u fma-def rem-log-exp add-cbrt-cube log1p-expm1-u
2×log-div flip3-+ associate-*r/ prod-exp log-pow flip-+
1×+-commutative log-prod hypot-udef 1-exp pow-prod-down sum-log distribute-lft-out
Counts
3 → 44
Calls
3 calls:
0.0ms
(hypot x (sqrt 1.0))
3.0ms
(+ (hypot x (sqrt 1.0)) x)
4.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

series529.0ms

Counts
3 → 9
Calls
3 calls:
104.0ms
(hypot x (sqrt 1.0))
128.0ms
(+ (hypot x (sqrt 1.0)) x)
296.0ms
(log (* 1 (+ (hypot x (sqrt 1.0)) x)))

simplify32.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0288336
11100310
25002294

prune150.0ms

Pruning

7 alts after pruning (5 fresh and 2 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))
14.6b
(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)))))
16.6b
(/ (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)))

rewrite38.0ms

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:
7.0ms
(* 1/6 (pow x 3))
5.0ms
(/ 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)))))
21.0ms
(/ (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)))

series684.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* 1/6 (pow x 3))
24.0ms
(/ x (/ 1.0 x))
177.0ms
(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)))))
440.0ms
(/ (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)))

simplify105.0ms

Algorithm
egg-herbie
Counts
154 → 154
Iterations

Useful iterations: 2 (88.0ms)

IterNodesCost
07121997
137721707
250011700

prune557.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 31.8b

bsearch85.0ms

Steps
ItersRangePoint
7
0.0001516457190089863
0.003342748024832997
0.000917194589536015
9
-118.89002763209811
-0.00028315217264546786
-1.0102938707423672

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05532
16332
26632
36632

end0.0ms

sample2.0s

Algorithm
intervals
Results
975.0ms2324×body1280valid
395.0ms1603×body640valid
240.0ms825×body2560valid
121.0ms800×body320valid
66.0ms2044×body80valid
33.0ms404×body160valid