Details

Time bar (total: 10.3s)

sample140.0ms

Algorithm
intervals
Results
45.0ms101×body1280valid
17.0ms30×body10240exit
15.0ms46×body640valid
13.0ms29×body1280nan
8.0ms23×body640nan
8.0ms141×body80valid
7.0ms33×body320valid
6.0ms179×body80nan
2.0ms15×body160valid
2.0ms9×body320nan
1.0ms8×body160nan

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.8b

localize9.0ms

Local error

Found 3 expressions with local error:

1.0b
(pow (+ x 1.0) (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
76×*-un-lft-identity
73×unpow-prod-down
63×add-sqr-sqrt
56×prod-diff
51×add-cube-cbrt
26×pow-unpow
24×sqr-pow
18×times-frac
10×distribute-lft-out
9×difference-of-squares
8×fma-neg
5×pow1 add-exp-log add-log-exp
3×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
3 → 149
Calls
3 calls:
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
53.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series488.0ms

Counts
3 → 9
Calls
3 calls:
150.0ms
(pow (+ x 1.0) (/ 1.0 n))
57.0ms
(pow x (/ 1.0 n))
281.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06542164
121641642
250021637

prune333.0ms

Filtered
158 candidates to 95 candidates (60.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 19.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (+ x 1.0) (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
2.3b
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
195×sqrt-prod
127×*-un-lft-identity
118×add-sqr-sqrt
110×prod-diff
99×unpow-prod-down
94×add-cube-cbrt
39×pow-unpow
33×sqr-pow
27×times-frac
16×difference-of-squares
13×distribute-lft-out
11×fma-neg
7×pow1 add-exp-log
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
3×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 243
Calls
4 calls:
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
61.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series640.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(pow (+ x 1.0) (/ 1.0 n))
62.0ms
(pow x (/ 1.0 n))
61.0ms
(pow x (/ 1.0 n))
369.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify93.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
07785032
123933485
250013433

prune690.0ms

Filtered
255 candidates to 141 candidates (55.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.4b

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow (+ x 1.0) (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
1.2b
(pow x (/ 1.0 n))
2.3b
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

rewrite86.0ms

Algorithm
rewrite-expression-head
Rules
195×sqrt-prod
127×*-un-lft-identity
118×add-sqr-sqrt
110×prod-diff
99×unpow-prod-down
94×add-cube-cbrt
39×pow-unpow
33×sqr-pow
27×times-frac
16×difference-of-squares
13×distribute-lft-out
11×fma-neg
7×pow1 add-exp-log
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u distribute-lft-out--
3×pow-to-exp pow-pow pow-exp div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 243
Calls
4 calls:
6.0ms
(pow (+ x 1.0) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
61.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

series649.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(pow (+ x 1.0) (/ 1.0 n))
57.0ms
(pow x (/ 1.0 n))
63.0ms
(pow x (/ 1.0 n))
377.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))

simplify86.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07785032
123933485
250013433

prune818.0ms

Filtered
255 candidates to 141 candidates (55.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.4b

localize30.0ms

Local error

Found 4 expressions with local error:

1.7b
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
1.8b
(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
7.1b
(* x (pow n 2))
9.2b
(* (pow x 2) n)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
21×*-un-lft-identity
18×associate-*l*
16×add-exp-log
14×associate-*r*
12×add-cube-cbrt unpow-prod-down
10×add-cbrt-cube
9×unswap-sqr
7×prod-exp
6×pow1 sqrt-prod
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×*-commutative cbrt-unprod fma-udef
2×pow-to-exp associate-*l/ pow-exp
1×distribute-rgt-in distribute-lft-in flip3-+ pow-prod-down flip-+
Counts
4 → 96
Calls
4 calls:
117.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
0.0ms
(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
5.0ms
(* x (pow n 2))
6.0ms
(* (pow x 2) n)

series640.0ms

Counts
4 → 12
Calls
4 calls:
488.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))) (fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x)))
98.0ms
(fma (- 0.25) (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))) (/ (/ 0.5 n) x))
34.0ms
(* x (pow n 2))
19.0ms
(* (pow x 2) n)

simplify78.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
05631307
126391144
250021142

prune491.0ms

Filtered
108 candidates to 74 candidates (68.5%)
Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 19.3b

regimes315.0ms

Accuracy

81% (1.8b remaining)

Error of 22.3b against oracle of 20.5b and baseline of 29.9b

bsearch206.0ms

Steps
ItersRangePoint
6
927621.7061119184
6803969.331336576
6336551.062491215
11
-4240874295.0135207
-2.472407816558163e-13
-0.016233638685546038

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05857
15857

end0.0ms

sample4.1s

Algorithm
intervals
Results
1.5s3157×body1280valid
546.0ms1608×body640valid
487.0ms1158×body10240exit
273.0ms596×body1280nan
251.0ms4755×body80valid
207.0ms647×body640nan
193.0ms5185×body80nan
189.0ms852×body320valid
74.0ms358×body320nan
59.0ms436×body160valid
21.0ms190×body160nan