Details

Time bar (total: 4.0s)

sample31.0ms

Algorithm
intervals
Results
16.0ms100×body1280valid
4.0ms133×body80valid
2.0ms14×body640valid
0.0ms5×body320valid
0.0ms4×body160valid

simplify11.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0196
1246
2286
3306
4356
5376
6376

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.3b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
1.7b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
9×times-frac
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/r* associate-/l*
2×pow1
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv distribute-lft-out-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series91.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify46.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0157308
1484286
21409284
35001284

prune101.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
1.1b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
30×times-frac
29×add-sqr-sqrt add-cube-cbrt
10×add-exp-log associate-/r* add-cbrt-cube
9×associate-/l*
8×associate-*r/
6×add-log-exp
4×pow1 flip3-- associate--l+ frac-sub flip-- associate-/l/ distribute-lft-out
3×cbrt-undiv sub-neg frac-2neg div-exp clear-num div-inv
2×distribute-rgt-in distribute-lft-in associate-/r/
1×flip3-+ diff-log div-sub flip-+
Counts
4 → 110
Calls
4 calls:
11.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
10.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series201.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
33.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04071275
115941181
250011177

prune317.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.2b
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.1b
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
24×add-sqr-sqrt
22×add-cube-cbrt times-frac
17×add-exp-log add-cbrt-cube
10×associate-/r*
7×associate-/l*
6×cbrt-undiv div-exp associate-/r/ add-log-exp
5×div-inv
4×pow1
3×distribute-rgt-out-- frac-2neg flip3-+ clear-num flip-+
2×prod-exp cbrt-unprod distribute-lft-out
1×sub-neg flip3-- diff-log associate-*r/ frac-sub flip-- associate-/l/ distribute-lft-out-- sub-div difference-of-squares
Counts
4 → 101
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
8.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
16.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

series482.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
149.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
323.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
04011320
117401175
250011148

prune308.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 11.5b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.2b
(/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
0.6b
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
1.1b
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

rewrite97.0ms

Algorithm
rewrite-expression-head
Rules
165×times-frac
118×*-un-lft-identity
97×sqrt-prod
76×add-sqr-sqrt
68×add-cube-cbrt
29×add-exp-log add-cbrt-cube
24×distribute-lft-out
20×sqrt-div associate-/r/
17×associate-/r* associate-/l*
13×cbrt-undiv div-exp
11×div-inv
10×flip3-+ flip-+
6×add-log-exp
4×pow1 prod-exp cbrt-unprod
3×frac-2neg clear-num difference-of-squares
2×associate-/l/
1×sub-neg flip3-- diff-log associate-*r/ frac-sub flip-- distribute-lft-out--
Counts
4 → 210
Calls
4 calls:
3.0ms
(/ 1.0 (hypot 1.0 x))
19.0ms
(/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
10.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
56.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

series664.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(/ 1.0 (hypot 1.0 x))
148.0ms
(/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
188.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
317.0ms
(- (/ (* 1.0 (- 1.0 0.5)) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (/ (/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))) (sqrt (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))

simplify100.0ms

Algorithm
egg-herbie
Counts
222 → 222
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
07285651
131585056
250015048

prune493.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 11.5b

regimes75.0ms

Accuracy

0% (0.3b remaining)

Error of 15.1b against oracle of 14.8b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02020
12020

end0.0ms

sample788.0ms

Algorithm
intervals
Results
455.0ms2846×body1280valid
113.0ms4041×body80valid
78.0ms622×body640valid
29.0ms341×body320valid
8.0ms150×body160valid