Details

Time bar (total: 3.3s)

sample31.0ms

Algorithm
intervals
Results
15.0ms97×body1280valid
4.0ms29×body640valid
3.0ms121×body80valid
1.0ms4×body160valid
0.0ms5×body320valid

simplify10.0ms

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: 14.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot 1.0 x)
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
1.4b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
14×add-sqr-sqrt
12×add-cube-cbrt
9×times-frac
8×add-log-exp
6×add-exp-log add-cbrt-cube
4×pow1
3×associate-/r* associate-/l*
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg flip3-+ diff-log div-exp clear-num sum-log flip-- flip-+ div-inv distribute-lft-out distribute-lft-out-- difference-of-squares
Counts
4 → 60
Calls
4 calls:
1.0ms
(hypot 1.0 x)
3.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
1.0ms
(hypot 1.0 x)
5.0ms
(/ 1.0 (hypot 1.0 x))
30.0ms
(+ 1.0 (/ 1.0 (hypot 1.0 x)))
82.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify56.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0204408
1643378
21990376
35001375

prune145.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 14.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ 1.0 (hypot 1.0 x))
0.0b
(/ (- (* 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)))))))
0.9b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite27.0ms

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:
3.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(/ 1.0 (hypot 1.0 x))
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)))))))
6.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
151.0ms
(/ (- (* 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)))))))
36.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify55.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
04071275
115941181
250011177

prune300.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 14.2b

localize15.0ms

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)))))))
0.9b
(- (/ (* 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))))))))

rewrite37.0ms

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))
10.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
18.0ms
(- (/ (* 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))))))))

series480.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
5.0ms
(/ 1.0 (hypot 1.0 x))
151.0ms
(/ (* 0.5 (/ 1.0 (hypot 1.0 x))) (+ 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))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))

simplify49.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
04011320
117401175
250011148

prune312.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 14.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 0.5) (hypot 1.0 x))
0.0b
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
0.0b
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
0.9b
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
20×add-exp-log add-cbrt-cube
14×associate-*r/ associate-*l/
12×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cube-cbrt associate-*l* frac-sub
7×flip3-- flip--
6×flip3-+ associate-*r* prod-exp cbrt-unprod flip-+ associate-/l/ add-log-exp
4×cbrt-undiv div-exp
2×pow-prod-down associate-/r/ *-commutative associate--r+ unswap-sqr
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac diff-log clear-num associate-/r* div-inv distribute-lft-out associate-/l* difference-of-squares
Counts
4 → 89
Calls
4 calls:
6.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
6.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
14.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
7.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series136.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (+ 1.0 0.5) (hypot 1.0 x))
24.0ms
(* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x))
58.0ms
(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
36.0ms
(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify86.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05501145
13114962
25003962

prune304.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 13.9b

regimes86.0ms

Accuracy

0% (0.4b remaining)

Error of 15.2b against oracle of 14.7b and baseline of 15.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04238
14238

end0.0ms

sample801.0ms

Algorithm
intervals
Results
463.0ms2849×body1280valid
118.0ms4082×body80valid
81.0ms645×body640valid
25.0ms283×body320valid
8.0ms141×body160valid