Details

Time bar (total: 5.0s)

sample56.0ms

Algorithm
intervals
Results
28.0ms90×body1280valid
10.0ms123×body80valid
5.0ms20×body640valid
3.0ms15×body320valid
1.0ms8×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: 18.8b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (hypot 1.0 x))
2.7b
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite6.0ms

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:
2.0ms
(/ 1.0 (hypot 1.0 x))
3.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series90.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(/ 1.0 (hypot 1.0 x))
85.0ms
(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify45.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (12.0ms)

IterNodesCost
0157308
1484286
21409284
35001284

prune107.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 18.3b

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)))))))
2.3b
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite34.0ms

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:
2.0ms
(/ 1.0 (hypot 1.0 x))
2.0ms
(/ 1.0 (hypot 1.0 x))
18.0ms
(/ (- (* 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)))))))
9.0ms
(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series205.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(/ 1.0 (hypot 1.0 x))
6.0ms
(/ 1.0 (hypot 1.0 x))
161.0ms
(/ (- (* 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)))))))
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

prune318.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 18.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 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 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
2.3b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×times-frac
25×add-sqr-sqrt add-cube-cbrt
24×add-exp-log add-cbrt-cube
14×associate-*r/
12×associate-/r/
10×cbrt-undiv div-exp associate-/l*
9×flip3-+ flip-+ distribute-lft-out
8×add-log-exp
7×associate-/r* div-inv
4×pow1 associate-*l/ prod-exp frac-sub cbrt-unprod
3×flip3-- flip--
2×frac-2neg clear-num associate--r+
1×+-commutative distribute-rgt-in sub-neg distribute-lft-in diff-log sum-log associate-/l/
Counts
4 → 119
Calls
4 calls:
3.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms
(/ 1.0 (hypot 1.0 x))
37.0ms
(/ (/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
33.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series348.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms
(/ 1.0 (hypot 1.0 x))
222.0ms
(/ (/ (* 1.0 (- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))) (* (hypot 1.0 x) (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
40.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify136.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
08213208
148452826
250022826

prune507.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 18.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (hypot 1.0 x))
0.2b
(cbrt (hypot 1.0 x))
0.3b
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
2.3b
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
22×cbrt-prod add-sqr-sqrt
14×add-cube-cbrt *-un-lft-identity
11×pow1
8×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l* add-log-exp
4×associate-*r/ associate-*l/ frac-sub add-cbrt-cube unswap-sqr
3×flip3-- flip--
2×flip3-+ pow-prod-down pow-sqr pow-prod-up flip-+ associate--r+
1×pow2 distribute-rgt-in sub-neg distribute-lft-in pow-plus diff-log prod-exp *-commutative cbrt-unprod
Counts
4 → 80
Calls
4 calls:
0.0ms
(cbrt (hypot 1.0 x))
0.0ms
(cbrt (hypot 1.0 x))
6.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
30.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

series377.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(cbrt (hypot 1.0 x))
104.0ms
(cbrt (hypot 1.0 x))
122.0ms
(* (cbrt (hypot 1.0 x)) (cbrt (hypot 1.0 x)))
42.0ms
(- (* (- (pow 1.0 3) (pow 0.5 3)) (hypot 1.0 x)) (* 0.5 (+ (* 0.5 (+ 0.5 1.0)) (* 1.0 1.0))))

simplify63.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
0373810
11854730
25001703

prune436.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 18.3b

regimes355.0ms

Accuracy

0% (0.0b remaining)

Error of 15.4b against oracle of 15.3b and baseline of 15.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04036
14036

end0.0ms

sample1.6s

Algorithm
intervals
Results
924.0ms2867×body1280valid
300.0ms3989×body80valid
179.0ms662×body640valid
68.0ms331×body320valid
20.0ms151×body160valid