Details

Time bar (total: 9.0s)

sample463.0ms

Algorithm
intervals
Results
277.0ms3749×body80nan
49.0ms159×body640valid
12.0ms51×body320valid
3.0ms20×body160valid
2.0ms4×body1280valid
2.0ms22×body80valid

simplify30.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
05119
115619
290719
3500119

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.8b

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (sqrt (+ x 1.0)) (sqrt x))
3.4b
(- (sqrt (+ y 1.0)) (sqrt y))
3.9b
(- (sqrt (+ t 1.0)) (sqrt t))
4.3b
(- (sqrt (+ z 1.0)) (sqrt z))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
32×*-un-lft-identity sqrt-prod
16×difference-of-squares
12×distribute-lft-out-- add-log-exp
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
4 → 76
Calls
4 calls:
40.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
41.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
42.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
41.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

series256.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
65.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
64.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
66.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

simplify46.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0472702
11521635
25001620

prune575.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))
3.4b
(- (sqrt (+ y 1.0)) (sqrt y))
3.9b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
86×*-un-lft-identity
44×sqrt-prod
40×add-sqr-sqrt
30×distribute-lft-out
24×times-frac
16×add-cube-cbrt
12×difference-of-squares
10×add-log-exp
9×distribute-lft-out--
6×add-exp-log associate-/r* add-cbrt-cube
4×pow1 associate-/l*
3×sub-neg flip3-- diff-log flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 107
Calls
4 calls:
55.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
40.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
39.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
41.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series330.0ms

Counts
4 → 12
Calls
4 calls:
136.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
66.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
61.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
66.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify64.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06271071
12341979
25001943

prune795.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))
3.4b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
118×*-un-lft-identity
52×sqrt-prod
45×distribute-lft-out
43×add-sqr-sqrt
42×times-frac
27×add-cube-cbrt
12×associate-/r*
8×add-exp-log add-cbrt-cube add-log-exp difference-of-squares
7×associate-/l*
6×distribute-lft-out--
4×pow1 associate-/r/
3×flip3-+ flip-+
2×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- div-inv associate-/l/
Counts
4 → 129
Calls
4 calls:
41.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
55.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
42.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
40.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series389.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
134.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
66.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
61.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify74.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
07211296
127311177
250021135

prune974.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))) (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))))
2.5b
(- (sqrt (+ x 1.0)) (sqrt x))
3.4b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite349.0ms

Algorithm
rewrite-expression-head
Rules
263×*-un-lft-identity
242×sqrt-prod
126×times-frac
112×add-sqr-sqrt
101×distribute-lft-out
68×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
19×pow1
10×associate-/r/
9×unswap-sqr
8×add-exp-log sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp difference-of-squares
6×flip3-+ associate-/r* flip-+ distribute-lft-out--
5×pow-prod-up div-inv
4×sqrt-div associate-/l*
3×pow-prod-down pow-sqr
2×sub-neg flip3-- diff-log flip-- associate-/l/
1×cbrt-undiv pow2 frac-times frac-2neg pow-plus sqrt-unprod associate-*r/ div-exp associate-*l/ prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 220
Calls
4 calls:
55.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
196.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))) (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))))
40.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
42.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series424.0ms

Counts
4 → 12
Calls
4 calls:
130.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
156.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))) (sqrt (/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
68.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify132.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (102.0ms)

IterNodesCost
08632448
140592159
250022124

prune1.9s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

regimes679.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04239
15239
25239

end0.0ms

sample924.0ms

Algorithm
intervals
Results
566.0ms7758×body80nan
100.0ms336×body640valid
24.0ms111×body320valid
5.0ms36×body160valid
3.0ms8×body1280valid
3.0ms37×body80valid