Details

Time bar (total: 6.4s)

sample402.0ms

Algorithm
intervals
Results
232.0ms3916×body80nan
41.0ms163×body640valid
11.0ms59×body320valid
2.0ms13×body160valid
1.0ms18×body80valid
1.0ms3×body1280valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
05119
115619
290719
3500119

prune5.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (sqrt (+ y 1.0)) (sqrt y))
2.4b
(- (sqrt (+ z 1.0)) (sqrt z))
3.6b
(- (sqrt (+ t 1.0)) (sqrt t))
3.7b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite95.0ms

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:
24.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
22.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
22.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
24.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series277.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
68.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0472702
11521635
25001620

prune397.0ms

Filtered
88 candidates to 56 candidates (63.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 1.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.0b
(- (sqrt (+ y 1.0)) (sqrt y))
2.4b
(- (sqrt (+ z 1.0)) (sqrt z))
3.6b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite103.0ms

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:
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
22.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
22.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series347.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
68.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify64.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
06341073
12370978
25001942

prune531.0ms

Filtered
119 candidates to 71 candidates (59.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.0b
(- (sqrt (+ y 1.0)) (sqrt y))
2.4b
(- (sqrt (+ z 1.0)) (sqrt z))

rewrite106.0ms

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:
24.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
30.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
22.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

series429.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
145.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
71.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

simplify80.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07281298
127631176
250011134

prune675.0ms

Filtered
141 candidates to 83 candidates (58.9%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.7b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.5b
(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
2.0b
(- (sqrt (+ y 1.0)) (sqrt y))
2.4b
(- (sqrt (+ z 1.0)) (sqrt z))

rewrite136.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
44×sqrt-prod
42×add-sqr-sqrt
30×distribute-lft-out
24×times-frac
18×add-cube-cbrt
12×difference-of-squares
11×log-pow
10×exp-prod
9×distribute-lft-out--
8×add-log-exp
6×add-exp-log associate-/r* add-cbrt-cube
5×pow1 log-prod
4×associate-/l*
3×sub-neg
2×flip3-- flip3-+ diff-log exp-sum associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv log-div frac-2neg exp-diff div-exp rem-log-exp clear-num div-inv
Counts
4 → 113
Calls
4 calls:
31.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
54.0ms
(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
22.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
25.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

series362.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
73.0ms
(log (exp (- (sqrt (+ y 1.0)) (sqrt y))))
74.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
76.0ms
(- (sqrt (+ z 1.0)) (sqrt z))

simplify64.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
05611081
12074978
25001944

prune571.0ms

Filtered
125 candidates to 74 candidates (59.2%)
Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.5b

regimes866.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04225
15225
25225

end0.0ms

sample706.0ms

Algorithm
intervals
Results
417.0ms7036×body80nan
74.0ms302×body640valid
17.0ms96×body320valid
3.0ms29×body160valid
2.0ms6×body1280valid
2.0ms28×body80valid