Details

Time bar (total: 6.4s)

sample389.0ms

Algorithm
intervals
Results
223.0ms3808×body80nan
45.0ms172×body640valid
7.0ms40×body320valid
2.0ms19×body160valid
1.0ms21×body80valid
1.0ms4×body1280valid

simplify27.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 3.9b

localize21.0ms

Local error

Found 4 expressions with local error:

2.5b
(- (sqrt (+ z 1.0)) (sqrt z))
2.8b
(- (sqrt (+ y 1.0)) (sqrt y))
3.0b
(- (sqrt (+ t 1.0)) (sqrt t))
3.5b
(- (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 (+ z 1.0)) (sqrt z))
22.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
22.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
24.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series286.0ms

Counts
4 → 12
Calls
4 calls:
71.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
74.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
73.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify42.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0472702
11521635
25001620

prune382.0ms

Filtered
88 candidates to 56 candidates (63.6%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.5b
(- (sqrt (+ z 1.0)) (sqrt z))
2.8b
(- (sqrt (+ y 1.0)) (sqrt y))
3.0b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite105.0ms

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:
30.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
24.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
23.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series371.0ms

Counts
4 → 12
Calls
4 calls:
152.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
72.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify66.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06341073
12373978
25002942

prune525.0ms

Filtered
119 candidates to 71 candidates (59.7%)
Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.5b
(- (sqrt (+ z 1.0)) (sqrt z))
3.0b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite107.0ms

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 (+ y 1.0)) (sqrt y)))
30.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series437.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
145.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
74.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify71.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
07281298
127601176
250011134

prune631.0ms

Filtered
141 candidates to 83 candidates (58.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.7b
(+ z (- 1.0 z))
3.0b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
116×*-un-lft-identity
46×distribute-lft-out
44×sqrt-prod
42×times-frac
35×add-sqr-sqrt
27×add-cube-cbrt
12×associate-/r*
11×add-log-exp
8×add-exp-log add-cbrt-cube
7×associate-/l*
4×pow1 flip3-+ associate-/r/ flip-+ distribute-lft-out-- difference-of-squares
2×cbrt-undiv sub-neg associate-+r+ frac-2neg diff-log div-exp clear-num sum-log div-inv associate-/l/
1×+-commutative associate-+r- flip3-- flip--
Counts
4 → 127
Calls
4 calls:
25.0ms
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
32.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(+ z (- 1.0 z))
22.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series367.0ms

Counts
4 → 12
Calls
4 calls:
139.0ms
(/ 1.0 (+ (sqrt (+ y 1.0)) (sqrt y)))
149.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
1.0ms
(+ z (- 1.0 z))
77.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify74.0ms

Algorithm
egg-herbie
Counts
139 → 139
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
06831181
125931073
250011005

prune640.0ms

Filtered
139 candidates to 83 candidates (59.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

regimes461.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04526
15526
25526

end0.0ms

sample1.1s

Algorithm
intervals
Results
640.0ms10718×body80nan
120.0ms496×body640valid
28.0ms154×body320valid
5.0ms42×body160valid
4.0ms11×body1280valid
3.0ms50×body80valid