Details

Time bar (total: 6.9s)

sample362.0ms

Algorithm
intervals
Results
206.0ms3556×body80nan
39.0ms164×body640valid
9.0ms51×body320valid
2.0ms18×body160valid
1.0ms21×body80valid
1.0ms2×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: 5.1b

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
2.8b
(- (sqrt (+ z 1.0)) (sqrt z))
3.1b
(- (sqrt (+ y 1.0)) (sqrt y))
4.6b
(- (sqrt (+ t 1.0)) (sqrt t))

rewrite98.0ms

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:
25.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
23.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
25.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

series279.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
70.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
67.0ms
(- (sqrt (+ t 1.0)) (sqrt t))

simplify45.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0472702
11521635
25001620

prune397.0ms

Filtered
88 candidates to 56 candidates (63.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
2.8b
(- (sqrt (+ z 1.0)) (sqrt z))
3.1b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite108.0ms

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:
33.0ms
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
23.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
23.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
25.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series353.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
71.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
67.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify63.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
06341073
12368978
25001942

prune725.0ms

Filtered
119 candidates to 71 candidates (59.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.3b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
2.8b
(- (sqrt (+ z 1.0)) (sqrt z))
3.1b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite109.0ms

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:
33.0ms
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
25.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series432.0ms

Counts
4 → 12
Calls
4 calls:
147.0ms
(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
140.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
72.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify69.0ms

Algorithm
egg-herbie
Counts
141 → 141
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
07281298
127631179
250011136

prune626.0ms

Filtered
141 candidates to 83 candidates (58.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (sqrt (+ z 1.0)) (sqrt z))
3.1b
(- (sqrt (+ y 1.0)) (sqrt y))
4.3b
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
7.9b
(* (/ (+ 1.0 0) (+ (pow (sqrt (+ t 1.0)) 3) (pow (sqrt t) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

rewrite347.0ms

Algorithm
rewrite-expression-head
Rules
195×*-un-lft-identity
87×distribute-lft-out
80×sqrt-prod
74×associate-*l*
69×times-frac
48×add-sqr-sqrt unpow-prod-down sqrt-div cube-prod
34×frac-times
32×frac-add
27×add-cube-cbrt flip3-+ flip-+
26×associate-*r/
19×flip3-- flip--
10×add-log-exp
9×add-exp-log associate-*l/ add-cbrt-cube
8×difference-of-squares
6×pow1 distribute-lft-out--
4×sum-cubes
3×sub-neg diff-log associate-*r*
2×prod-exp associate-/r/ cbrt-unprod unswap-sqr
1×cbrt-undiv distribute-rgt-in distribute-rgt-out-- distribute-lft-in div-exp pow-prod-down *-commutative div-inv
Counts
4 → 182
Calls
4 calls:
25.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
5.0ms
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
279.0ms
(* (/ (+ 1.0 0) (+ (pow (sqrt (+ t 1.0)) 3) (pow (sqrt t) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

series516.0ms

Counts
4 → 12
Calls
4 calls:
73.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
76.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
90.0ms
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
276.0ms
(* (/ (+ 1.0 0) (+ (pow (sqrt (+ t 1.0)) 3) (pow (sqrt t) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

simplify71.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015474462
150024218

prune1.1s

Filtered
194 candidates to 110 candidates (56.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

regimes460.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04029
15029
25029

end0.0ms

sample575.0ms

Algorithm
intervals
Results
338.0ms5720×body80nan
62.0ms256×body640valid
15.0ms82×body320valid
3.0ms23×body160valid
2.0ms26×body80valid
1.0ms4×body1280valid