Details

Time bar (total: 5.0s)

sample390.0ms

Algorithm
intervals
Results
215.0ms3593×body80nan
47.0ms166×body640valid
11.0ms56×body320valid
2.0ms6×body1280valid
1.0ms11×body160valid
1.0ms17×body80valid

simplify26.0ms

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 5.7b

Counts
2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
3.1b
(- (sqrt (+ z 1.0)) (sqrt z))
3.2b
(- (sqrt (+ t 1.0)) (sqrt t))
3.3b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
4×sub-neg flip3-- flip--
Counts
4 → 16
Calls
4 calls:
4.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
3.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
3.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
4.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series270.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms
(- (sqrt (+ z 1.0)) (sqrt z))
67.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify37.0ms

Algorithm
egg-herbie
Counts
28 → 28
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0417250
11391200
25001188

prune152.0ms

Filtered
28 candidates to 20 candidates (71.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New23528
Fresh000
Picked101
Done000
Total24529

Merged error: 0.4b

Counts
29 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
3.2b
(- (sqrt (+ t 1.0)) (sqrt t))
3.3b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
3×sub-neg flip3-- flip--
2×flip3-+ associate-/r/ flip-+ associate-/l/
1×frac-2neg clear-num div-inv
Counts
4 → 19
Calls
4 calls:
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
3.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
3.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
4.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series343.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
69.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
70.0ms
(- (sqrt (+ t 1.0)) (sqrt t))
65.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify43.0ms

Algorithm
egg-herbie
Counts
31 → 31
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0490292
11883244
25002230

prune181.0ms

Filtered
31 candidates to 24 candidates (77.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New28331
Fresh314
Picked101
Done000
Total32436

Merged error: 0.2b

Counts
36 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
3.3b
(- (sqrt (+ y 1.0)) (sqrt y))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
4×associate-/r/
3×flip3-+ flip-+
2×sub-neg flip3-- frac-2neg clear-num flip-- div-inv associate-/l/
Counts
4 → 20
Calls
4 calls:
6.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
4.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
4.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
4.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

series413.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
137.0ms
(/ 1.0 (+ (sqrt (+ t 1.0)) (sqrt t)))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms
(- (sqrt (+ y 1.0)) (sqrt y))

simplify45.0ms

Algorithm
egg-herbie
Counts
32 → 32
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
0518320
12027271
25001264

prune204.0ms

Filtered
32 candidates to 26 candidates (81.3%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New31132
Fresh033
Picked011
Done000
Total31536

Merged error: 0.1b

Counts
36 → 5

localize40.0ms

Local error

Found 4 expressions with local error:

2.7b
(- (sqrt (+ x 1.0)) (sqrt x))
3.1b
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
3.3b
(- (sqrt (+ y 1.0)) (sqrt y))
10.2b
(* (/ 1.0 (fma t (sqrt t) (pow (sqrt (+ t 1.0)) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
96×sqrt-div
86×frac-times
64×frac-add
52×flip3-+ flip-+
35×flip3-- flip--
34×associate-*r/
19×frac-2neg associate-*l/ clear-num
18×*-commutative
12×associate-+r+ prod-diff
8×distribute-rgt-in distribute-lft-in
5×sub-neg
2×+-commutative distribute-rgt-out-- fma-neg distribute-lft-out--
1×associate-*l* div-inv
Counts
4 → 115
Calls
4 calls:
3.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
7.0ms
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
3.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
19.0ms
(* (/ 1.0 (fma t (sqrt t) (pow (sqrt (+ t 1.0)) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
72.0ms
(- (sqrt (+ x 1.0)) (sqrt x))
89.0ms
(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
76.0ms
(- (sqrt (+ y 1.0)) (sqrt y))
304.0ms
(* (/ 1.0 (fma t (sqrt t) (pow (sqrt (+ t 1.0)) 3))) (+ (* (sqrt (+ t 1.0)) (sqrt (+ t 1.0))) (- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))))

simplify70.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
017335138
150024471

prune961.0ms

Filtered
127 candidates to 80 candidates (63.0%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New1261127
Fresh033
Picked011
Done011
Total1266132

Merged error: 0.1b

Counts
132 → 6

regimes614.0ms

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04838
15838
25838

end0.0ms

sample502.0ms

Algorithm
intervals
Results
288.0ms4842×body80nan
56.0ms222×body640valid
17.0ms69×body320valid
2.0ms6×body1280valid
2.0ms14×body160valid
2.0ms26×body80valid