Details

sample419.0ms

Algorithm

intervals

Results

242.0ms	3946×	body	80	nan
47.0ms	170×	body	640	valid
10.0ms	53×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	5×	body	1280	valid
1.0ms	13×	body	80	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.0b

localize23.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (+ x 1.0)) (sqrt x))
2.2b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

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))
24.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
25.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series271.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
68.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
67.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune394.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.2b	(- (sqrt (+ z 1.0)) (sqrt z))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
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 (+ x 1.0)) (sqrt x)))
23.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
25.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series353.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
71.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify68.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	634	1073
1	2370	978
2	5001	942

prune535.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite111.0ms

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:

26.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
26.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series432.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify76.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	721	1296
1	2733	1177
2	5001	1171

prune693.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize38.0ms

Local error

Found 4 expressions with local error:

1.8b	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
2.9b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))
11.1b	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

130×	`*-un-lft-identity`
64×	`sqrt-prod`
57×	`associate-l`
53×	`distribute-lft-out`
52×	`times-frac`
48×	`sqrt-div`
47×	`add-sqr-sqrt`
36×	`unpow-prod-down` `cube-prod`
34×	`frac-times`
32×	`frac-add`
27×	`flip3-+` `flip-+`
26×	`add-cube-cbrt` `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--`
3×	`sub-neg` `diff-log` `associate-r` `sum-cubes`
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 → 165

Calls

4 calls:

5.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
25.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
266.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

series520.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
278.0ms	(* (/ 1.0 (+ (pow (sqrt (+ z 1.0)) 3) (pow (sqrt z) 3))) (+ (* (sqrt (+ z 1.0)) (sqrt (+ z 1.0))) (- (* (sqrt z) (sqrt z)) (* (sqrt (+ z 1.0)) (sqrt z)))))

simplify74.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1521	4094
1	5001	3803

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

regimes444.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	39
1	60	39
2	60	39

end0.0ms

sample1.2s

Algorithm

intervals

Results

747.0ms	11966×	body	80	nan
127.0ms	503×	body	640	valid
31.0ms	159×	body	320	valid
8.0ms	51×	body	160	valid
5.0ms	15×	body	1280	valid
3.0ms	55×	body	80	valid