Details

sample378.0ms

Algorithm

intervals

Results

216.0ms	3556×	body	80	nan
40.0ms	164×	body	640	valid
9.0ms	51×	body	320	valid
2.0ms	18×	body	160	valid
1.0ms	21×	body	80	valid
1.0ms	2×	body	1280	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 5.1b

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))

rewrite89.0ms

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:

21.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
21.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
21.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
23.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

series277.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
70.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune380.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize24.0ms

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))

rewrite98.0ms

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:

29.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
21.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
23.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
21.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series344.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
69.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
69.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	634	1073
1	2371	978
2	5002	942

prune527.0ms

Pruning

8 alts after pruning (8 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)))
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))

rewrite104.0ms

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:

31.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
23.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
25.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series422.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ t 1.0)) (sqrt t)))
135.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify73.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	728	1298
1	2760	1179
2	5002	1136

prune635.0ms

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)))))

rewrite315.0ms

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:

21.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
21.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
5.0ms	(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
255.0ms	(* (/ (+ 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)))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
72.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
88.0ms	(- (* (sqrt t) (sqrt t)) (* (sqrt (+ t 1.0)) (sqrt t)))
273.0ms	(* (/ (+ 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 (29.0ms)

Iter	Nodes	Cost
0	1547	4462
1	5002	4218

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

regimes464.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	41
1	62	41
2	62	41

end0.0ms

sample588.0ms

Algorithm

intervals

Results

341.0ms	5720×	body	80	nan
62.0ms	256×	body	640	valid
15.0ms	82×	body	320	valid
3.0ms	23×	body	160	valid
3.0ms	26×	body	80	valid
1.0ms	4×	body	1280	valid