Details

sample427.0ms

Algorithm

intervals

Results

216.0ms	3791×	body	80	nan
40.0ms	168×	body	640	valid
8.0ms	47×	body	320	valid
2.0ms	15×	body	160	valid
1.0ms	23×	body	80	valid
1.0ms	3×	body	1280	valid

simplify27.0ms

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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize28.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ y 1.0)) (sqrt y))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))
5.3b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite173.0ms

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:

41.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
43.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
43.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
42.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series253.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
65.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
64.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify42.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

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

prune422.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.3b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))
5.3b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite209.0ms

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:

58.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
41.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
61.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
44.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series331.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
69.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
63.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	634	1073
1	2368	978
2	5001	942

prune576.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
5.3b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite198.0ms

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:

45.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
61.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
45.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
41.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series604.0ms

Counts

4 → 12

Calls

4 calls:

341.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
133.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
61.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify76.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	728	1298
1	2760	1176
2	5001	1134

prune663.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
1.7b	(- (sqrt (+ t 1.0)) (sqrt t))
5.3b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite197.0ms

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:

45.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
59.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
42.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
45.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series385.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
123.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
65.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify77.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	728	1298
1	2760	1176
2	5001	1134

prune706.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.7b

regimes587.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	26
1	53	26
2	53	26

end0.0ms

sample533.0ms

Algorithm

intervals

Results

272.0ms	4716×	body	80	nan
55.0ms	215×	body	640	valid
11.0ms	62×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	29×	body	80	valid
1.0ms	3×	body	1280	valid