Details

sample418.0ms

Algorithm

intervals

Results

216.0ms	3573×	body	80	nan
39.0ms	152×	body	640	valid
12.0ms	58×	body	320	valid
2.0ms	29×	body	80	valid
2.0ms	14×	body	160	valid
1.0ms	3×	body	1280	valid

simplify29.0ms

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: 3.2b

localize26.0ms

Local error

Found 4 expressions with local error:

2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))
2.8b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite174.0ms

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:

43.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
43.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
45.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
41.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series255.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
65.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
65.0ms	(- (sqrt (+ z 1.0)) (sqrt z))
62.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune410.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.5b

localize30.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))
2.7b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite191.0ms

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)))
42.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
45.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
42.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series333.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
66.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
61.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
67.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify66.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (55.0ms)

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

prune555.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite193.0ms

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:

57.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
44.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
42.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
44.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series405.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (+ 1.0 0) (+ (sqrt (+ y 1.0)) (sqrt y)))
131.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
69.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify73.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	721	1296
1	2734	1180
2	5001	1137

prune681.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
1.9b	(log (exp (- (sqrt (+ x 1.0)) (sqrt x))))
2.6b	(- (sqrt (+ t 1.0)) (sqrt t))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

66×	`*-un-lft-identity`
41×	`add-sqr-sqrt`
40×	`sqrt-prod`
19×	`distribute-lft-out`
18×	`times-frac`
17×	`add-cube-cbrt`
12×	`difference-of-squares`
11×	`log-pow`
10×	`exp-prod`
9×	`distribute-lft-out--`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1` `log-prod`
3×	`sub-neg` `associate-/l*`
2×	`flip3--` `diff-log` `exp-sum` `associate-/r/` `flip--`
1×	`cbrt-undiv` `log-div` `frac-2neg` `flip3-+` `exp-diff` `div-exp` `rem-log-exp` `clear-num` `flip-+` `div-inv`

Counts

4 → 104

Calls

4 calls:

44.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
92.0ms	(log (exp (- (sqrt (+ x 1.0)) (sqrt x))))
42.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
44.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series340.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ 1.0 (+ (sqrt (+ z 1.0)) (sqrt z)))
67.0ms	(log (exp (- (sqrt (+ x 1.0)) (sqrt x))))
61.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
71.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify54.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	511	945
1	1777	854
2	5002	821

prune578.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

regimes691.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	26
1	52	26
2	52	26

end0.0ms

sample707.0ms

Algorithm

intervals

Results

373.0ms	6257×	body	80	nan
64.0ms	255×	body	640	valid
18.0ms	91×	body	320	valid
3.0ms	23×	body	160	valid
2.0ms	40×	body	80	valid
2.0ms	6×	body	1280	valid