Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	213×	body	160	nan
10.0ms	438×	body	80	nan
7.0ms	256×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	5
1	12	5
2	12	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 28.1b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1.0))))
0.0b	(+ x (sqrt (- (* x x) 1.0)))
26.2b	(sqrt (- (* x x) 1.0))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
10×	`sqrt-prod`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp` `difference-of-squares`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `sqrt-div` `flip-+` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `rem-log-exp` `associate-l` `sum-log` `log-pow` `*-commutative` `flip--` `unswap-sqr`

Counts

3 → 58

Calls

3 calls:

11.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
11.0ms	(+ x (sqrt (- (* x x) 1.0)))
16.0ms	(sqrt (- (* x x) 1.0))

series329.0ms

Counts

3 → 9

Calls

3 calls:

206.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
70.0ms	(+ x (sqrt (- (* x x) 1.0)))
52.0ms	(sqrt (- (* x x) 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	357	472
1	1291	436
2	5001	427

prune162.0ms

Filtered

67 candidates to 54 candidates (80.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	65	2	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	2	68

Merged error: 0b

Counts

68 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- x (sqrt 1.0)))
0.0b	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
22×	`sqrt-prod`
14×	`sqrt-div`
11×	`add-cube-cbrt`
10×	`pow1`
9×	`associate-r` `associate-l`
7×	`add-exp-log`
6×	`add-cbrt-cube` `add-log-exp`
5×	`log-prod` `flip3-+` `flip-+` `distribute-lft-out`
4×	`expm1-log1p-u` `frac-times` `flip3--` `flip--` `log1p-expm1-u` `difference-of-squares` `unswap-sqr`
3×	`fma-def` `sqrt-pow1` `pow1/2` `pow-prod-down`
2×	`log-div` `associate-r/` `associate-l/` `distribute-lft-out--`
1×	`+-commutative` `rem-sqrt-square` `sqrt-unprod` `rem-log-exp` `prod-exp` `sum-log` `log-pow` `*-commutative` `cbrt-unprod`

Counts

4 → 100

Calls

4 calls:

9.0ms	(sqrt (- x (sqrt 1.0)))
15.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
15.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series719.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(sqrt (- x (sqrt 1.0)))
296.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
149.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
198.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	527	1217
1	1862	1096
2	5001	1079

prune310.0ms

Filtered

112 candidates to 87 candidates (77.7%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	113	1	114

Merged error: 0b

Counts

114 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.5b	(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`sqrt-prod`
57×	`add-sqr-sqrt`
36×	`sqrt-div`
31×	`associate-l`
27×	`pow1`
26×	`associate-r`
21×	`add-cube-cbrt`
20×	`distribute-lft-out`
16×	`swap-sqr`
13×	`flip3-+` `flip-+`
12×	`frac-times` `sqrt-pow1` `pow1/2` `unswap-sqr`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down`
6×	`flip3--` `associate-r/` `associate-l/` `flip--` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `difference-of-squares`
3×	`fma-def` `sqrt-unprod` `prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`distribute-lft-out--`
1×	`+-commutative` `pow2` `pow-plus` `sum-log` `rem-square-sqrt`

Counts

4 → 177

Calls

4 calls:

15.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
39.0ms	(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

series725.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
212.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
151.0ms	(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	472	2310
1	1876	2072
2	5001	2025

prune546.0ms

Filtered

189 candidates to 117 candidates (61.9%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	189	1	190

Merged error: 0b

Counts

190 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms

sample1.4s

Algorithm

intervals

Results

388.0ms	17075×	body	80	nan
359.0ms	7816×	body	160	nan
233.0ms	8000×	body	80	valid