Details

sample43.0ms

Algorithm

intervals

Results

11.0ms	250×	body	160	nan
10.0ms	533×	body	80	nan
7.0ms	256×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (sqrt (- (* x x) 1.0)))
31.2b	(sqrt (- (* x x) 1.0))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

5×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `sum-log` `flip--` `flip-+` `distribute-lft-out` `difference-of-squares`

Counts

2 → 28

Calls

2 calls:

9.0ms	(+ x (sqrt (- (* x x) 1.0)))
5.0ms	(sqrt (- (* x x) 1.0))

series124.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ x (sqrt (- (* x x) 1.0)))
54.0ms	(sqrt (- (* x x) 1.0))

simplify75.0ms

Algorithm

egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	217	221
1	657	211
2	2555	205
3	5001	204

prune88.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`sqrt-prod`
12×	`sqrt-div`
10×	`*-un-lft-identity`
9×	`associate-r`
7×	`associate-l`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `frac-times` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp` `unswap-sqr`
3×	`flip3--` `pow-prod-down` `flip--`
2×	`sqrt-pow1` `pow1/2` `associate-r/` `associate-l/` `difference-of-squares`
1×	`+-commutative` `sqrt-unprod` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 53

Calls

2 calls:

2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
29.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series352.0ms

Counts

2 → 6

Calls

2 calls:

146.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
206.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	656
1	1271	612
2	5002	600

prune160.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
0.4b	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
0.4b	(* (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)))))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
51×	`sqrt-prod`
38×	`sqrt-div`
29×	`*-un-lft-identity`
28×	`pow1`
24×	`associate-r`
21×	`add-cube-cbrt`
20×	`associate-l`
13×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+`
12×	`frac-times` `unswap-sqr`
10×	`add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down`
8×	`swap-sqr`
6×	`flip3--` `associate-r/` `associate-l/` `flip--`
5×	`pow-prod-up`
4×	`add-log-exp` `difference-of-squares`
3×	`sqrt-unprod` `prod-exp` `pow-sqr` `*-commutative` `cbrt-unprod`
2×	`distribute-lft-out` `distribute-lft-out--`
1×	`pow2` `rem-sqrt-square` `pow-plus` `rem-square-sqrt`

Counts

4 → 156

Calls

4 calls:

3.0ms	(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
32.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
30.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
16.0ms	(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

series763.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
203.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
203.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
156.0ms	(* (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))) (sqrt (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	480	2217
1	1880	2019
2	5001	1975

prune693.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	20
1	15	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

343.0ms	7673×	body	160	nan
313.0ms	16296×	body	80	nan
218.0ms	8000×	body	80	valid