Details

sample45.0ms

Algorithm

intervals

Results

11.0ms	244×	body	160	nan
10.0ms	490×	body	80	nan
8.0ms	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: 30.6b

localize10.0ms

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)))
28.5b	(sqrt (- (* x x) 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

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

series323.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
69.0ms	(+ x (sqrt (- (* x x) 1.0)))
50.0ms	(sqrt (- (* x x) 1.0))

simplify134.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (129.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5002	365

prune129.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 3 expressions with local error:

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))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 67

Calls

3 calls:

2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
2.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
32.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series631.0ms

Counts

3 → 9

Calls

3 calls:

287.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
148.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
197.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify53.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	440	941
1	1553	864
2	5001	848

prune214.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x (sqrt 1.0))))
0.5b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.5b	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
0.5b	(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

rewrite203.0ms

Algorithm

rewrite-expression-head

Rules

484×	`sqrt-div`
144×	`frac-times`
102×	`sqrt-prod`
89×	`pow1`
84×	`sqrt-pow1`
64×	`add-sqr-sqrt`
63×	`pow-prod-down`
61×	`flip3-+` `flip-+`
60×	`flip3--` `flip--`
48×	`associate-r/` `associate-l/`
42×	`pow1/2`
28×	`*-un-lft-identity`
25×	`associate-r`
21×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`add-cube-cbrt` `unswap-sqr`
12×	`pow-prod-up`
10×	`prod-exp` `cbrt-unprod`
8×	`pow-sqr`
7×	`sqrt-unprod`
4×	`add-log-exp` `difference-of-squares`
3×	`*-commutative` `distribute-lft-out`
2×	`rem-sqrt-square` `pow-plus` `distribute-lft-out--`
1×	`pow2` `swap-sqr` `rem-square-sqrt`

Counts

4 → 264

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
35.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
37.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
99.0ms	(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt (sqrt (+ x (sqrt 1.0))))
367.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
390.0ms	(* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0)))))
198.0ms	(* (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))) (* (sqrt (sqrt (+ x (sqrt 1.0)))) (sqrt (sqrt (- x (sqrt 1.0))))))

simplify145.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	1167	5584
1	4469	4837
2	5001	4816

prune790.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes17.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

end0.0ms

sample1.3s

Algorithm

intervals

Results

370.0ms	7745×	body	160	nan
343.0ms	16329×	body	80	nan
235.0ms	8000×	body	80	valid