Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	107×	body	2560	nan
12.0ms	82×	body	1280	nan
10.0ms	256×	body	80	valid
9.0ms	263×	body	80	nan
5.0ms	46×	body	640	nan
2.0ms	18×	body	320	nan
1.0ms	13×	body	160	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune6.0ms

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: 32.1b

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)))
29.9b	(sqrt (- (* x x) 1.0))

rewrite17.0ms

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:

6.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
6.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

series19.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(log (+ x (sqrt (- (* x x) 1.0))))
5.0ms	(+ x (sqrt (- (* x x) 1.0)))
4.0ms	(sqrt (- (* x x) 1.0))

simplify136.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 3 (130.0ms)

Iter	Nodes	Cost
0	316	408
1	1042	379
2	4663	366
3	5001	365

prune86.0ms

Filtered

43 candidates to 52 candidates (-20.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	51	1	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	1	53

Merged error: 0.0b

Counts

53 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
2.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

series33.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
13.0ms	(log (+ x (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))))
11.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	426	932
1	1622	865
2	5001	852

prune173.0ms

Filtered

58 candidates to 76 candidates (-31.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	1	77

Merged error: 0b

Counts

77 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

12.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
10.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
10.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0))))
23.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
23.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))
23.0ms	(cbrt (* (sqrt (+ x (sqrt 1.0))) (sqrt (- x (sqrt 1.0)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	490	1710
1	1866	1625
2	5002	1599

prune600.0ms

Filtered

88 candidates to 105 candidates (-19.3%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	105	1	106

Merged error: 0b

Counts

106 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	28
1	17	28

end0.0ms

sample2.1s

Algorithm

intervals

Results

543.0ms	2964×	body	2560	nan
360.0ms	2432×	body	1280	nan
311.0ms	8000×	body	80	valid
283.0ms	8269×	body	80	nan
154.0ms	1264×	body	640	nan
57.0ms	632×	body	320	nan
18.0ms	297×	body	160	nan

Details

sample73.0ms

simplify4.0ms

prune6.0ms

localize7.0ms

rewrite17.0ms

series19.0ms

simplify136.0ms

prune86.0ms

localize10.0ms

rewrite19.0ms

series33.0ms

simplify46.0ms

prune173.0ms

localize15.0ms

rewrite49.0ms

series82.0ms

simplify55.0ms

prune600.0ms

simplify1.0ms

end0.0ms

sample2.1s

Profiling