Details

analyze2.7s

Algorithm

sampling

Space saved by range analysis: 0.243902%

Space saved by search: 11.93407%

Guaranteed chance to sample good point: 34.706858%

sample34.0ms

Algorithm

intervals

Results

13.0ms	256×	body	80	valid
2.0ms	40×	body	80	nan
1.0ms	28×	body	80	invalid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune5.0ms

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: 26.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
4.9b	(* (* x y) z)
8.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
8.0ms	(sqrt (- (* z z) (* t a)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
31.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune132.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 2.8b

Counts

89 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
1.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
34.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	428	1014
1	2153	912
2	5002	894

prune124.0ms

Filtered

82 candidates to 124 candidates (-51.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	124	8	132

Merged error: 2.8b

Counts

132 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(* y (/ z (sqrt (- (* z z) (* t a)))))
0.8b	(- (* z z) (* t a))
1.5b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(- (* z z) (* t a))
11.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(- (* z z) (* t a))
34.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	400	774
1	1768	676
2	5001	668

prune110.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	104	8	112

Merged error: 2.8b

Counts

112 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.8b	(- (* z z) (* t a))
1.5b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
26.3b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt` `*-un-lft-identity`
33×	`sqrt-prod`
25×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
3×	`flip3--` `flip--`
2×	`frac-2neg` `prod-exp` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/r/`

Counts

4 → 132

Calls

4 calls:

6.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
9.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(/ (sqrt (- (* z z) (* t a))) z)
7.0ms	(- (* z z) (* t a))
31.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
16.0ms	(sqrt (- (* z z) (* t a)))

simplify63.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	512	1325
1	2358	1230
2	5002	1214

prune109.0ms

Filtered

99 candidates to 144 candidates (-45.5%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	144	8	152

Merged error: 2.8b

Counts

152 → 8

Details

analyze2.7s

sample34.0ms

simplify10.0ms

prune5.0ms

localize11.0ms

rewrite27.0ms

series57.0ms

simplify51.0ms

prune132.0ms

localize11.0ms

rewrite30.0ms

series66.0ms

simplify61.0ms

prune124.0ms

localize11.0ms

rewrite33.0ms

series74.0ms

simplify49.0ms

prune110.0ms

localize11.0ms

rewrite27.0ms

series68.0ms

simplify63.0ms

prune109.0ms

regimes866.0ms

bsearch1.0ms

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