Details

sample35.0ms

Algorithm

intervals

Results

15.0ms	283×	body	80	valid
5.0ms	99×	body	80	nan

simplify11.0ms

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

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: 25.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.3b	(* (* x y) z)
8.7b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
57.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5001	510

prune210.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	10	89

Merged error: 3.8b

Counts

89 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.4b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.3b	(sqrt (- (* z z) (* t a)))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
48×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
15×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 141

Calls

4 calls:

9.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
24.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series299.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
83.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
62.0ms	(sqrt (- (* z z) (* t a)))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	629	1951
1	3362	1738
2	5001	1614

prune367.0ms

Filtered

153 candidates to 101 candidates (66.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	153	10	163

Merged error: 3.7b

Counts

163 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

2.2b	(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
7.4b	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.3b	(sqrt (- (* z z) (* t a)))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

109×	`add-sqr-sqrt`
87×	`times-frac`
84×	`sqrt-prod`
75×	`add-exp-log`
57×	`add-cbrt-cube`
51×	`add-cube-cbrt` `*-un-lft-identity`
46×	`associate-l`
34×	`associate-r`
31×	`prod-exp`
26×	`div-exp`
22×	`cbrt-unprod`
17×	`cbrt-undiv`
16×	`unswap-sqr`
13×	`pow1`
12×	`sqrt-div`
6×	`frac-times` `associate-*r/`
5×	`1-exp`
4×	`flip3--` `pow-prod-down` `associate-*l/` `associate-/r/` `flip--` `add-log-exp`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative`

Counts

4 → 188

Calls

4 calls:

19.0ms	(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
33.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series276.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(* (/ x 1) (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
53.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
59.0ms	(sqrt (- (* z z) (* t a)))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify158.0ms

Algorithm

egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 2 (114.0ms)

Iter	Nodes	Cost
0	859	3153
1	4291	2707
2	5001	2501

prune553.0ms

Filtered

200 candidates to 121 candidates (60.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	201	9	210

Merged error: 3.7b

Counts

210 → 9

localize31.0ms

Local error

Found 4 expressions with local error:

2.1b	(* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a))))))
5.9b	(* (* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
24.3b	(sqrt (- (* z z) (* t a)))
24.3b	(sqrt (- (* z z) (* t a)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
66×	`associate-r` `sqrt-prod`
60×	`times-frac`
46×	`add-cube-cbrt` `*-un-lft-identity`
30×	`add-exp-log`
24×	`add-cbrt-cube`
13×	`pow1`
12×	`sqrt-div` `prod-exp` `cbrt-unprod`
8×	`unswap-sqr`
7×	`cbrt-prod` `associate-l`
6×	`cbrt-undiv` `div-exp`
4×	`flip3--` `associate-*r/` `pow-prod-down` `associate-/r/` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `*-commutative` `div-inv`
1×	`frac-times` `associate-*l/`

Counts

4 → 150

Calls

4 calls:

27.0ms	(* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a))))))
39.0ms	(* (* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
6.0ms	(sqrt (- (* z z) (* t a)))
6.0ms	(sqrt (- (* z z) (* t a)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

186.0ms	(* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a))))))
151.0ms	(* (* (cbrt x) (/ y (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
58.0ms	(sqrt (- (* z z) (* t a)))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	722	2036
1	4008	1832
2	5002	1800

prune453.0ms

Filtered

162 candidates to 106 candidates (65.4%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	160	11	171

Merged error: 3.7b

Counts

171 → 11

Details

sample35.0ms

simplify11.0ms

prune2.0ms

localize10.0ms

rewrite25.0ms

series197.0ms

simplify52.0ms

prune210.0ms

localize13.0ms

rewrite45.0ms

series299.0ms

simplify83.0ms

prune367.0ms

localize14.0ms

rewrite69.0ms

series276.0ms

simplify158.0ms

prune553.0ms

localize31.0ms

rewrite89.0ms

series463.0ms

simplify104.0ms

prune453.0ms

regimes487.0ms

bsearch3.0ms

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