Details

analyze967.0ms (26.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

sample24.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	24×	body	80	invalid

simplify121.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4786	11
1	4786	11

prune13.0ms (0.3%)

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: 0.1b

Counts

2 → 2

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+ x (* (- y z) (/ t (- a z))))
0.0b	(/ t (- a z))
8.9b	(* (- y z) (/ t (- a z)))

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-l` `associate-/r*` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`associate-/l*`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`+-commutative` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 94

Calls

3 calls:

12.0ms	(* (- y z) (/ t (- a z)))
5.0ms	(/ t (- a z))
3.0ms	(+ x (* (- y z) (/ t (- a z))))

series48.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (* (- y z) (/ t (- a z))))
16.0ms	(* (- y z) (/ t (- a z)))
7.0ms	(/ t (- a z))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4978	1059
1	4978	1059

prune162.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	9	103
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	95	10	105

Merged error: 0.0b

Counts

105 → 10

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
2.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))

rewrite51.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
55×	`cbrt-prod`
38×	`associate-r`
36×	`times-frac`
31×	`add-cube-cbrt`
30×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
18×	`add-cbrt-cube`
15×	`flip3--` `flip--`
13×	`pow1`
12×	`distribute-lft-out--`
10×	`swap-sqr` `associate-/r/` `difference-of-squares` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
8×	`pow1/3`
7×	`cbrt-undiv` `div-exp`
5×	`associate-r/` `associate-l/`
4×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`pow2` `pow-plus`

Counts

4 → 163

Calls

4 calls:

28.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))
10.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series116.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (- a z))
30.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
26.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ t (cbrt (- a z))))
26.0ms	(cbrt (- a z))

simplify82.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4946	2242
1	4946	2242

prune254.0ms (6.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	175	0	175
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	175	10	185

Merged error: 0.0b

Counts

185 → 10

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(* (- y z) t)
0.0b	(+ x (* (* (- y z) t) (/ 1 (- a z))))
0.0b	(/ 1 (- a z))
8.9b	(* (* (- y z) t) (/ 1 (- a z)))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
41×	`*-un-lft-identity`
32×	`add-exp-log`
30×	`times-frac`
25×	`add-cube-cbrt`
24×	`associate-r`
20×	`add-cbrt-cube`
13×	`prod-exp`
12×	`pow1`
8×	`associate-*l/` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `associate-l` `add-log-exp`
5×	`flip3--` `associate-/r*` `flip--`
4×	`pow-prod-down` `associate-/r/`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*`
2×	`frac-times` `*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `frac-2neg` `flip3-+` `associate-*r/` `clear-num` `sum-log` `un-div-inv` `flip-+` `inv-pow` `unswap-sqr`

Counts

4 → 124

Calls

4 calls:

13.0ms	(* (* (- y z) t) (/ 1 (- a z)))
8.0ms	(* (- y z) t)
5.0ms	(/ 1 (- a z))
4.0ms	(+ x (* (* (- y z) t) (/ 1 (- a z))))

series51.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ x (* (* (- y z) t) (/ 1 (- a z))))
15.0ms	(* (* (- y z) t) (/ 1 (- a z)))
7.0ms	(* (- y z) t)
4.0ms	(/ 1 (- a z))

simplify41.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4978	1230
1	4978	1230

prune185.0ms (5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	136	10	146

Merged error: 0.0b

Counts

146 → 10

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

3.8b	(- (* a a) (* z z))
7.5b	(/ t (- (* a a) (* z z)))
10.6b	(* (- y z) (/ t (- (* a a) (* z z))))
13.0b	(* (* (- y z) (/ t (- (* a a) (* z z)))) (+ a z))

rewrite40.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
25×	`times-frac`
23×	`add-cube-cbrt`
22×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
18×	`frac-times`
13×	`associate-*l/`
11×	`pow1` `flip3--` `flip--`
9×	`difference-of-squares`
7×	`prod-exp` `cbrt-unprod`
6×	`flip3-+` `associate-r/` `associate-l*` `flip-+` `add-log-exp`
4×	`pow-prod-down` `associate-/r*` `associate-/r/`
3×	`cbrt-undiv` `div-exp` `associate-/l*`
2×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `clear-num` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 128

Calls

4 calls:

14.0ms	(* (* (- y z) (/ t (- (* a a) (* z z)))) (+ a z))
12.0ms	(* (- y z) (/ t (- (* a a) (* z z))))
5.0ms	(/ t (- (* a a) (* z z)))
4.0ms	(- (* a a) (* z z))

series76.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* (- y z) (/ t (- (* a a) (* z z)))) (+ a z))
23.0ms	(* (- y z) (/ t (- (* a a) (* z z))))
15.0ms	(/ t (- (* a a) (* z z)))
6.0ms	(- (* a a) (* z z))

simplify65.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4973	2145
1	4973	2145

prune164.0ms (4.4%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	3	3	6
Picked	0	1	1
Done	0	3	3
Total	140	10	150

Merged error: 0.0b

Counts

150 → 10

regimes476.0ms (12.9%)

Accuracy

Total 1.9b remaining (99%)

Threshold costs 0b (0%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	22
1	27	22

end0.0ms (0%)

sample588.0ms (15.9%)

Algorithm

1×

intervals

Results

301.0ms	7998×	body	80	valid
26.0ms	737×	body	80	invalid
0.0ms	1×	body	640	valid
0.0ms	1×	body	160	valid

Details

analyze967.0ms (26.2%)

sample24.0ms (0.6%)

simplify121.0ms (3.3%)

prune13.0ms (0.3%)

localize13.0ms (0.3%)

rewrite24.0ms (0.6%)

series48.0ms (1.3%)

simplify65.0ms (1.8%)

prune162.0ms (4.4%)

localize15.0ms (0.4%)

rewrite51.0ms (1.4%)

series116.0ms (3.1%)

simplify82.0ms (2.2%)

prune254.0ms (6.9%)

localize10.0ms (0.3%)

rewrite34.0ms (0.9%)

series51.0ms (1.4%)

simplify41.0ms (1.1%)

prune185.0ms (5%)

localize13.0ms (0.4%)

rewrite40.0ms (1.1%)

series76.0ms (2.1%)

simplify65.0ms (1.8%)

prune164.0ms (4.4%)

regimes476.0ms (12.9%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample588.0ms (15.9%)

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