Details

analyze693.0ms (19.6%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

sample23.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

valid

simplify45.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4937	13
1	4937	13

prune12.0ms (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: 0.0b

Counts

2 → 2

localize9.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(- (/ z y) (/ t (* 2.0 z)))
0.0b	(+ x (/ -1 (- (/ z y) (/ t (* 2.0 z)))))
0.8b	(/ -1 (- (/ z y) (/ t (* 2.0 z))))

rewrite43.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
23×	`times-frac`
14×	`add-cube-cbrt`
10×	`difference-of-squares`
7×	`add-log-exp`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
3×	`pow1` `associate-/r/` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-exp` `clear-num` `sum-log` `flip-+` `div-inv` `distribute-lft-out`

Counts

3 → 69

Calls

3 calls:

19.0ms	(+ x (/ -1 (- (/ z y) (/ t (* 2.0 z)))))
12.0ms	(/ -1 (- (/ z y) (/ t (* 2.0 z))))
10.0ms	(- (/ z y) (/ t (* 2.0 z)))

series26.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

11.0ms	(+ x (/ -1 (- (/ z y) (/ t (* 2.0 z)))))
8.0ms	(/ -1 (- (/ z y) (/ t (* 2.0 z))))
6.0ms	(- (/ z y) (/ t (* 2.0 z)))

simplify46.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5516	1239

prune148.0ms (4.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	5	78
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	74	6	80

Merged error: 0b

Counts

80 → 6

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(/ -1 (- (/ z y) (/ t (* z 2.0))))
14.3b	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
14.3b	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
14.3b	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))

rewrite52.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`add-sqr-sqrt`
85×	`times-frac`
75×	`cbrt-prod`
71×	`*-un-lft-identity`
45×	`add-cube-cbrt`
26×	`difference-of-squares`
13×	`distribute-lft-out--`
12×	`associate-/r/`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `flip3--` `frac-sub` `flip--` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3` `associate-/l*`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num`

Counts

4 → 144

Calls

4 calls:

13.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
11.0ms	(/ -1 (- (/ z y) (/ t (* z 2.0))))
11.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
11.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))

series105.0ms (3%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
32.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
31.0ms	(cbrt (/ -1 (- (/ z y) (/ t (* z 2.0)))))
8.0ms	(/ -1 (- (/ z y) (/ t (* z 2.0))))

simplify73.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4963	3185
1	4963	3185

prune532.0ms (15%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	156	6	162

Merged error: 0b

Counts

162 → 6

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z))))
0.4b	(/ -1 (- (* z (* z 2.0)) (* y t)))
0.9b	(- (* z (* z 2.0)) (* y t))
17.3b	(* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z)))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
15×	`associate-l`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
8×	`add-log-exp`
6×	`pow-prod-down`
4×	`cbrt-undiv` `div-exp` `associate-/r/`
3×	`flip3--` `associate-/r` `flip--` `associate-/l`
2×	`div-inv`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `associate-r` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

4 → 91

Calls

4 calls:

13.0ms	(* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z)))
7.0ms	(/ -1 (- (* z (* z 2.0)) (* y t)))
5.0ms	(- (* z (* z 2.0)) (* y t))
4.0ms	(+ x (* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z))))

series51.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

20.0ms	(+ x (* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z))))
15.0ms	(* (/ -1 (- (* z (* z 2.0)) (* y t))) (* y (* 2.0 z)))
8.0ms	(/ -1 (- (* z (* z 2.0)) (* y t)))
8.0ms	(- (* z (* z 2.0)) (* y t))

simplify55.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5002	1644

prune176.0ms (5%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	103	6	109

Merged error: 0b

Counts

109 → 6

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0))))))
0.6b	(/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))
0.8b	(/ 1 (- (/ z y) (/ t (* z 2.0))))
24.1b	(/ (+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))) (+ (/ 1 (- (/ z y) (/ t (* z 2.0)))) x))

rewrite79.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`times-frac`
27×	`add-cube-cbrt`
20×	`associate-/r/`
15×	`add-exp-log`
13×	`add-cbrt-cube`
12×	`associate-/r*`
9×	`frac-times` `flip3--` `frac-sub` `flip--` `associate-/l*`
8×	`distribute-lft-out` `difference-of-squares`
7×	`div-inv`
6×	`add-log-exp`
5×	`pow1` `div-exp`
4×	`cbrt-undiv` `distribute-lft-out--`
3×	`frac-2neg` `flip3-+` `associate-r/` `associate-l/` `clear-num` `flip-+`
2×	`associate-/l/`
1×	`+-commutative` `rec-exp` `pow-flip` `1-exp` `prod-exp` `sum-log` `cbrt-unprod` `inv-pow`

Counts

4 → 132

Calls

4 calls:

28.0ms	(/ (+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))) (+ (/ 1 (- (/ z y) (/ t (* z 2.0)))) x))
24.0ms	(/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))
11.0ms	(/ 1 (- (/ z y) (/ t (* z 2.0))))
11.0ms	(+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0))))))

series68.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))) (+ (/ 1 (- (/ z y) (/ t (* z 2.0)))) x))
19.0ms	(+ (* x x) (/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0))))))
13.0ms	(/ -1 (* (- (/ z y) (/ t (* z 2.0))) (- (/ z y) (/ t (* z 2.0)))))
7.0ms	(/ 1 (- (/ z y) (/ t (* z 2.0))))

simplify58.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5193	4073

prune319.0ms (9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	144	6	150

Merged error: 0b

Counts

150 → 6

regimes261.0ms (7.4%)

Accuracy

Total 0.1b remaining (72%)

Threshold costs 0.1b (72%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	13
1	30	13

end0.0ms (0%)

sample586.0ms (16.6%)

Algorithm

1×

intervals

Results

375.0ms

8000×

body

valid

Details

analyze693.0ms (19.6%)

sample23.0ms (0.6%)

simplify45.0ms (1.3%)

prune12.0ms (0.3%)

localize9.0ms (0.3%)

rewrite43.0ms (1.2%)

series26.0ms (0.7%)

simplify46.0ms (1.3%)

prune148.0ms (4.2%)

localize14.0ms (0.4%)

rewrite52.0ms (1.5%)

series105.0ms (3%)

simplify73.0ms (2.1%)

prune532.0ms (15%)

localize13.0ms (0.4%)

rewrite31.0ms (0.9%)

series51.0ms (1.4%)

simplify55.0ms (1.6%)

prune176.0ms (5%)

localize15.0ms (0.4%)

rewrite79.0ms (2.2%)

series68.0ms (1.9%)

simplify58.0ms (1.7%)

prune319.0ms (9%)

regimes261.0ms (7.4%)

bsearch0.0ms (0%)

simplify1.0ms (0%)

end0.0ms (0%)

sample586.0ms (16.6%)

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