Details

analyze1.0s (23%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

sample31.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	214×	body	80	valid
2.0ms	16×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	28×	body	80	invalid
1.0ms	5×	body	1280	valid
1.0ms	8×	body	160	valid

simplify112.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4885	13
1	4885	13

prune20.0ms (0.4%)

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: 12.4b

Counts

2 → 1

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.6b	(+ x (* (- y z) (/ (- t x) (- a z))))
5.0b	(* (- y z) (/ (- t x) (- a z)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 119

Calls

3 calls:

17.0ms	(* (- y z) (/ (- t x) (- a z)))
7.0ms	(/ (- t x) (- a z))
4.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))

series100.0ms (2.2%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ x (* (- y z) (/ (- t x) (- a z))))
38.0ms	(* (- y z) (/ (- t x) (- a z)))
13.0ms	(/ (- t x) (- a z))

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5183	1602

prune216.0ms (4.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	115	13	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	13	129

Merged error: 3.8b

Counts

129 → 13

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.2b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite51.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

35.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
4.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series164.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
26.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))

simplify39.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5314	2524

prune220.0ms (4.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	146	13	159

Merged error: 3.5b

Counts

159 → 13

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
1.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
7.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))

rewrite40.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-div`
25×	`add-exp-log`
20×	`frac-times` `flip3--` `flip--`
17×	`associate-l`
16×	`add-sqr-sqrt`
15×	`add-cbrt-cube`
14×	`-un-lft-identity` `associate-r/`
11×	`prod-exp` `cbrt-unprod`
10×	`cbrt-prod`
9×	`pow1`
8×	`add-cube-cbrt` `associate-/r/`
7×	`associate-*l/`
6×	`times-frac` `add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow-prod-down` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 100

Calls

4 calls:

25.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
5.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))

series287.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

179.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x))))
54.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (- t x)) (cbrt (- t x)))) (/ (cbrt (- t x)) (cbrt (- a z)))))
28.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))

simplify46.0ms (1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5013	2202

prune196.0ms (4.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	112	13	125

Merged error: 3.5b

Counts

125 → 13

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.3b	(* (- t x) (/ 1 (- a z)))
4.8b	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
5.0b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 146

Calls

4 calls:

17.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
13.0ms	(* (- t x) (/ 1 (- a z)))
5.0ms	(/ 1 (- a z))
4.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))

series104.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(+ x (* (- y z) (* (- t x) (/ 1 (- a z)))))
35.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))
13.0ms	(* (- t x) (/ 1 (- a z)))
4.0ms	(/ 1 (- a z))

simplify45.0ms (1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5717	1769

prune183.0ms (4.1%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	158	13	171

Merged error: 3.5b

Counts

171 → 13

regimes544.0ms (12.2%)

Accuracy

Total 6.8b remaining (66.1%)

Threshold costs 0b (0%)

bsearch61.0ms (1.4%)

Steps

Iters	Range		Point
9	6.993586934865164e-116	5.485377558850572e-107	1.2161147335711477e-113
10	-8.727727116639551e-172	-8.488667879315993e-182	-4.807158068872457e-172

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	73	78
1	73	78

end0.0ms (0%)

sample803.0ms (18%)

Algorithm

1×

intervals

Results

267.0ms	6525×	body	80	valid
79.0ms	543×	body	640	valid
48.0ms	271×	body	1280	valid
47.0ms	1181×	body	80	invalid
45.0ms	391×	body	320	valid
19.0ms	256×	body	160	valid
3.0ms	14×	body	2560	valid

Details

analyze1.0s (23%)

sample31.0ms (0.7%)

simplify112.0ms (2.5%)

prune20.0ms (0.4%)

localize9.0ms (0.2%)

rewrite33.0ms (0.7%)

series100.0ms (2.2%)

simplify45.0ms (1%)

prune216.0ms (4.8%)

localize13.0ms (0.3%)

rewrite51.0ms (1.2%)

series164.0ms (3.7%)

simplify39.0ms (0.9%)

prune220.0ms (4.9%)

localize19.0ms (0.4%)

rewrite40.0ms (0.9%)

series287.0ms (6.4%)

simplify46.0ms (1%)

prune196.0ms (4.4%)

localize10.0ms (0.2%)

rewrite45.0ms (1%)

series104.0ms (2.3%)

simplify45.0ms (1%)

prune183.0ms (4.1%)

regimes544.0ms (12.2%)

bsearch61.0ms (1.4%)

simplify2.0ms (0%)

end0.0ms (0%)

sample803.0ms (18%)

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