Details

sample27.0ms

Algorithm

intervals

Results

9.0ms	248×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	16×	body	320	valid
2.0ms	9×	body	1280	valid
0.0ms	4×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1493	6
6	3393	6
7	5002	6

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: 25.5b

Counts

2 → 1

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.9b	(+ x (/ (* (- y x) (- z t)) (- a t)))
19.2b	(/ (* (- y x) (- z t)) (- a t))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 81

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
7.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
12.0ms	(/ (* (- y x) (- z t)) (- a t))

series303.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y x) (- z t))
156.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
113.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	468	583
1	2162	534
2	5003	534

prune224.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 2.9b

Counts

91 → 9

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.9b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.4b	(/ (- y x) (/ (- a t) (- z t)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

330×	`times-frac`
323×	`*-un-lft-identity`
321×	`add-sqr-sqrt`
113×	`add-cube-cbrt`
104×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
15×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
9×	`flip3--` `flip--`
8×	`div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `div-sub`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `associate-+r-` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 274

Calls

3 calls:

8.0ms	(/ (- a t) (- z t))
37.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
20.0ms	(/ (- y x) (/ (- a t) (- z t)))

series400.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(/ (- a t) (- z t))
157.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
198.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify109.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1030	3053
1	4263	2984
2	5001	2984

prune555.0ms

Filtered

283 candidates to 172 candidates (60.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	275	8	283
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	281	11	292

Merged error: 2.6b

Counts

292 → 11

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.9b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.2b	(* (- y x) (/ (- z t) (- a t)))

rewrite32.0ms

Algorithm

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:

7.0ms	(/ (- z t) (- a t))
3.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
16.0ms	(* (- y x) (/ (- z t) (- a t)))

series315.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms	(/ (- z t) (- a t))
149.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
115.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify52.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	476	869
1	2018	820
2	5002	820

prune243.0ms

Filtered

128 candidates to 87 candidates (68.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	128	11	139

Merged error: 2.6b

Counts

139 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- z t))
0.2b	(* (- a t) (/ 1 (- z t)))
2.4b	(/ (- y x) (* (- a t) (/ 1 (- z t))))
3.1b	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
37×	`times-frac`
32×	`add-exp-log`
26×	`add-cube-cbrt`
21×	`associate-r`
20×	`add-cbrt-cube`
11×	`div-exp`
10×	`associate-/r/` `distribute-lft-out--` `difference-of-squares`
8×	`prod-exp` `associate-/l*`
7×	`pow1` `flip3--` `flip--`
6×	`cbrt-undiv` `associate-/r*` `add-log-exp`
5×	`associate-l`
4×	`frac-times` `associate-*l/` `cbrt-unprod`
3×	`rec-exp` `1-exp` `div-inv` `unswap-sqr`
2×	`frac-2neg` `div-sub` `associate-*r/` `clear-num` `un-div-inv` `associate-/l/`
1×	`+-commutative` `associate-+r-` `pow-flip` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `distribute-lft-out` `inv-pow`

Counts

4 → 142

Calls

4 calls:

5.0ms	(/ 1 (- z t))
13.0ms	(* (- a t) (/ 1 (- z t)))
18.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
8.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (- z t))
52.0ms	(* (- a t) (/ 1 (- z t)))
197.0ms	(/ (- y x) (* (- a t) (/ 1 (- z t))))
155.0ms	(+ x (/ (- y x) (* (- a t) (/ 1 (- z t)))))

simplify61.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	559	958
1	2445	830
2	5002	783

prune252.0ms

Filtered

154 candidates to 93 candidates (60.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	153	12	165

Merged error: 2.6b

Counts

165 → 12

Details

sample27.0ms

simplify67.0ms

prune2.0ms

localize14.0ms

rewrite31.0ms

series303.0ms

simplify54.0ms

prune224.0ms

localize9.0ms

rewrite85.0ms

series400.0ms

simplify109.0ms

prune555.0ms

localize9.0ms

rewrite32.0ms

series315.0ms

simplify52.0ms

prune243.0ms

localize10.0ms

rewrite49.0ms

series437.0ms

simplify61.0ms

prune252.0ms

regimes290.0ms

bsearch3.0ms

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