Details

analyze879.0ms

Algorithm

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
24.9%	74.9%	0.2%	13
26.2%	73.6%	0.2%	14

sample25.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
1.0ms	25×	body	80	invalid

simplify114.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	4881	11
1	4881	11

prune14.0ms

Filtered

1 candidates to 1 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: 0.0b

Counts

2 → 2

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (* y (/ (- z t) (- a t))))
0.0b	(/ (- z t) (- a t))
3.9b	(* y (/ (- z t) (- a t)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

76×	`add-sqr-sqrt`
71×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
22×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `associate-l` `flip--`
2×	`cbrt-undiv` `div-exp` `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 → 113

Calls

3 calls:

3.0ms	(+ x (* y (/ (- z t) (- a t))))
7.0ms	(/ (- z t) (- a t))
18.0ms	(* y (/ (- z t) (- a t)))

series51.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(+ x (* y (/ (- z t) (- a t))))
9.0ms	(/ (- z t) (- a t))
16.0ms	(* y (/ (- z t) (- a t)))

simplify34.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5057	1366

prune148.0ms

Filtered

82 candidates to 122 candidates (-48.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	117	5	122
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	117	7	124

Merged error: 0.0b

Counts

124 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))
0.5b	(cbrt (- z t))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

20×	`cbrt-prod`
16×	`add-sqr-sqrt` `*-un-lft-identity`
8×	`add-cube-cbrt` `cbrt-div`
4×	`pow1` `add-exp-log` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

4 → 60

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))
3.0ms	(cbrt (- z t))

series105.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a t))
28.0ms	(cbrt (- z t))
26.0ms	(cbrt (- z t))
26.0ms	(cbrt (- z t))

simplify46.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5273	580

prune110.0ms

Filtered

56 candidates to 72 candidates (-28.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	72	7	79

Merged error: 0.0b

Counts

79 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* y (/ 1 (/ (- a t) (- z t)))))
0.0b	(/ (- a t) (- z t))
0.8b	(/ 1 (/ (- a t) (- z t)))
3.9b	(* y (/ 1 (/ (- a t) (- z t))))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

392×	`times-frac`
336×	`add-sqr-sqrt`
324×	`*-un-lft-identity`
158×	`add-cube-cbrt`
98×	`associate-r`
82×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log` `associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`flip3--` `flip--`
8×	`associate-/l*`
7×	`pow1` `cbrt-undiv` `prod-exp`
6×	`add-log-exp`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`associate-l` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `flip-+` `inv-pow`

Counts

4 → 338

Calls

4 calls:

3.0ms	(+ x (* y (/ 1 (/ (- a t) (- z t)))))
8.0ms	(/ (- a t) (- z t))
12.0ms	(/ 1 (/ (- a t) (- z t)))
31.0ms	(* y (/ 1 (/ (- a t) (- z t))))

series88.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ x (* y (/ 1 (/ (- a t) (- z t)))))
9.0ms	(/ (- a t) (- z t))
17.0ms	(/ 1 (/ (- a t) (- z t)))
31.0ms	(* y (/ 1 (/ (- a t) (- z t))))

simplify66.0ms

Algorithm

egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5117	4579

prune326.0ms

Filtered

203 candidates to 350 candidates (-72.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	347	3	350
Fresh	2	2	4
Picked	1	0	1
Done	2	0	2
Total	352	5	357

Merged error: 0b

Counts

357 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ y (/ (- a t) (- z t))))
0.0b	(/ (- a t) (- z t))
3.9b	(/ y (/ (- a t) (- z t)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

218×	`times-frac`
197×	`*-un-lft-identity`
195×	`add-sqr-sqrt`
91×	`add-cube-cbrt`
52×	`distribute-lft-out--` `difference-of-squares`
36×	`associate-/r*`
11×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/l*`
6×	`flip3--` `flip--` `div-inv`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`pow1`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`+-commutative` `flip3-+` `div-sub` `sum-log` `flip-+` `distribute-lft-out`

Counts

3 → 206

Calls

3 calls:

25.0ms	(+ x (/ y (/ (- a t) (- z t))))
7.0ms	(/ (- a t) (- z t))
11.0ms	(/ y (/ (- a t) (- z t)))

series67.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(+ x (/ y (/ (- a t) (- z t))))
9.0ms	(/ (- a t) (- z t))
26.0ms	(/ y (/ (- a t) (- z t)))

simplify54.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5107	3372

prune180.0ms

Filtered

146 candidates to 215 candidates (-47.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	213	2	215
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	216	4	220

Merged error: 0b

Counts

220 → 4

regimes356.0ms

Accuracy

5.1% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 1.2b

bsearch58.0ms

Steps

Iters	Range	Point
10	4.257588026174734e-196	6.799480672852909e-178	3.463479683183646e-184
7	-1.3694685158537877e-297	-7.57072460689368e-299	-7.963335789005759e-299
6	-4.818927921588728e-73	-1.0432199357999105e-73	-1.0801682615967219e-73

Iters

Range

Point

4.257588026174734e-196

6.799480672852909e-178

3.463479683183646e-184

-1.3694685158537877e-297

-7.57072460689368e-299

-7.963335789005759e-299

-4.818927921588728e-73

-1.0432199357999105e-73

-1.0801682615967219e-73

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	116	63
1	116	63

end0.0ms

sample642.0ms

Algorithm

intervals

Results

311.0ms	7998×	body	80	valid
36.0ms	794×	body	80	invalid
0.0ms	1×	body	1280	valid
0.0ms	1×	body	160	valid

Details

analyze879.0ms

sample25.0ms

simplify114.0ms

prune14.0ms

localize8.0ms

rewrite33.0ms

series51.0ms

simplify34.0ms

prune148.0ms

localize19.0ms

rewrite14.0ms

series105.0ms

simplify46.0ms

prune110.0ms

localize9.0ms

rewrite75.0ms

series88.0ms

simplify66.0ms

prune326.0ms

localize8.0ms

rewrite58.0ms

series67.0ms

simplify54.0ms

prune180.0ms

regimes356.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample642.0ms

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