Details

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 1.437274%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

8.0ms	216×	body	80	valid
2.0ms	14×	body	640	valid
2.0ms	9×	body	1280	valid
1.0ms	37×	body	80	invalid
1.0ms	11×	body	320	valid
0.0ms	6×	body	160	valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune10.0ms

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: 23.4b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
1.7b	(+ x (/ (* (- y x) (- z t)) (- a t)))
16.6b	(/ (* (- 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))

series97.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
54.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
34.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune148.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	12	91

Merged error: 3.8b

Counts

91 → 12

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) (- z t))
1.7b	(+ x (/ (- y x) (/ (- a t) (- z t))))
2.5b	(/ (- y x) (/ (- a t) (- z t)))

rewrite81.0ms

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:

7.0ms	(/ (- a t) (- z t))
40.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
15.0ms	(/ (- y x) (/ (- a t) (- z t)))

series105.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(/ (- a t) (- z t))
48.0ms	(+ x (/ (- y x) (/ (- a t) (- z t))))
46.0ms	(/ (- y x) (/ (- a t) (- z t)))

simplify98.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 1 (20.0ms)

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

prune229.0ms

Filtered

172 candidates to 283 candidates (-64.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	276	7	283
Fresh	4	6	10
Picked	0	1	1
Done	1	0	1
Total	281	14	295

Merged error: 3.8b

Counts

295 → 14

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
1.7b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.5b	(* (- y x) (/ (- z t) (- a t)))

rewrite33.0ms

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

series93.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
51.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
32.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify50.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

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

prune141.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	127	15	142

Merged error: 3.8b

Counts

142 → 15

localize19.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a t))
0.6b	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
0.8b	(* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t))))
6.8b	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

rewrite647.0ms

Algorithm

rewrite-expression-head

Rules

1732×	`times-frac`
1452×	`add-sqr-sqrt`
1242×	`*-un-lft-identity`
1075×	`cbrt-prod`
568×	`add-cube-cbrt`
373×	`associate-r`
337×	`distribute-lft-out--` `difference-of-squares`
117×	`associate-l`
63×	`add-exp-log`
53×	`associate-/r/`
49×	`unswap-sqr`
46×	`associate-/r*`
30×	`cbrt-undiv` `div-exp`
28×	`div-inv`
27×	`flip3--` `add-cbrt-cube` `flip--`
20×	`cbrt-div`
15×	`prod-exp` `cbrt-unprod`
8×	`associate-/l*`
6×	`pow1` `add-log-exp`
2×	`associate-/l/`
1×	`+-commutative` `frac-times` `frac-2neg` `flip3-+` `pow1/3` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `*-commutative` `flip-+`

Counts

4 → 1040

Calls

4 calls:

3.0ms	(cbrt (- a t))
21.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
507.0ms	(* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t))))
3.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

series193.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a t))
65.0ms	(/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))
44.0ms	(* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t))))
57.0ms	(+ x (* (/ (cbrt (- y x)) (/ (* (cbrt (- a t)) (cbrt (- a t))) (cbrt (- y x)))) (/ (cbrt (- y x)) (/ (cbrt (- a t)) (- z t)))))

simplify247.0ms

Algorithm

egg-herbie

Counts

1052 → 1052

Iterations

Useful iterations: 1 (62.0ms)

Iter	Nodes	Cost
0	3473	21187
1	5002	20894

prune864.0ms

Filtered

709 candidates to 1052 candidates (-48.4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	1050	2	1052
Fresh	1	11	12
Picked	0	1	1
Done	0	2	2
Total	1051	16	1067

Merged error: 3.8b

Counts

1067 → 16

regimes644.0ms

Accuracy

14.5% (6.2b remaining)

Error of 10.3b against oracle of 4.1b and baseline of 11.4b

bsearch101.0ms

Steps

Iters	Range		Point
8	1.6905072243393982e-158	9.679044154014748e-155	4.0878357442468504e-156
9	-1.7894724490380666e-215	-3.737783590937258e-221	-2.1677179627935304e-218

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	18
1	32	18

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 1.437274%

Space saved by search: 0.243902%

Guaranteed chance to sample good point: 0%

Results

270.0ms	6584×	body	80	valid
73.0ms	475×	body	640	valid
65.0ms	265×	body	1280	valid
44.0ms	1154×	body	80	invalid
42.0ms	393×	body	320	valid
20.0ms	268×	body	160	valid
3.0ms	15×	body	2560	valid

Details

sample2.9s

simplify68.0ms

prune10.0ms

localize9.0ms

rewrite31.0ms

series97.0ms

simplify59.0ms

prune148.0ms

localize9.0ms

rewrite81.0ms

series105.0ms

simplify98.0ms

prune229.0ms

localize9.0ms

rewrite33.0ms

series93.0ms

simplify50.0ms

prune141.0ms

localize19.0ms

rewrite647.0ms

series193.0ms

simplify247.0ms

prune864.0ms

regimes644.0ms

bsearch101.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling