Details

sample2.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.520264%

Guaranteed chance to sample good point: 44.983934%

Results

14.0ms	213×	body	80	valid
2.0ms	10×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	26×	body	80	invalid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify117.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	109	6
3	195	6
4	445	6
5	828	6
6	1434	6
7	2520	6
8	4830	6
9	5001	6

prune4.0ms

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: 13.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z t) y)
1.8b	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.9b	(/ (* (- z t) y) (- a t))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 70

Calls

3 calls:

6.0ms	(* (- z t) y)
10.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
8.0ms	(/ (* (- z t) y) (- a t))

series56.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(* (- z t) y)
35.0ms	(- (+ x y) (/ (* (- z t) y) (- a t)))
15.0ms	(/ (* (- z t) y) (- a t))

simplify43.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	383	461
1	1704	422
2	5001	422

prune135.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	10	79
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	10	80

Merged error: 4.0b

Counts

80 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
2.5b	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.4b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
36×	`times-frac`
35×	`*-un-lft-identity`
30×	`associate-r`
27×	`cbrt-prod`
25×	`add-exp-log`
23×	`add-cube-cbrt`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
10×	`flip3--` `associate-/r/` `flip--`
9×	`add-log-exp`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `frac-times` `div-exp`
6×	`pow1` `frac-sub` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
5×	`associate-r/` `associate-l/`
3×	`flip3-+` `flip-+`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 127

Calls

4 calls:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
31.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a t))
25.0ms	(cbrt (- a t))
24.0ms	(* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t))))
33.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (cbrt (- a t)))) (/ y (cbrt (- a t)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	793	1744
1	3353	1585
2	5001	1502

prune208.0ms

Filtered

104 candidates to 139 candidates (-33.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	133	6	139
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	135	14	149

Merged error: 3.9b

Counts

149 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
2.5b	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
6.2b	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

366×	`cbrt-div`
143×	`frac-times`
117×	`flip3--` `flip--`
89×	`associate-l`
82×	`associate-/r/`
55×	`associate-*r/`
49×	`associate-*l/`
40×	`add-sqr-sqrt`
36×	`add-exp-log`
32×	`*-un-lft-identity`
31×	`times-frac`
30×	`associate-r`
24×	`add-cbrt-cube`
22×	`cbrt-prod` `add-cube-cbrt`
14×	`prod-exp` `cbrt-unprod`
10×	`cbrt-undiv` `div-exp`
9×	`add-log-exp`
6×	`pow1` `frac-sub`
5×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3-+` `flip-+` `unswap-sqr`
2×	`pow1/3` `diff-log` `div-inv`
1×	`sub-neg` `pow-prod-down` `associate--l+` `sum-log` `*-commutative`

Counts

4 → 202

Calls

4 calls:

3.0ms	(cbrt (- a t))
12.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
72.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
6.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a t))
30.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
27.0ms	(* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t))))
34.0ms	(- (+ x y) (* (/ (- z t) (* (cbrt (- a t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t)))))) (/ y (cbrt (- a t)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1314	4168
1	5001	3888

prune626.0ms

Filtered

184 candidates to 214 candidates (-16.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	3	9	12
Picked	1	0	1
Done	1	0	1
Total	215	13	228

Merged error: 3.9b

Counts

228 → 13

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
2.6b	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))
4.0b	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-exp-log`
52×	`prod-exp` `cbrt-unprod`
51×	`add-cbrt-cube`
35×	`cbrt-undiv` `div-exp`
24×	`cbrt-div`
19×	`frac-times`
17×	`associate-*r/`
14×	`associate-l` `frac-sub`
12×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`cbrt-prod` `associate-*l/`
9×	`pow1` `flip3--` `flip--` `add-log-exp`
8×	`add-cube-cbrt` `times-frac`
7×	`flip3-+` `flip-+`
3×	`pow-prod-down`
2×	`pow1/3` `diff-log` `associate-/r/` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `associate-r` `associate--l+` `sum-log` `*-commutative` `div-inv`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a t))
10.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
36.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))
7.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a t))
31.0ms	(cbrt (* (cbrt (- a t)) (cbrt (- a t))))
22.0ms	(* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t)))))
34.0ms	(- (+ x y) (* (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (- a t))) (* (/ (cbrt (- z t)) (* (cbrt (* (cbrt (- a t)) (cbrt (- a t)))) (cbrt (cbrt (- a t))))) (/ y (cbrt (- a t))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1053	4140
1	4394	3303
2	5002	3115

prune139.0ms

Filtered

84 candidates to 146 candidates (-73.8%)

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: 3.9b

Counts

159 → 13

regimes708.0ms

Accuracy

4.7% (7.0b remaining)

Error of 11.0b against oracle of 4.0b and baseline of 11.3b

bsearch106.0ms

Steps

Iters	Range	Point
9	3.268207405408368e+205	8.817347799902998e+210	2.636351036622143e+207
10	6.0618215581065586e+141	2.4285537929706423e+154	3.1507887152865127e+145
8	-3.100622236865136e+70	-3.298262264667684e+66	-2.256261902629788e+70

Iters

Range

Point

3.268207405408368e+205

8.817347799902998e+210

2.636351036622143e+207

6.0618215581065586e+141

2.4285537929706423e+154

3.1507887152865127e+145

-3.100622236865136e+70

-3.298262264667684e+66

-2.256261902629788e+70

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	159
1	53	159

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 14.520264%

Guaranteed chance to sample good point: 44.983934%

Results

303.0ms	6588×	body	80	valid
81.0ms	452×	body	640	valid
69.0ms	274×	body	1280	valid
48.0ms	396×	body	320	valid
32.0ms	742×	body	80	invalid
22.0ms	270×	body	160	valid
5.0ms	20×	body	2560	valid

Details

sample2.5s

simplify117.0ms

prune4.0ms

localize9.0ms

rewrite26.0ms

series56.0ms

simplify43.0ms

prune135.0ms

localize13.0ms

rewrite47.0ms

series108.0ms

simplify88.0ms

prune208.0ms

localize19.0ms

rewrite110.0ms

series117.0ms

simplify62.0ms

prune626.0ms

localize24.0ms

rewrite63.0ms

series113.0ms

simplify122.0ms

prune139.0ms

regimes708.0ms

bsearch106.0ms

simplify3.0ms

end0.0ms

sample3.4s

Profiling