Details

sample2.9s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.531006%

Guaranteed chance to sample good point: 40.633245%

Results

8.0ms	211×	body	80	valid
2.0ms	53×	body	80	invalid
2.0ms	14×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	10×	body	320	valid
1.0ms	9×	body	160	valid
0.0ms	1×	body	2560	valid

simplify70.0ms

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

prune7.0ms

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: 21.2b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y x) (- z t))
2.4b	(+ x (/ (* (- y x) (- z t)) (- a t)))
15.3b	(/ (* (- y x) (- z t)) (- a t))

rewrite55.0ms

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:

15.0ms	(* (- y x) (- z t))
12.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
24.0ms	(/ (* (- y x) (- z t)) (- a t))

series95.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y x) (- z t))
49.0ms	(+ x (/ (* (- y x) (- z t)) (- a t)))
38.0ms	(/ (* (- y x) (- z t)) (- a t))

simplify51.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune135.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 5.0b

Counts

91 → 10

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.4b	(+ x (* (- y x) (/ (- z t) (- a t))))
2.5b	(* (- y x) (/ (- z t) (- a t)))

rewrite31.0ms

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)))

series89.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
50.0ms	(+ x (* (- y x) (/ (- z t) (- a t))))
30.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (11.0ms)

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

prune156.0ms

Filtered

84 candidates to 128 candidates (-52.4%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	119	9	128
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	122	16	138

Merged error: 5.0b

Counts

138 → 16

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
1.3b	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))
6.9b	(+ x (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))

rewrite52.0ms

Algorithm

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:

3.0ms	(cbrt (- a t))
3.0ms	(cbrt (- a t))
37.0ms	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))
3.0ms	(+ x (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))

series142.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(cbrt (- a t))
25.0ms	(cbrt (- a t))
40.0ms	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t))))
50.0ms	(+ x (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (- z t) (cbrt (- a t)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	756	1850
1	3320	1682
2	5001	1591

prune197.0ms

Filtered

106 candidates to 146 candidates (-37.7%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	1	13	14
Picked	0	1	1
Done	0	1	1
Total	144	18	162

Merged error: 4.7b

Counts

162 → 18

localize25.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(* (cbrt (- z t)) (cbrt (- z t)))
1.2b	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))))
6.1b	(+ x (* (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- a t))))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
46×	`cbrt-div`
42×	`add-exp-log`
36×	`cbrt-prod`
35×	`*-un-lft-identity`
25×	`associate-l`
24×	`associate-r`
22×	`add-cbrt-cube`
19×	`flip3--` `flip--`
17×	`add-cube-cbrt`
16×	`times-frac` `prod-exp` `associate-/r/` `cbrt-unprod`
13×	`pow1` `frac-times`
12×	`cbrt-undiv` `div-exp`
10×	`swap-sqr` `unswap-sqr`
8×	`distribute-lft-out--`
7×	`pow1/3` `associate-r/` `associate-l/`
6×	`add-log-exp` `difference-of-squares`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

3.0ms	(cbrt (- a t))
10.0ms	(* (cbrt (- z t)) (cbrt (- z t)))
30.0ms	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))))
4.0ms	(+ x (* (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- a t))))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a t))
31.0ms	(* (cbrt (- z t)) (cbrt (- z t)))
125.0ms	(* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t))))))
52.0ms	(+ x (* (* (/ (- y x) (* (cbrt (- a t)) (cbrt (- a t)))) (/ (* (cbrt (- z t)) (cbrt (- z t))) (cbrt (* (cbrt (- a t)) (cbrt (- a t)))))) (/ (cbrt (- z t)) (cbrt (cbrt (- a t))))))

simplify113.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	1027	2872
1	4056	2481
2	5003	2399

prune180.0ms

Filtered

112 candidates to 163 candidates (-45.5%)

Pruning

19 alts after pruning (16 fresh and 3 done)

	Pruned	Kept	Total
New	161	2	163
Fresh	1	14	15
Picked	0	1	1
Done	0	2	2
Total	162	19	181

Merged error: 4.7b

Counts

181 → 19

regimes798.0ms

Accuracy

19.3% (6.3b remaining)

Error of 10.4b against oracle of 4.1b and baseline of 11.9b

bsearch61.0ms

Steps

Iters	Range		Point
9	2.753655882223894e-258	3.332614103285771e-252	2.0470113914970033e-252
8	-7.869397327173629e-149	-6.276072160411456e-152	-1.403605417769513e-149

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	31	12

end0.0ms

sample3.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.531006%

Guaranteed chance to sample good point: 40.633245%

Results

274.0ms	6534×	body	80	valid
69.0ms	499×	body	640	valid
57.0ms	1279×	body	80	invalid
48.0ms	277×	body	1280	valid
43.0ms	414×	body	320	valid
19.0ms	259×	body	160	valid
4.0ms	17×	body	2560	valid

Details

sample2.9s

simplify70.0ms

prune7.0ms

localize15.0ms

rewrite55.0ms

series95.0ms

simplify51.0ms

prune135.0ms

localize11.0ms

rewrite31.0ms

series89.0ms

simplify51.0ms

prune156.0ms

localize12.0ms

rewrite52.0ms

series142.0ms

simplify90.0ms

prune197.0ms

localize25.0ms

rewrite54.0ms

series233.0ms

simplify113.0ms

prune180.0ms

regimes798.0ms

bsearch61.0ms

simplify1.0ms

end0.0ms

sample3.6s

Profiling