Details

sample1.6s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867532%

Guaranteed chance to sample good point: 52.693199%

Results

18.0ms	286×	body	80	valid
4.0ms	83×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

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: 24.5b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
4.7b	(* (* x y) z)
9.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
9×	`sqrt-prod`
6×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`sqrt-div`
3×	`cbrt-undiv` `flip3--` `div-exp` `associate-r` `pow-prod-down` `flip--`
2×	`associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
35.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	343	583
1	1850	515
2	5003	510

prune133.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	11	89

Merged error: 3.9b

Counts

89 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
3.7b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
34×	`add-sqr-sqrt`
33×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r` `sqrt-prod`
18×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
6×	`sqrt-div` `prod-exp` `associate-/r*` `cbrt-unprod` `add-log-exp`
4×	`flip3--` `associate-/r/` `flip--`
3×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-/l*`
2×	`div-inv`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `associate-l` `clear-num` `-commutative`

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
14.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
32.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	428	1014
1	2153	912
2	5002	894

prune132.0ms

Filtered

80 candidates to 124 candidates (-55.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	2	7	9
Picked	0	1	1
Done	0	1	1
Total	123	12	135

Merged error: 3.7b

Counts

135 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.3b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
34.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	400	774
1	1768	676
2	5001	668

prune115.0ms

Filtered

67 candidates to 104 candidates (-55.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	106	10	116

Merged error: 3.7b

Counts

116 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

13.4b	(cbrt (* (* x y) (/ z (sqrt (- (* z z) (* t a))))))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))
23.2b	(sqrt (- (* z z) (* t a)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/`

Counts

4 → 55

Calls

4 calls:

9.0ms	(cbrt (* (* x y) (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(cbrt (* (* x y) (/ z (sqrt (- (* z z) (* t a))))))
14.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (70.0ms)

Iter	Nodes	Cost
0	283	501
1	858	475
2	3295	459
3	5001	453

prune92.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	67	10	77

Merged error: 3.7b

Counts

77 → 10

regimes944.0ms

Accuracy

83.7% (3.2b remaining)

Error of 6.7b against oracle of 3.5b and baseline of 23.3b

bsearch94.0ms

Steps

Iters	Range	Point
8	4.678344490429734e+40	3.77789447231718e+44	3.5372716625526583e+44
8	-2.11609763151972e-251	-1.3057492578280995e-254	-1.112106327758909e-252
8	-1.082453083988915e+156	-6.1931550552468625e+152	-1.0061199819888628e+154

Iters

Range

Point

4.678344490429734e+40

3.77789447231718e+44

3.5372716625526583e+44

-2.11609763151972e-251

-1.3057492578280995e-254

-1.112106327758909e-252

-1.082453083988915e+156

-6.1931550552468625e+152

-1.0061199819888628e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	17
1	39	17
2	39	17

end0.0ms

sample2.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 5.867532%

Guaranteed chance to sample good point: 52.693199%

Results

471.0ms	8872×	body	80	valid
110.0ms	2357×	body	80	nan

Details

sample1.6s

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite23.0ms

series62.0ms

simplify50.0ms

prune133.0ms

localize10.0ms

rewrite31.0ms

series63.0ms

simplify61.0ms

prune132.0ms

localize10.0ms

rewrite33.0ms

series75.0ms

simplify49.0ms

prune115.0ms

localize15.0ms

rewrite21.0ms

series148.0ms

simplify77.0ms

prune92.0ms

regimes944.0ms

bsearch94.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling