Details

sample44.0ms

Algorithm

intervals

Results

15.0ms	285×	body	80	valid
4.0ms	76×	body	80	nan

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	14
1	86	14

prune18.0ms

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: 25.1b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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))
11.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* z z) (* t a))
37.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
21.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify39.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5214	1242

prune173.0ms

Filtered

74 candidates to 104 candidates (-40.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	94	10	104
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 4.9b

Counts

106 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.8b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
2.0b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
28.2b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
27×	`associate-l`
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×	`add-log-exp`
4×	`sqrt-div` `associate-r` `pow-prod-down`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-l/` `associate-/r/` `-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `div-inv`

Counts

4 → 92

Calls

4 calls:

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

series79.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* z z) (* t a))
32.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
24.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
14.0ms	(sqrt (- (* z z) (* t a)))

simplify37.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5083	1274

prune176.0ms

Filtered

78 candidates to 104 candidates (-33.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	100	4	104
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 4.8b

Counts

115 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
7.5b	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
28.2b	(sqrt (- (* z z) (* t a)))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

103×	`add-sqr-sqrt`
84×	`sqrt-prod`
78×	`times-frac`
45×	`add-cube-cbrt` `*-un-lft-identity`
36×	`associate-l`
34×	`add-exp-log` `associate-r` `add-cbrt-cube`
16×	`unswap-sqr`
13×	`pow1` `prod-exp` `cbrt-unprod`
12×	`sqrt-div`
8×	`cbrt-undiv` `div-exp`
5×	`associate-*r/`
4×	`flip3--` `pow-prod-down` `associate-/r/` `flip--` `add-log-exp`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `div-inv`

Counts

4 → 159

Calls

4 calls:

23.0ms	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
34.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
5.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series89.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* x (* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
22.0ms	(* (/ y (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
14.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4992	3118
1	4992	3118

prune182.0ms

Filtered

110 candidates to 171 candidates (-55.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	171	11	182

Merged error: 4.8b

Counts

182 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

12.5b	(cbrt (* y (* (/ z (sqrt (- (* z z) (* t a)))) x)))
28.2b	(sqrt (- (* z z) (* t a)))
28.2b	(sqrt (- (* z z) (* t a)))
28.2b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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/` `associate-l/`

Counts

4 → 55

Calls

4 calls:

10.0ms	(cbrt (* y (* (/ z (sqrt (- (* z z) (* t a)))) x)))
4.0ms	(sqrt (- (* z z) (* t a)))
5.0ms	(sqrt (- (* z z) (* t a)))
5.0ms	(sqrt (- (* z z) (* t a)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(cbrt (* y (* (/ z (sqrt (- (* z z) (* t a)))) x)))
14.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))
14.0ms	(sqrt (- (* z z) (* t a)))

simplify42.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5257	782

prune89.0ms

Filtered

57 candidates to 67 candidates (-17.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	67	11	78

Merged error: 4.8b

Counts

78 → 11

regimes1.2s

Accuracy

80.9% (3.9b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 23.9b

bsearch67.0ms

Steps

Iters	Range		Point
10	1.070528705284242e+17	2.3885905512890262e+30	2.3611091436003512e+30
8	-4.929111521398201e+98	-1.0818131077010441e+94	-2.2997304670758846e+98

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	52
1	45	52

end0.0ms

sample1.3s

Algorithm

intervals

Results

488.0ms	8938×	body	80	valid
149.0ms	2938×	body	80	nan

Details

sample44.0ms

simplify3.0ms

prune18.0ms

localize11.0ms

rewrite35.0ms

series80.0ms

simplify39.0ms

prune173.0ms

localize12.0ms

rewrite35.0ms

series79.0ms

simplify37.0ms

prune176.0ms

localize13.0ms

rewrite75.0ms

series89.0ms

simplify65.0ms

prune182.0ms

localize16.0ms

rewrite25.0ms

series118.0ms

simplify42.0ms

prune89.0ms

regimes1.2s

bsearch67.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling