Details

sample43.0ms

Algorithm

intervals

Results

14.0ms	278×	body	80	valid
5.0ms	104×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	86	14
1	86	14

prune17.0ms

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: 22.0b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.3b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.4b	(* y (/ z (sqrt (- (* z z) (* t a)))))
26.6b	(sqrt (- (* z z) (* t a)))

rewrite32.0ms

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
32.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
19.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify50.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5214	1242

prune149.0ms

Filtered

74 candidates to 104 candidates (-40.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	8	104
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 3.6b

Counts

106 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

1.3b	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
26.6b	(sqrt (- (* z z) (* t a)))
26.6b	(sqrt (- (* z z) (* t a)))
26.6b	(sqrt (- (* z z) (* t a)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-exp-log`
37×	`prod-exp` `add-cbrt-cube` `cbrt-unprod`
21×	`pow1`
11×	`add-sqr-sqrt`
10×	`pow-prod-down`
9×	`cbrt-undiv` `div-exp` `sqrt-prod`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r/`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `flip--`
1×	`frac-times` `associate-r` `associate-l/` `-commutative`

Counts

4 → 86

Calls

4 calls:

28.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (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)))

series76.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* x (* (* y (* (cbrt z) (/ (cbrt z) (* (cbrt (sqrt (- (* z z) (* t a)))) (cbrt (sqrt (- (* z z) (* t a)))))))) (/ (cbrt z) (cbrt (sqrt (- (* z z) (* t a)))))))
12.0ms	(sqrt (- (* z z) (* t a)))
16.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4938	1175
1	4938	1175

prune119.0ms

Filtered

63 candidates to 98 candidates (-55.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 3.6b

Counts

107 → 9

localize27.0ms

Local error

Found 4 expressions with local error:

26.6b	(sqrt (- (* z z) (* t a)))
26.6b	(sqrt (- (* z z) (* t a)))
26.6b	(sqrt (- (* z z) (* t a)))
27.5b	(cbrt (- (* z z) (* t a)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* z z) (* t a)))
12.0ms	(sqrt (- (* z z) (* t a)))
13.0ms	(sqrt (- (* z z) (* t a)))
22.0ms	(cbrt (- (* z z) (* t a)))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6205	773

prune130.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	69	1	70
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	69	10	79

Merged error: 3.6b

Counts

79 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.8b	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
1.9b	(* (/ z (sqrt (- (* z z) (* t a)))) x)
26.6b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

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

series68.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
28.0ms	(* y (* (/ z (sqrt (- (* z z) (* t a)))) x))
18.0ms	(* (/ z (sqrt (- (* z z) (* t a)))) x)
15.0ms	(sqrt (- (* z z) (* t a)))

simplify44.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5083	1274

prune110.0ms

Filtered

78 candidates to 104 candidates (-33.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	104	10	114

Merged error: 3.6b

Counts

114 → 10

regimes1.0s

Accuracy

85% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 22.3b

bsearch50.0ms

Steps

Iters	Range		Point
6	4.4018716591457833e+61	3.90140251811331e+62	3.850226367482441e+62
8	-2.906824906855336e+100	-5.300894277964108e+96	-2.1852152297756325e+100

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	79
1	55	79

end0.0ms

sample1.2s

Algorithm

intervals

Results

448.0ms	8873×	body	80	valid
138.0ms	3052×	body	80	nan

Details

sample43.0ms

simplify4.0ms

prune17.0ms

localize11.0ms

rewrite32.0ms

series71.0ms

simplify50.0ms

prune149.0ms

localize22.0ms

rewrite43.0ms

series76.0ms

simplify51.0ms

prune119.0ms

localize27.0ms

rewrite16.0ms

series62.0ms

simplify48.0ms

prune130.0ms

localize12.0ms

rewrite31.0ms

series68.0ms

simplify44.0ms

prune110.0ms

regimes1.0s

bsearch50.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling