Details

sample48.0ms

Algorithm

intervals

Results

14.0ms	293×	body	80	valid
6.0ms	135×	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

prune5.0ms

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: 23.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.3b	(* (* x y) z)
10.0b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.3b	(sqrt (- (* z z) (* t a)))

rewrite22.0ms

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

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
6.0ms	(* (* x y) z)
30.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (44.0ms)

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

prune116.0ms

Filtered

60 candidates to 88 candidates (-46.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	82	6	88
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	7	89

Merged error: 2.2b

Counts

89 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.0b	(- (* z z) (* t a))
2.4b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.3b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ z (sqrt (- (* z z) (* t a))))
7.0ms	(- (* z z) (* t a))
32.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
12.0ms	(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (49.0ms)

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

prune133.0ms

Filtered

81 candidates to 124 candidates (-53.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	124	7	131

Merged error: 2.2b

Counts

131 → 7

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
5.5b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
23.3b	(sqrt (- (* z z) (* t a)))
23.3b	(sqrt (- (* z z) (* t a)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
23.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
3.0ms	(sqrt (- (* z z) (* t a)))
3.0ms	(sqrt (- (* z z) (* t a)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
30.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
12.0ms	(sqrt (- (* z z) (* t a)))
15.0ms	(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	585	1654
1	2957	1472
2	5002	1358

prune120.0ms

Filtered

85 candidates to 130 candidates (-52.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	129	8	137

Merged error: 2.2b

Counts

137 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ x (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
23.3b	(sqrt (- (* z z) (* t a)))
23.3b	(sqrt (- (* z z) (* t a)))
23.3b	(sqrt (- (* z z) (* t a)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
45×	`add-exp-log` `add-cbrt-cube`
42×	`associate-l`
36×	`times-frac`
35×	`add-sqr-sqrt`
32×	`add-cube-cbrt` `*-un-lft-identity`
18×	`prod-exp` `cbrt-unprod`
13×	`cbrt-undiv` `div-exp`
12×	`pow1` `sqrt-div`
5×	`frac-times` `associate-*r/`
4×	`flip3--` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-*l/`
2×	`associate-/r/`
1×	`associate-r` `*-commutative` `div-inv`

Counts

4 → 125

Calls

4 calls:

30.0ms	(* (/ x (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
3.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series70.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (/ x (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (* (/ y (sqrt (sqrt (sqrt (- (* z z) (* t a)))))) (/ z (sqrt (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)))

simplify68.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	571	2516
1	2756	2106
2	5001	1988

prune136.0ms

Filtered

96 candidates to 137 candidates (-42.7%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	137	8	145

Merged error: 2.2b

Counts

145 → 8

regimes754.0ms

Accuracy

77.2% (4.5b remaining)

Error of 7.7b against oracle of 3.2b and baseline of 22.7b

bsearch68.0ms

Steps

Iters	Range		Point
10	2.5474259792606686e+32	2.0777144108672062e+42	9.322590315760622e+40
10	-1.1446708155820095e+92	-4.7885483061419374e+76	-6.9117204301731425e+78

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	10
1	33	10
2	33	10

end0.0ms

sample1.3s

Algorithm

intervals

Results

481.0ms	8875×	body	80	valid
148.0ms	2978×	body	80	nan

Details

sample48.0ms

simplify9.0ms

prune5.0ms

localize14.0ms

rewrite22.0ms

series55.0ms

simplify53.0ms

prune116.0ms

localize10.0ms

rewrite27.0ms

series61.0ms

simplify59.0ms

prune133.0ms

localize20.0ms

rewrite38.0ms

series63.0ms

simplify69.0ms

prune120.0ms

localize18.0ms

rewrite46.0ms

series70.0ms

simplify68.0ms

prune136.0ms

regimes754.0ms

bsearch68.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling