Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	275×	body	80	valid
3.0ms	91×	body	80	nan

simplify11.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 26.0b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
6.3b	(* (* x y) z)
9.5b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.8b	(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))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
3.0ms	(sqrt (- (* z z) (* t a)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
95.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
78.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune393.0ms

Filtered

88 candidates to 60 candidates (68.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 3.8b

Counts

89 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
4.8b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.8b	(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))))
4.0ms	(- (* z z) (* t a))
11.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
3.0ms	(sqrt (- (* z z) (* t a)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ z (sqrt (- (* z z) (* t a))))
31.0ms	(- (* z z) (* t a))
79.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	431	1015
1	2166	912
2	5002	893

prune318.0ms

Filtered

124 candidates to 82 candidates (66.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	124	8	132

Merged error: 3.8b

Counts

132 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
2.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
25.8b	(sqrt (- (* z z) (* t a)))

rewrite62.0ms

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:

6.0ms	(- (* z z) (* t a))
18.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
7.0ms	(sqrt (- (* z z) (* t a)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- (* z z) (* t a))
81.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
56.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
79.0ms	(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	403	775
1	1781	676
2	5001	667

prune239.0ms

Filtered

104 candidates to 68 candidates (65.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	101	3	104
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	102	10	112

Merged error: 3.8b

Counts

112 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a)))))))
1.2b	(* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a))))))
2.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
25.8b	(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-exp-log`
33×	`pow1` `add-cbrt-cube`
30×	`add-sqr-sqrt`
29×	`prod-exp` `cbrt-unprod`
26×	`associate-r`
21×	`add-cube-cbrt` `*-un-lft-identity`
20×	`times-frac`
19×	`pow-prod-down`
13×	`sqrt-prod`
10×	`associate-l`
6×	`associate-*r/`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `add-log-exp`
3×	`cbrt-prod` `*-commutative` `unswap-sqr`
2×	`flip3--` `associate-/r/` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-inv`

Counts

4 → 116

Calls

4 calls:

15.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a)))))))
14.0ms	(* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a)))))))
139.0ms	(* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a))))))
57.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
56.0ms	(sqrt (- (* z z) (* t a)))

simplify70.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	528	1292
1	2477	1010
2	5001	968

prune271.0ms

Filtered

128 candidates to 77 candidates (60.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	123	5	128
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	124	14	138

Merged error: 3.8b

Counts

138 → 14

regimes525.0ms

Accuracy

84.8% (2.9b remaining)

Error of 6.4b against oracle of 3.4b and baseline of 22.8b

bsearch185.0ms

Steps

Iters	Range		Point
9	8.436446852564666e+52	2.852486117178445e+60	2.813233055263119e+60
8	3.8537525104719113e-197	2.300190071843605e-194	2.1724877368709443e-195
9	-2.5987841252092732e-51	-9.632127386993044e-60	-1.9042471861239938e-51
8	-2.6687907650031294e+103	-6.933841510816238e+98	-1.1693171824099425e+101

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	32
1	54	32
2	54	32

end0.0ms

sample796.0ms

Algorithm

intervals

Results

343.0ms	8854×	body	80	valid
104.0ms	2892×	body	80	nan