Details

sample37.0ms

Algorithm

intervals

Results

15.0ms	287×	body	80	valid
5.0ms	112×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	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: 24.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
4.8b	(* (* x y) z)
8.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.0b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

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

series197.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
25.0ms	(* (* x y) z)
81.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune244.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	87	11	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	11	99

Merged error: 3.1b

Counts

99 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
6.4b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
25.9b	(cbrt (- (* z z) (* t a)))
25.9b	(cbrt (- (* z z) (* t a)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
147×	`add-sqr-sqrt`
102×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
24×	`sqrt-prod`
18×	`cbrt-prod`
13×	`associate-/r*`
12×	`cbrt-undiv` `div-exp` `unswap-sqr`
10×	`div-inv`
6×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*`
2×	`pow1/3` `sqrt-div`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 217

Calls

4 calls:

6.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
36.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series541.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
314.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
82.0ms	(cbrt (- (* z z) (* t a)))
86.0ms	(cbrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1093	3523
1	5001	3265

prune756.0ms

Filtered

229 candidates to 190 candidates (83.0%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	225	4	229
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	228	12	240

Merged error: 3.1b

Counts

240 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

4.0b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
7.4b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
25.9b	(cbrt (- (* z z) (* t a)))
25.9b	(cbrt (- (* z z) (* t a)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
93×	`add-sqr-sqrt`
84×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
13×	`associate-/r*`
9×	`div-inv`
6×	`pow1` `cbrt-undiv` `cbrt-prod` `div-exp`
4×	`expm1-log1p-u` `cbrt-div` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `prod-exp` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`flip3--` `pow1/3` `associate-/r/` `flip--`
1×	`frac-2neg` `pow-prod-down` `associate-l/` `clear-num` `-commutative`

Counts

4 → 170

Calls

4 calls:

6.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
14.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
4.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
93.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) z)
82.0ms	(cbrt (- (* z z) (* t a)))
84.0ms	(cbrt (- (* z z) (* t a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	688	2073
1	2829	1935
2	5002	1929

prune637.0ms

Filtered

182 candidates to 154 candidates (84.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	182	12	194

Merged error: 3.1b

Counts

194 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
5.8b	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
25.0b	(sqrt (- (* z z) (* t a)))
25.0b	(sqrt (- (* z z) (* t a)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

63×	`sqrt-prod`
48×	`add-sqr-sqrt` `times-frac`
35×	`add-cube-cbrt` `*-un-lft-identity`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
16×	`sqrt-div`
15×	`associate-l`
9×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r*` `cbrt-unprod`
8×	`pow1`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `associate-/l`

Counts

4 → 149

Calls

4 calls:

9.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
26.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* x y) (sqrt (sqrt (- (* z z) (* t a)))))
82.0ms	(* (/ (* x y) (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a))))))
60.0ms	(sqrt (- (* z z) (* t a)))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify85.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	643	2017
1	3408	1804
2	5001	1678

prune370.0ms

Filtered

161 candidates to 109 candidates (67.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	161	12	173

Merged error: 3.1b

Counts

173 → 12

regimes504.0ms

Accuracy

81.7% (4.1b remaining)

Error of 7.4b against oracle of 3.4b and baseline of 25.6b

bsearch172.0ms

Steps

Iters	Range		Point
10	4.522873592780775e+27	5.978781725101664e+38	4.935646888674816e+38
10	-1.5429529165087941e-18	-2.3261434869364345e-32	-4.59212318019564e-25
8	-4.624215200523427e+124	-2.5454028151105053e+120	-5.143913370988061e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	31
1	45	31
2	45	31

end0.0ms

sample1.0s

Algorithm

intervals

Results

471.0ms	8841×	body	80	valid
148.0ms	2983×	body	80	nan