Details

sample36.0ms

Algorithm

intervals

Results

14.0ms	280×	body	80	valid
5.0ms	114×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.0b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
9.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
65.0ms	(sqrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (50.0ms)

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

prune250.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	90	9	99

Merged error: 4.3b

Counts

99 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
2.9b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
24.7b	(sqrt (- (* z z) (* t a)))

rewrite35.0ms

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×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `-commutative`

Counts

4 → 122

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
16.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ z (sqrt (- (* z z) (* t a))))
39.0ms	(- (* z z) (* t a))
86.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	453	1067
1	2239	963
2	5001	942

prune284.0ms

Filtered

134 candidates to 92 candidates (68.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	134	9	143

Merged error: 4.3b

Counts

143 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
1.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
1.2b	(* y (/ z (sqrt (- (* z z) (* t a)))))
24.7b	(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×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
11.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series237.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
83.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	425	829
1	1848	729
2	5001	717

prune233.0ms

Filtered

114 candidates to 80 candidates (70.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	113	10	123

Merged error: 4.3b

Counts

123 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.1b	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
6.6b	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
25.4b	(cbrt (- (* z z) (* t a)))
25.4b	(cbrt (- (* z z) (* t a)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-exp-log` `associate-r` `add-cbrt-cube`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-prod`
17×	`cbrt-prod`
16×	`associate-l`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`cbrt-div`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `sqrt-div` `associate-l/` `associate-/r/` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

12.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
22.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
3.0ms	(cbrt (- (* z z) (* t a)))
4.0ms	(cbrt (- (* z z) (* t a)))

series502.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
137.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
84.0ms	(cbrt (- (* z z) (* t a)))
85.0ms	(cbrt (- (* z z) (* t a)))

simplify87.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	756	2247
1	3399	1947
2	5002	1937

prune418.0ms

Filtered

147 candidates to 112 candidates (76.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	146	11	157

Merged error: 4.3b

Counts

157 → 11

regimes588.0ms

Accuracy

83.7% (3.1b remaining)

Error of 6.9b against oracle of 3.8b and baseline of 22.9b

bsearch90.0ms

Steps

Iters	Range		Point
9	4.568020066610325e+96	9.807841792622673e+101	6.755685967114483e+98
7	-3.1359278362435325e+82	-1.3978856188747051e+80	-2.8528546366111457e+82

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

sample1.2s

Algorithm

intervals

Results

628.0ms	8899×	body	80	valid
157.0ms	3079×	body	80	nan