Details

sample35.0ms

Algorithm

intervals

Results

14.0ms	286×	body	80	valid
5.0ms	113×	body	80	nan

simplify11.0ms

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: 26.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
9.6b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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))
6.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
8.0ms	(sqrt (- (* z z) (* t a)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
29.0ms	(* (* x y) z)
84.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (48.0ms)

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

prune272.0ms

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: 5.4b

Counts

99 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
1.2b	(- (* z z) (* t a))
3.8b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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:

9.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series249.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ z (sqrt (- (* z z) (* t a))))
37.0ms	(- (* z z) (* t a))
84.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify67.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (55.0ms)

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

prune302.0ms

Filtered

134 candidates to 91 candidates (67.9%)

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: 4.9b

Counts

143 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
2.4b	(* y (/ z (sqrt (- (* z z) (* t a)))))
3.6b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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))
12.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
58.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
85.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (43.0ms)

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

prune256.0ms

Filtered

114 candidates to 79 candidates (69.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	112	2	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	11	123

Merged error: 4.7b

Counts

123 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b	(* 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)))))))
25.5b	(sqrt (- (* z z) (* t a)))
25.5b	(sqrt (- (* z z) (* t a)))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-exp-log`
46×	`add-cbrt-cube`
43×	`prod-exp` `cbrt-unprod`
16×	`pow1`
14×	`cbrt-undiv` `div-exp`
11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `associate-*r/` `pow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u` `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 → 97

Calls

4 calls:

31.0ms	(* 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)))

series292.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* 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)))))))
62.0ms	(sqrt (- (* z z) (* t a)))
58.0ms	(sqrt (- (* z z) (* t a)))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify86.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	638	1930
1	3123	1322
2	5001	988

prune311.0ms

Filtered

109 candidates to 73 candidates (67.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	108	12	120

Merged error: 4.7b

Counts

120 → 12

regimes529.0ms

Accuracy

78.8% (4.1b remaining)

Error of 7.5b against oracle of 3.4b and baseline of 22.7b

bsearch109.0ms

Steps

Iters	Range		Point
8	9.865387479601035e+48	1.0433903392957286e+52	9.375790730632526e+51
9	-1.628339896851984e+59	-1.0205942138599043e+52	-5.070658730829399e+58

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	17
1	33	17
2	33	17

end0.0ms

sample965.0ms

Algorithm

intervals

Results

456.0ms	8847×	body	80	valid
142.0ms	2949×	body	80	nan

Details

sample35.0ms

simplify11.0ms

prune3.0ms

localize10.0ms

rewrite30.0ms

series205.0ms

simplify56.0ms

prune272.0ms

localize10.0ms

rewrite34.0ms

series249.0ms

simplify67.0ms

prune302.0ms

localize10.0ms

rewrite34.0ms

series238.0ms

simplify53.0ms

prune256.0ms

localize22.0ms

rewrite48.0ms

series292.0ms

simplify86.0ms

prune311.0ms

regimes529.0ms

bsearch109.0ms

simplify2.0ms

end0.0ms

sample965.0ms

Profiling