Details

sample31.0ms

Algorithm

intervals

Results

12.0ms	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	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

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)))

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

series199.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
82.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (52.0ms)

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

prune264.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	90	8	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	8	99

Merged error: 3.8b

Counts

99 → 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)))

rewrite30.0ms

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

series219.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(/ z (sqrt (- (* z z) (* t a))))
32.0ms	(- (* z z) (* t a))
81.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (55.0ms)

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

prune329.0ms

Filtered

134 candidates to 93 candidates (69.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	134	8	142

Merged error: 3.8b

Counts

142 → 8

localize10.0ms

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)))

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)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* z z) (* t a))
81.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
55.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (46.0ms)

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

prune276.0ms

Filtered

114 candidates to 80 candidates (70.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	112	10	122

Merged error: 3.8b

Counts

122 → 10

localize18.0ms

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)))

rewrite47.0ms

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` `expm1-log1p-u` `sqrt-div` `div-exp` `log1p-expm1-u` `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 → 124

Calls

4 calls:

16.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a)))))))
11.0ms	(* (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)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(* (* (cbrt x) (cbrt x)) (* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a)))))))
139.0ms	(* (cbrt x) (* y (/ z (sqrt (- (* z z) (* t a))))))
53.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify71.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	544	1360
1	2530	1078
2	5002	1027

prune301.0ms

Filtered

136 candidates to 86 candidates (63.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	132	14	146

Merged error: 3.8b

Counts

146 → 14

regimes499.0ms

Accuracy

84.8% (2.9b remaining)

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

bsearch184.0ms

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	50	33
1	68	33
2	68	33

end0.0ms

sample791.0ms

Algorithm

intervals

Results

337.0ms	8854×	body	80	valid
102.0ms	2892×	body	80	nan