Details

sample31.0ms

Algorithm

intervals

Results

15.0ms	93×	body	1280	valid
4.0ms	129×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

prune2.0ms

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: 16.9b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
2.0b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-cube-cbrt`
9×	`times-frac`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`pow1`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 41

Calls

2 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series89.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
84.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify46.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (12.0ms)

Iter	Nodes	Cost
0	157	308
1	484	286
2	1409	284
3	5001	284

prune99.0ms

Filtered

47 candidates to 34 candidates (72.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	3	48

Merged error: 16.4b

Counts

48 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify136.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4851	560
3	5001	560

prune247.0ms

Filtered

96 candidates to 69 candidates (71.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	95	4	99

Merged error: 16.4b

Counts

99 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
17.6b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`cube-div` `associate-*r/` `associate--l+`
3×	`sub-neg` `pow-unpow` `cbrt-div` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `distribute-rgt-in` `cube-mult` `flip3--` `distribute-lft-in` `unpow3` `div-exp` `pow-exp` `frac-sub` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `diff-log` `clear-num` `rem-cbrt-cube`

Counts

4 → 133

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
5.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series83.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
37.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
34.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	463	917
1	2143	815
2	5001	807

prune306.0ms

Filtered

145 candidates to 77 candidates (53.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	145	4	149

Merged error: 16.4b

Counts

149 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))))
0.1b	(pow (/ 1.0 (hypot 1.0 x)) 3)
1.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
17.6b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `times-frac`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
8×	`associate-*r/`
7×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cube-div` `add-log-exp`
5×	`cbrt-div`
4×	`log-div` `exp-prod` `flip3--` `exp-diff` `associate--l+` `frac-sub` `flip--` `div-inv`
3×	`sub-neg` `pow-unpow` `log-prod` `exp-sum`
2×	`distribute-rgt-in` `cube-mult` `distribute-lft-in` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `pow-pow` `pow1/3` `diff-log` `div-exp` `log-pow` `rem-cbrt-cube` `rem-exp-log`

Counts

4 → 125

Calls

4 calls:

8.0ms	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))))
5.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
5.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

series109.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(exp (log (- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))))
38.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
6.0ms	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

simplify62.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	495	1067
1	2092	942
2	5002	913

prune341.0ms

Filtered

137 candidates to 72 candidates (52.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	136	1	137
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	137	4	141

Merged error: 16.4b

Counts

141 → 4

regimes123.0ms

Accuracy

0% (0.0b remaining)

Error of 15.1b against oracle of 15.1b and baseline of 15.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

end0.0ms

sample813.0ms

Algorithm

intervals

Results

464.0ms	2908×	body	1280	valid
119.0ms	3983×	body	80	valid
80.0ms	614×	body	640	valid
27.0ms	313×	body	320	valid
10.0ms	182×	body	160	valid