Details

sample60.0ms

Algorithm

intervals

Results

33.0ms	102×	body	1280	valid
7.0ms	125×	body	80	valid
4.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

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: 16.5b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
1.9b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series183.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
70.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
81.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune145.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	3	79

Merged error: 16.0b

Counts

79 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite20.0ms

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 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(/ 1.0 (hypot 1.0 x))
77.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify141.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (31.0ms)

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

prune210.0ms

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: 16.0b

Counts

99 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
4.4b	(log (exp (/ 1.0 (hypot 1.0 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (log (exp (/ 1.0 (hypot 1.0 x))))))
5.0ms	(log (exp (/ 1.0 (hypot 1.0 x))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify119.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	326	652
1	964	592
2	3858	578
3	5001	576

prune233.0ms

Filtered

98 candidates to 72 candidates (73.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 16.0b

Counts

102 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (+ (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))) (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))))))
4.4b	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))
4.4b	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`log-pow`
28×	`sqrt-pow1`
26×	`exp-prod`
24×	`*-un-lft-identity`
22×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
12×	`log-prod`
8×	`pow1` `associate-*r/` `add-log-exp`
6×	`add-exp-log` `sqrt-prod`
4×	`associate--l+` `frac-sub` `add-cbrt-cube`
3×	`distribute-rgt-in` `sub-neg` `flip3--` `distribute-lft-in` `flip3-+` `flip--` `flip-+`
2×	`pow1/2` `rem-log-exp` `div-inv` `associate--r+`
1×	`+-commutative` `diff-log` `sum-log` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (+ (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))) (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))))))
6.0ms	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))
8.0ms	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
133.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (+ (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))) (log (sqrt (exp (/ 1.0 (hypot 1.0 x))))))))
101.0ms	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))
101.0ms	(log (sqrt (exp (/ 1.0 (hypot 1.0 x)))))

simplify70.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	409	1053
1	1505	908
2	5003	890

prune304.0ms

Filtered

106 candidates to 76 candidates (71.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	103	3	106
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Merged error: 15.8b

Counts

110 → 4

regimes81.0ms

Accuracy

0% (0.2b remaining)

Error of 15.3b against oracle of 15.0b and baseline of 15.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	17
1	23	17

end0.0ms

sample824.0ms

Algorithm

intervals

Results

488.0ms	2909×	body	1280	valid
116.0ms	4032×	body	80	valid
80.0ms	611×	body	640	valid
26.0ms	285×	body	320	valid
9.0ms	163×	body	160	valid