Details

analyze1.0ms

Algorithm: search

sample35.0ms

Algorithm

intervals

Results

18.0ms	86×	body	1280	valid
5.0ms	135×	body	80	valid
3.0ms	16×	body	640	valid
2.0ms	13×	body	320	valid
0.0ms	6×	body	160	valid

simplify9.0ms

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

prune3.0ms

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: 13.3b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(hypot 1.0 x)
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.2b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

Calls

4 calls:

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(hypot 1.0 x)
16.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	201	433
1	602	413
2	1984	411
3	5001	411

prune129.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Merged error: 12.8b

Counts

74 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
11.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
31.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	403	1245
1	1428	1156
2	5002	1151

prune252.0ms

Filtered

67 candidates to 93 candidates (-38.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	91	6	97

Merged error: 12.8b

Counts

97 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.1b	(exp (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

12.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
9.0ms	(exp (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
16.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
31.0ms	(exp (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify56.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	458	1858
1	1613	1737
2	5002	1695

prune318.0ms

Filtered

77 candidates to 111 candidates (-44.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	113	4	117

Merged error: 12.8b

Counts

117 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp (* (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
1.6b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

12×	`associate-*r/` `associate--l+`
11×	`add-log-exp`
9×	`sub-neg`
7×	`add-sqr-sqrt` `add-cube-cbrt` `pow-unpow` `*-un-lft-identity`
6×	`pow1` `distribute-rgt-in` `flip3--` `distribute-lft-in` `frac-sub` `flip--`
4×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
3×	`unpow-prod-down` `pow-pow` `diff-log`
1×	`pow-to-exp` `exp-prod` `exp-to-pow` `pow-exp` `log-pow` `sqr-pow`

Counts

4 → 77

Calls

4 calls:

4.0ms	(pow (exp (* (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
7.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series292.0ms

Counts

4 → 12

Calls

4 calls:

274.0ms	(pow (exp (* (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))) (cbrt (log (/ (- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify127.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 3 (110.0ms)

Iter	Nodes	Cost
0	290	1954
1	891	1761
2	4584	1729
3	5001	1725

prune592.0ms

Filtered

58 candidates to 89 candidates (-53.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 12.8b

Counts

93 → 5

regimes380.0ms

Accuracy

0% (0.0b remaining)

Error of 14.8b against oracle of 14.7b and baseline of 14.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	62
1	34	62

end0.0ms

analyze1.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

623.0ms	2814×	body	1280	valid
163.0ms	4110×	body	80	valid
103.0ms	577×	body	640	valid
39.0ms	319×	body	320	valid
14.0ms	180×	body	160	valid

Details

analyze1.0ms

sample35.0ms

simplify9.0ms

prune3.0ms

localize8.0ms

rewrite15.0ms

series35.0ms

simplify61.0ms

prune129.0ms

localize13.0ms

rewrite31.0ms

series63.0ms

simplify52.0ms

prune252.0ms

localize17.0ms

rewrite37.0ms

series84.0ms

simplify56.0ms

prune318.0ms

localize26.0ms

rewrite26.0ms

series292.0ms

simplify127.0ms

prune592.0ms

regimes380.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

analyze1.0ms

sample1.1s

Profiling