Details

sample40.0ms

Algorithm

intervals

Results

22.0ms	104×	body	1280	valid
5.0ms	125×	body	80	valid
2.0ms	13×	body	640	valid
1.0ms	9×	body	160	valid
1.0ms	5×	body	320	valid

simplify11.0ms

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: 14.5b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.4b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite20.0ms

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:

3.0ms	(/ 1.0 (hypot 1.0 x))
5.0ms	(+ 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 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
73.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
84.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify72.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2309	463
3	5002	463

prune133.0ms

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: 14.1b

Counts

79 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 96

Calls

4 calls:

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

series268.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
72.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
158.0ms	(/ (- (* 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)))))))
33.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	450	1238
1	1712	1158
2	5001	1154

prune233.0ms

Filtered

108 candidates to 78 candidates (72.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	107	4	111

Merged error: 14.0b

Counts

111 → 4

localize12.0ms

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	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.9b	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
7.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

series293.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
70.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
158.0ms	(/ (- 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))) (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
33.0ms	(- 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))

simplify42.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	321	962
1	1095	888
2	5001	884

prune164.0ms

Filtered

85 candidates to 60 candidates (70.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	85	4	89

Merged error: 14.0b

Counts

89 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)) (* 0.5 (+ 0.5 (* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))))))
0.0b	(* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))))
0.1b	(pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)
1.9b	(- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

52×	`add-sqr-sqrt`
28×	`add-exp-log`
24×	`times-frac` `difference-of-squares`
22×	`*-un-lft-identity`
20×	`add-cbrt-cube`
19×	`sqr-pow`
15×	`add-cube-cbrt`
13×	`associate-l` `associate-/l*`
9×	`pow1` `prod-exp`
7×	`unpow-prod-down` `cube-prod`
6×	`div-exp` `add-log-exp`
5×	`associate-*r/` `pow-exp` `cbrt-unprod`
4×	`cbrt-undiv`
3×	`difference-cubes` `pow-unpow` `flip3-+` `associate-r` `flip-+` `distribute-lft-out--` `rem-cube-cbrt` `unswap-sqr`
2×	`cube-div` `frac-times` `rec-exp` `flip3--` `pow-pow` `1-exp` `pow-prod-down` `associate-/r/` `flip--` `div-inv` `associate-/l/`
1×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `sub-neg` `frac-2neg` `distribute-lft-in` `diff-log` `unpow3` `div-sub` `associate-l/` `clear-num` `associate-/r` `un-div-inv` `*-commutative`

Counts

4 → 137

Calls

4 calls:

15.0ms	(/ (- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)) (* 0.5 (+ 0.5 (* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))))))
8.0ms	(* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))))
6.0ms	(pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)
9.0ms	(- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3))

series330.0ms

Counts

4 → 12

Calls

4 calls:

192.0ms	(/ (- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)) (* 0.5 (+ 0.5 (* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x))))))))
37.0ms	(* (/ 1 (hypot 1.0 x)) (+ 0.5 (* 0.5 (/ 1 (hypot 1.0 x)))))
33.0ms	(pow (* 0.5 (/ 1 (hypot 1.0 x))) 3)
67.0ms	(- (pow 0.5 3) (pow (* 0.5 (/ 1 (hypot 1.0 x))) 3))

simplify119.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	734	1839
1	4171	1614
2	5002	1611

prune415.0ms

Filtered

149 candidates to 105 candidates (70.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	148	5	153

Merged error: 13.8b

Counts

153 → 5

regimes81.0ms

Accuracy

0% (0.3b remaining)

Error of 15.0b against oracle of 14.7b and baseline of 15.0b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample1.0s

Algorithm

intervals

Results

609.0ms	2868×	body	1280	valid
155.0ms	4047×	body	80	valid
103.0ms	617×	body	640	valid
38.0ms	312×	body	320	valid
12.0ms	156×	body	160	valid

Details

sample40.0ms

simplify11.0ms

prune2.0ms

localize8.0ms

rewrite20.0ms

series189.0ms

simplify72.0ms

prune133.0ms

localize13.0ms

rewrite30.0ms

series268.0ms

simplify54.0ms

prune233.0ms

localize12.0ms

rewrite24.0ms

series293.0ms

simplify42.0ms

prune164.0ms

localize23.0ms

rewrite44.0ms

series330.0ms

simplify119.0ms

prune415.0ms

regimes81.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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