Details

sample38.0ms

Algorithm

intervals

Results

19.0ms	92×	body	1280	valid
5.0ms	132×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	2×	body	160	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: 12.9b

Counts

2 → 1

localize8.0ms

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))
1.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite24.0ms

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:

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

series188.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
69.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ 1.0 (hypot 1.0 x))
85.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2311	463
3	5001	463

prune138.0ms

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: 12.4b

Counts

79 → 3

localize13.0ms

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

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 (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))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (* 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)))))))
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
37.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	407	1275
1	1594	1181
2	5002	1177

prune263.0ms

Filtered

122 candidates to 88 candidates (72.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	4	122
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	121	4	125

Merged error: 12.4b

Counts

125 → 4

localize20.0ms

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

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
17.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
63.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
6.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify81.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	625	1165
1	3259	984
2	5001	984

prune282.0ms

Filtered

98 candidates to 72 candidates (73.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 12.4b

Counts

102 → 4

localize16.0ms

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)
0.5b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))))
20.0b	(cbrt (pow (/ 1.0 (hypot 1.0 x)) 3))

rewrite28.0ms

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)
11.0ms	(- (* 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))

series81.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (hypot 1.0 x))
37.0ms	(pow (/ 1.0 (hypot 1.0 x)) 3)
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))

simplify68.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (55.0ms)

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

prune254.0ms

Filtered

145 candidates to 77 candidates (53.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	145	4	149

Merged error: 12.4b

Counts

149 → 4

regimes74.0ms

Accuracy

0% (0.0b remaining)

Error of 14.9b against oracle of 14.9b and baseline of 14.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

end0.0ms

sample1.0s

Algorithm

intervals

Results

600.0ms	2810×	body	1280	valid
156.0ms	4066×	body	80	valid
113.0ms	677×	body	640	valid
35.0ms	306×	body	320	valid
11.0ms	141×	body	160	valid

Details

sample38.0ms

simplify11.0ms

prune2.0ms

localize8.0ms

rewrite24.0ms

series188.0ms

simplify68.0ms

prune138.0ms

localize13.0ms

rewrite29.0ms

series206.0ms

simplify65.0ms

prune263.0ms

localize20.0ms

rewrite34.0ms

series180.0ms

simplify81.0ms

prune282.0ms

localize16.0ms

rewrite28.0ms

series81.0ms

simplify68.0ms

prune254.0ms

regimes74.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

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