Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample38.0ms

Algorithm

intervals

Results

23.0ms	107×	body	1280	valid
5.0ms	115×	body	80	valid
3.0ms	19×	body	640	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify18.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.9b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

3 → 61

Calls

3 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series134.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(/.f64 1/2 (hypot.f64 1 x))
52.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
59.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify94.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4930	1146
1	4930	1146

prune58.0ms

Filtered

46 candidates to 70 candidates (-52.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 15.2b

Counts

71 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.4b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
44×	`times-frac_binary64`
33×	`distribute-lft-out_binary64`
20×	`sqrt-prod_binary64`
19×	`add-cube-cbrt_binary64`
16×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
6×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
5×	`pow1_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
17.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series291.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
53.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
143.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
41.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify94.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4975	3605
1	4975	3605

prune139.0ms

Filtered

71 candidates to 121 candidates (-70.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	118	3	121
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	120	4	124

Merged error: 15.2b

Counts

124 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.2b	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
1.4b	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

rewrite147.0ms

Algorithm

rewrite-expression-head

Rules

217×	`*-un-lft-identity_binary64`
188×	`times-frac_binary64`
147×	`add-sqr-sqrt_binary64`
89×	`distribute-lft-out_binary64`
81×	`add-cube-cbrt_binary64`
48×	`sqrt-prod_binary64`
16×	`associate-/l*_binary64`
12×	`associate-/r*_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
8×	`associate-/r/_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`distribute-rgt-out--_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 204

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
11.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
15.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
100.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

series563.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
104.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
137.0ms	(/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
269.0ms	(-.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 (/.f64 1/2 (hypot.f64 1 x)) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))

simplify144.0ms

Algorithm

egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4911	8113
1	4911	8113

prune435.0ms

Filtered

124 candidates to 216 candidates (-74.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	211	5	216
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	215	5	220

Merged error: 15.0b

Counts

220 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.1b	(*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.1b	(/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
1.4b	(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64` `times-frac_binary64`
19×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`sqrt-prod_binary64`
8×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip-+_binary64`
3×	`cbrt-undiv_binary64` `associate-l_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `distribute-rgt-out_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 104

Calls

4 calls:

11.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
12.0ms	(*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
13.0ms	(/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
27.0ms	(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

series567.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
78.0ms	(*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
131.0ms	(/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
261.0ms	(+.f64 (/.f64 1/2 (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))) (/.f64 -1/2 (*.f64 (hypot.f64 1 x) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))))

simplify109.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5406	3368

prune185.0ms

Filtered

73 candidates to 116 candidates (-58.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Merged error: 15.0b

Counts

121 → 4

regimes32.0ms

Accuracy

0% (0.3b remaining)

Error of 14.8b against oracle of 14.5b and baseline of 14.8b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	67
1	25	67

end0.0ms

sample1.0s

Algorithm

intervals

Results

619.0ms	2797×	body	1280	valid
160.0ms	4124×	body	80	valid
108.0ms	598×	body	640	valid
38.0ms	316×	body	320	valid
13.0ms	165×	body	160	valid

Details

analyze2.0ms

sample38.0ms

simplify18.0ms

prune4.0ms

localize7.0ms

rewrite20.0ms

series134.0ms

simplify94.0ms

prune58.0ms

localize9.0ms

rewrite46.0ms

series291.0ms

simplify94.0ms

prune139.0ms

localize10.0ms

rewrite147.0ms

series563.0ms

simplify144.0ms

prune435.0ms

localize11.0ms

rewrite67.0ms

series567.0ms

simplify109.0ms

prune185.0ms

regimes32.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling