Details

analyze2.0ms

Algorithm

Search

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

sample38.0ms

Algorithm

intervals

Results

21.0ms	97×	body	1280	valid
5.0ms	29×	body	640	valid
4.0ms	115×	body	80	valid
1.0ms	10×	body	320	valid
0.0ms	5×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	46	15
1	46	15

prune5.0ms

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: 17.5b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.7b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`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

4 → 68

Calls

4 calls:

1.0ms	(hypot.f64 1 x)
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series140.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(hypot.f64 1 x)
54.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
25.0ms	(/.f64 1/2 (hypot.f64 1 x))
59.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify95.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4840	1209
1	4840	1209

prune65.0ms

Filtered

53 candidates to 80 candidates (-50.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	3	81

Merged error: 17.1b

Counts

81 → 3

localize9.0ms

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 (hypot.f64 1 x))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series131.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
22.0ms	(/.f64 1/2 (hypot.f64 1 x))
22.0ms	(/.f64 1/2 (hypot.f64 1 x))
38.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (128.0ms)

Iter	Nodes	Cost
0	4818	1342
1	4818	1342

prune111.0ms

Filtered

68 candidates to 96 candidates (-41.2%)

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: 16.8b

Counts

99 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.5b	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

62×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
34×	`sqrt-prod_binary64`
20×	`add-cube-cbrt_binary64`
19×	`pow1_binary64`
15×	`times-frac_binary64`
13×	`swap-sqr_binary64`
12×	`difference-of-squares_binary64` `sqrt-div_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
8×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-/l_binary64` `pow-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

3.0ms	(/.f64 1/2 (hypot.f64 1 x))
19.0ms	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series139.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/.f64 1/2 (hypot.f64 1 x))
35.0ms	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
42.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
38.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify121.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4812	2164
1	4812	2164

prune187.0ms

Filtered

78 candidates to 135 candidates (-73.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Merged error: 16.8b

Counts

139 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.2b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
1.2b	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64`
20×	`sqrt-prod_binary64`
14×	`log-pow_binary64`
13×	`associate-r_binary64`
12×	`exp-prod_binary64`
11×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `difference-of-squares_binary64`
9×	`associate-l_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`distribute-lft-out--_binary64` `times-frac_binary64`
4×	`log-prod_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-log-exp_binary64` `sqrt-unprod_binary64` `exp-diff_binary64` `exp-sum_binary64` `prod-exp_binary64` `log-div_binary64` `*-commutative_binary64`

Counts

4 → 90

Calls

4 calls:

23.0ms	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
8.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series146.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(*.f64 (sqrt.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))) (sqrt.f64 (log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))))
39.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
36.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
35.0ms	(log.f64 (exp.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify91.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4833	1662
1	4833	1662

prune170.0ms

Filtered

69 candidates to 102 candidates (-47.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	100	2	102
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	101	5	106

Merged error: 16.8b

Counts

106 → 5

regimes35.0ms

Accuracy

0% (0.7b remaining)

Error of 15.6b against oracle of 14.8b and baseline of 15.6b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	60	71
1	60	71

end0.0ms

sample1.1s

Algorithm

intervals

Results

654.0ms	2906×	body	1280	valid
158.0ms	3995×	body	80	valid
114.0ms	648×	body	640	valid
38.0ms	307×	body	320	valid
11.0ms	144×	body	160	valid

Details

analyze2.0ms

sample38.0ms

simplify19.0ms

prune5.0ms

localize7.0ms

rewrite21.0ms

series140.0ms

simplify95.0ms

prune65.0ms

localize9.0ms

rewrite21.0ms

series131.0ms

simplify149.0ms

prune111.0ms

localize12.0ms

rewrite40.0ms

series139.0ms

simplify121.0ms

prune187.0ms

localize16.0ms

rewrite48.0ms

series146.0ms

simplify91.0ms

prune170.0ms

regimes35.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling