Details

analyze1.0ms (0%)

Algorithm

1×

Search

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

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	89×	body	1280	valid
9.0ms	129×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid

simplify24.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune5.0ms (0.1%)

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: 17.0b

Counts

2 → 1

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
0.0b	(/.f64 1.0 (hypot.f64 1.0 x))
0.0b	(hypot.f64 1.0 x)
2.8b	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))

rewrite16.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

4 → 60

Calls

4 calls:

7.0ms	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
4.0ms	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
3.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
1.0ms	(hypot.f64 1.0 x)

series51.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
21.0ms	(sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x)))))
6.0ms	(/.f64 1.0 (hypot.f64 1.0 x))
1.0ms	(hypot.f64 1.0 x)

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5551	757

prune107.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	3	73

Merged error: 16.5b

Counts

73 → 3

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1.0 x)
0.0b	(hypot.f64 1.0 x)
0.0b	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
2.4b	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
9×	`add-sqr-sqrt_binary64`
4×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`diff-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`flip3-+_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 46

Calls

4 calls:

11.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))
3.0ms	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
1.0ms	(hypot.f64 1.0 x)
1.0ms	(hypot.f64 1.0 x)

series29.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 1.0 (sqrt.f64 (*.f64 0.5 (+.f64 1.0 (/.f64 1.0 (hypot.f64 1.0 x))))))
9.0ms	(-.f64 (-.f64 1.0 0.5) (/.f64 0.5 (hypot.f64 1.0 x)))
1.0ms	(hypot.f64 1.0 x)
1.0ms	(hypot.f64 1.0 x)

simplify48.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	647
1	4973	647

prune107.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	57	1	58
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	57	4	61

Merged error: 16.5b

Counts

61 → 4

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
0.1b	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
0.5b	(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
2.3b	(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))

rewrite60.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
52×	`sqrt-prod_binary64`
46×	`sqrt-div_binary64`
41×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
17×	`flip3--_binary64` `flip--_binary64`
16×	`frac-times_binary64`
12×	`associate-r_binary64` `difference-of-squares_binary64` `frac-sub_binary64`
10×	`frac-add_binary64`
9×	`distribute-lft-out--_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

32.0ms	(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
14.0ms	(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))
6.0ms	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
3.0ms	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))

series81.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (+.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))) (-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))))
16.0ms	(-.f64 (sqrt.f64 (-.f64 1.0 0.5)) (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))))
15.0ms	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))
14.0ms	(sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x)))

simplify47.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5118	2888

prune494.0ms (8.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	139	1	140
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	140	4	144

Merged error: 16.5b

Counts

144 → 4

localize42.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.8b	(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)
1.0b	(.f64 (sqrt.f64 (+.f64 (.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))
1.0b	(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
2.3b	(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))

rewrite78.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

136×	`add-sqr-sqrt_binary64`
102×	`sqrt-prod_binary64`
70×	`unpow-prod-down_binary64` `cube-prod_binary64`
64×	`*-un-lft-identity_binary64`
50×	`difference-of-squares_binary64`
30×	`add-cube-cbrt_binary64` `times-frac_binary64`
19×	`distribute-lft-out--_binary64`
16×	`sqr-pow_binary64`
12×	`pow1_binary64`
9×	`sqrt-div_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`cube-div_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `associate-r_binary64` `pow-pow_binary64` `associate-l_binary64`
4×	`pow1/2_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `flip--_binary64`
2×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `rem-cube-cbrt_binary64` `div-inv_binary64` `frac-sub_binary64` `pow-exp_binary64` `unpow3_binary64` `associate-*l/_binary64` `cube-mult_binary64`
1×	`difference-cubes_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 198

Calls

4 calls:

46.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))
10.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))
6.0ms	(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
6.0ms	(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)

series71.0ms (1.2%)

Counts

4 → 8

Calls

4 calls:

48.0ms	(-.f64 (pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3) (pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3))
23.0ms	(pow.f64 (sqrt.f64 (/.f64 0.5 (hypot.f64 1.0 x))) 3)
0.0ms	(pow.f64 (sqrt.f64 (-.f64 1.0 0.5)) 3)
0.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 1.0 1.0) (*.f64 0.5 (+.f64 1.0 0.5)))) (sqrt.f64 0.5))

simplify53.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5185	3816

prune2.9s (50.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	203	3	206
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	205	5	210

Merged error: 16.1b

Counts

210 → 5

regimes291.0ms (5.1%)

Accuracy

Total 0.3b remaining (1.7%)

Threshold costs 0.3b (1.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	24
1	37	24

end0.0ms (0%)

sample1.1s (18.4%)

Algorithm

1×

intervals

Results

638.0ms	2899×	body	1280	valid
157.0ms	4050×	body	80	valid
108.0ms	595×	body	640	valid
37.0ms	305×	body	320	valid
12.0ms	151×	body	160	valid

Details

analyze1.0ms (0%)

sample40.0ms (0.7%)

simplify24.0ms (0.4%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite16.0ms (0.3%)

series51.0ms (0.9%)

simplify60.0ms (1%)

prune107.0ms (1.9%)

localize13.0ms (0.2%)

rewrite17.0ms (0.3%)

series29.0ms (0.5%)

simplify48.0ms (0.8%)

prune107.0ms (1.9%)

localize18.0ms (0.3%)

rewrite60.0ms (1%)

series81.0ms (1.4%)

simplify47.0ms (0.8%)

prune494.0ms (8.6%)

localize42.0ms (0.7%)

rewrite78.0ms (1.4%)

series71.0ms (1.2%)

simplify53.0ms (0.9%)

prune2.9s (50.9%)

regimes291.0ms (5.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.1s (18.4%)

Profiling