Details

analyze337.0ms (14.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50%	13
49.9%	0%	50%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample20.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify32.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))
0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

rewrite38.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`sqrt-prod_binary64`
26×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
13×	`distribute-lft-out_binary64`
9×	`distribute-lft-out--_binary64`
6×	`associate-/l*_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `flip-+_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`

Counts

3 → 100

Calls

3 calls:

10.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
9.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series58.0ms (2.4%)

Counts

3 → 9

Calls

3 calls:

33.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
13.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
12.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))

simplify75.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6106	2062

prune122.0ms (5.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	108	2	110

Merged error: 0b

Counts

110 → 2

Compiler

Compiled 2006 to 1618 computations (19.3% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))
0.0b	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))

rewrite56.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64`
92×	`cbrt-prod_binary64`
85×	`add-sqr-sqrt_binary64`
73×	`times-frac_binary64`
40×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64` `sqrt-prod_binary64`
24×	`difference-of-squares_binary64`
18×	`distribute-lft-out_binary64`
12×	`distribute-lft-out--_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`cbrt-div_binary64` `flip3-+_binary64` `associate-l_binary64` `div-inv_binary64` `flip-+_binary64`
2×	`pow1/3_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `sqrt-div_binary64` `-commutative_binary64`

Counts

4 → 140

Calls

4 calls:

23.0ms	(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
7.0ms	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
7.0ms	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

series123.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))))
28.0ms	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
26.0ms	(cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
22.0ms	(atan.f64 (*.f64 (fabs.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))))

simplify98.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4938	4330
1	4938	4330

prune301.0ms (12.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	152	2	154

Merged error: 0b

Counts

154 → 2

Compiler

Compiled 4807 to 3931 computations (18.2% saved)

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (-.f64 1 x))
0.0b	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))

rewrite33.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`sqrt-prod_binary64`
91×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
63×	`times-frac_binary64`
42×	`add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
11×	`distribute-lft-out_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-div_binary64`
7×	`associate-/r*_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`
1×	`cbrt-undiv_binary64` `sqrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 137

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
4.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))
4.0ms	(sqrt.f64 (-.f64 1 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series58.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (+.f64 1 x))
14.0ms	(sqrt.f64 (-.f64 1 x))
8.0ms	(atan.f64 (/.f64 (sqrt.f64 (-.f64 1 x)) (sqrt.f64 (+.f64 1 x))))

simplify83.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5069	3200

prune183.0ms (7.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	149	2	151

Merged error: 0b

Counts

151 → 2

Compiler

Compiled 2974 to 2439 computations (18% saved)

regimes87.0ms (3.6%)

Compiler: Compiled 720 to 638 computations (11.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	35
1	26	35

end0.0ms (0%)

sample651.0ms (27.2%)

Algorithm

1×

intervals

Results

358.0ms

8000×

body

128

valid

Compiler

Compiled 138 to 123 computations (10.9% saved)

Details

analyze337.0ms (14.1%)

sample20.0ms (0.8%)

simplify32.0ms (1.4%)

prune4.0ms (0.2%)

localize9.0ms (0.4%)

rewrite38.0ms (1.6%)

series58.0ms (2.4%)

simplify75.0ms (3.1%)

prune122.0ms (5.1%)

localize11.0ms (0.4%)

rewrite56.0ms (2.4%)

series123.0ms (5.1%)

simplify98.0ms (4.1%)

prune301.0ms (12.6%)

localize10.0ms (0.4%)

rewrite33.0ms (1.4%)

series58.0ms (2.4%)

simplify83.0ms (3.5%)

prune183.0ms (7.7%)

regimes87.0ms (3.6%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample651.0ms (27.2%)

Profiling