Details

analyze12.0ms (0.3%)

Algorithm

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)

sample22.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify126.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	466	17
1	466	17

prune4.0ms (0.1%)

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

Error

0.0b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 6 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)))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0b	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0b	(/.f64 (-.f64 1 x) (+.f64 1 x))

rewrite43.0ms (1%)

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

6 calls:

21.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
9.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
1.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
0.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))
0.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))

series70.0ms (1.7%)

Counts

3 → 17

Calls

3 calls:

32.0ms	(/.f64 (-.f64 1 x) (+.f64 1 x))
19.0ms	(atan.f64 (sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x))))
19.0ms	(sqrt.f64 (/.f64 (-.f64 1 x) (+.f64 1 x)))

Compiler

Compiled 260 to 252 computations (3.1% saved)

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6419	2047

prune182.0ms (4.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	115	3	118

Error

Counts

118 → 3

Compiler

Compiled 2032 to 1639 computations (19.3% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite74.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`*-un-lft-identity_binary64`
66×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
23×	`sqrt-prod_binary64`
18×	`cancel-sign-sub-inv_binary64`
17×	`distribute-lft-out_binary64`
16×	`distribute-lft-out--_binary64`
14×	`div-inv_binary64`
12×	`distribute-rgt-out--_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64` `sqrt-div_binary64`
3×	`associate-/l*_binary64`
2×	`flip3--_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64`

Counts

4 → 128

Calls

8 calls:

28.0ms	(sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x))))
26.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
5.0ms	(/.f64 x (+.f64 1 x))
1.0ms	(atan.f64 (sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))))
0.0ms	(/.f64 1 (+.f64 1 x))

series93.0ms (2.2%)

Counts

4 → 25

Calls

4 calls:

27.0ms	(-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))
26.0ms	(/.f64 x (+.f64 1 x))
21.0ms	(sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x))))
19.0ms	(atan.f64 (sqrt.f64 (-.f64 (/.f64 1 (+.f64 1 x)) (/.f64 x (+.f64 1 x)))))

Compiler

Compiled 446 to 416 computations (6.7% saved)

simplify71.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4980	2592
1	4980	2592

prune172.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	153	3	156

Error

Counts

156 → 3

Compiler

Compiled 2985 to 2392 computations (19.9% saved)

localize12.0ms (0.3%)

Local error

Found 8 expressions with local error:

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

rewrite95.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`times-frac_binary64`
153×	`*-un-lft-identity_binary64`
124×	`cbrt-div_binary64`
107×	`add-sqr-sqrt_binary64`
104×	`cbrt-prod_binary64`
74×	`associate-/r/_binary64`
69×	`add-cube-cbrt_binary64`
62×	`flip3-+_binary64` `flip-+_binary64`
40×	`frac-times_binary64`
26×	`distribute-lft-out_binary64`
24×	`associate-/l*_binary64`
20×	`associate-r/_binary64` `add-exp-log_binary64` `difference-of-squares_binary64` `associate-l/_binary64`
11×	`pow1_binary64` `add-cbrt-cube_binary64`
10×	`distribute-lft-out--_binary64` `div-inv_binary64`
9×	`swap-sqr_binary64`
8×	`associate-/r*_binary64`
7×	`associate-r_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `associate-l_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`associate-/l/_binary64` `cbrt-unprod_binary64` `div-sub_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64`
1×	`flip3--_binary64` `pow-plus_binary64` `flip--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 276

Calls

8 calls:

23.0ms	(/.f64 (/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 1 x)))
19.0ms	(/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
12.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
0.0ms	(sqrt.f64 (/.f64 (/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 1 x))))

series180.0ms (4.3%)

Counts

4 → 31

Calls

4 calls:

54.0ms	(*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))
53.0ms	(/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x))))
41.0ms	(cbrt.f64 (+.f64 1 x))
31.0ms	(/.f64 (/.f64 (-.f64 1 x) (*.f64 (cbrt.f64 (+.f64 1 x)) (cbrt.f64 (+.f64 1 x)))) (cbrt.f64 (+.f64 1 x)))

Compiler

Compiled 842 to 760 computations (9.7% saved)

simplify123.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5040	8762

prune736.0ms (17.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	307	3	310

Error

Counts

310 → 3

Compiler

Compiled 8911 to 7130 computations (20% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	174	513
1	174	513

regimes204.0ms (4.9%)

Accuracy

Total 0.0b remaining (93.6%)

Threshold costs 0.0b (93.6%)

Compiler

Compiled 1944 to 1750 computations (10% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	23
1	30	23

end0.0ms (0%)

sample1.9s (44.5%)

Algorithm

1×

intervals

Results

381.0ms

8000×

body

128

valid

Compiler

Compiled 990 to 882 computations (10.9% saved)

Pareto

0.8512777604450087

Details

analyze12.0ms (0.3%)

sample22.0ms (0.5%)

simplify126.0ms (3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite43.0ms (1%)

series70.0ms (1.7%)

simplify81.0ms (1.9%)

prune182.0ms (4.3%)

localize9.0ms (0.2%)

rewrite74.0ms (1.8%)

series93.0ms (2.2%)

simplify71.0ms (1.7%)

prune172.0ms (4.1%)

localize12.0ms (0.3%)

rewrite95.0ms (2.3%)

series180.0ms (4.3%)

simplify123.0ms (2.9%)

prune736.0ms (17.5%)

simplify9.0ms (0.2%)

regimes204.0ms (4.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.9s (44.5%)

Profiling