Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.3%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify164.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

prune2.0ms (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: 0.2b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite25.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64_3488`
26×	`add-sqr-sqrt_binary64_3510`
21×	`distribute-lft-out_binary64_3439`
18×	`times-frac_binary64_3494`
15×	`add-cube-cbrt_binary64_3523`
14×	`sqrt-prod_binary64_3504`
6×	`associate-/r*_binary64_3432`
5×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `add-log-exp_binary64_3527`
4×	`pow1_binary64_3549`
3×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/l*_binary64_3433`
2×	`sqrt-div_binary64_3505` `associate-/r/_binary64_3434`
1×	`clear-num_binary64_3487` `+-commutative_binary64_3418` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `div-exp_binary64_3539` `sum-log_binary64_3579` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `rem-sqrt-square_binary64_3501`

Counts

3 → 71

Calls

3 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series176.0ms (4.7%)

Counts

3 → 9

Calls

3 calls:

121.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
29.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify56.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5025	1543

prune83.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	76	5	81

Merged error: 0b

Counts

81 → 5

Compiler

Compiled 1350 to 1005 computations (25.6% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.1b	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite48.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_3488`
51×	`add-sqr-sqrt_binary64_3510`
38×	`times-frac_binary64_3494`
33×	`distribute-lft-out_binary64_3439`
27×	`add-cube-cbrt_binary64_3523`
24×	`associate-r_binary64_3428`
20×	`sqrt-prod_binary64_3504`
17×	`add-exp-log_binary64_3526`
11×	`add-cbrt-cube_binary64_3524`
8×	`pow1_binary64_3549`
6×	`associate-/r*_binary64_3432` `add-log-exp_binary64_3527`
4×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434` `div-exp_binary64_3539` `prod-exp_binary64_3537`
3×	`unswap-sqr_binary64_3456` `associate-/l_binary64_3433` `associate-l*_binary64_3429`
2×	`1-exp_binary64_3532` `sqrt-div_binary64_3505` `cbrt-unprod_binary64_3521` `rec-exp_binary64_3538` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485`
1×	`clear-num_binary64_3487` `pow-flip_binary64_3562` `+-commutative_binary64_3418` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `inv-pow_binary64_3573` `pow1/2_binary64_3568` `-commutative_binary64_3419` `sqrt-pow1_binary64_3506` `sum-log_binary64_3579` `un-div-inv_binary64_3486` `rem-sqrt-square_binary64_3501`

Counts

4 → 122

Calls

4 calls:

16.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
9.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

series252.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(*.f64 x (/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
85.0ms	(/.f64 1 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify81.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5002	2480

prune138.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	134	5	139

Merged error: 0b

Counts

139 → 5

Compiler

Compiled 2449 to 1968 computations (19.6% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.4b	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.4b	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
0.7b	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite104.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`*-un-lft-identity_binary64_3488`
150×	`add-sqr-sqrt_binary64_3510`
131×	`sqrt-prod_binary64_3504`
130×	`times-frac_binary64_3494`
73×	`add-cube-cbrt_binary64_3523`
60×	`distribute-lft-out_binary64_3439`
33×	`associate-l_binary64_3429` `associate-r_binary64_3428`
32×	`add-exp-log_binary64_3526`
20×	`add-cbrt-cube_binary64_3524`
18×	`associate-/r*_binary64_3432`
15×	`unswap-sqr_binary64_3456`
11×	`div-exp_binary64_3539`
10×	`sqrt-div_binary64_3505`
9×	`pow1_binary64_3549`
8×	`associate-/r/_binary64_3434` `prod-exp_binary64_3537`
6×	`associate-/l*_binary64_3433` `cbrt-undiv_binary64_3522`
5×	`flip-+_binary64_3462` `flip3-+_binary64_3491`
4×	`cbrt-unprod_binary64_3521` `add-log-exp_binary64_3527` `div-inv_binary64_3485`
3×	`1-exp_binary64_3532` `pow-flip_binary64_3562` `rec-exp_binary64_3538`
2×	`clear-num_binary64_3487` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `sqrt-pow1_binary64_3506`
1×	`associate-l/_binary64_3431` `frac-times_binary64_3498` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `inv-pow_binary64_3573` `*-commutative_binary64_3419` `rem-sqrt-square_binary64_3501`

Counts

4 → 235

Calls

4 calls:

43.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
7.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series566.0ms (15.3%)

Counts

4 → 12

Calls

4 calls:

228.0ms	(/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
154.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
120.0ms	(*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 x (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
63.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify93.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4982	6905
1	4982	6905

prune478.0ms (12.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	247	0	247
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	247	5	252

Merged error: 0b

Counts

252 → 5

Compiler

Compiled 7061 to 5784 computations (18.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.1b	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))

rewrite64.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64_3488`
92×	`add-sqr-sqrt_binary64_3510`
79×	`sqrt-prod_binary64_3504`
76×	`times-frac_binary64_3494`
57×	`distribute-lft-out_binary64_3439`
47×	`add-cube-cbrt_binary64_3523`
42×	`associate-r_binary64_3428`
11×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
7×	`pow1_binary64_3549`
6×	`associate-/r_binary64_3432` `unswap-sqr_binary64_3456` `associate-/l_binary64_3433` `associate-l_binary64_3429` `add-log-exp_binary64_3527`
4×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `associate-/r/_binary64_3434`
2×	`sqrt-div_binary64_3505` `cbrt-unprod_binary64_3521` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `prod-exp_binary64_3537`
1×	`clear-num_binary64_3487` `+-commutative_binary64_3418` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `pow1/2_binary64_3568` `-commutative_binary64_3419` `sqrt-pow1_binary64_3506` `sum-log_binary64_3579` `rem-sqrt-square_binary64_3501`

Counts

4 → 160

Calls

4 calls:

26.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series339.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
111.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
27.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4951	3818
1	4951	3818

prune176.0ms (4.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	172	5	177

Merged error: 0b

Counts

177 → 5

Compiler

Compiled 3642 to 2305 computations (36.7% saved)

regimes67.0ms (1.8%)

Compiler: Compiled 578 to 478 computations (17.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample653.0ms (17.6%)

Algorithm

1×

intervals

Results

227.0ms	7997×	body	128	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 297 to 247 computations (16.8% saved)

Details

analyze3.0ms (0.1%)

sample12.0ms (0.3%)

simplify164.0ms (4.4%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite25.0ms (0.7%)

series176.0ms (4.7%)

simplify56.0ms (1.5%)

prune83.0ms (2.2%)

localize6.0ms (0.2%)

rewrite48.0ms (1.3%)

series252.0ms (6.8%)

simplify81.0ms (2.2%)

prune138.0ms (3.7%)

localize11.0ms (0.3%)

rewrite104.0ms (2.8%)

series566.0ms (15.3%)

simplify93.0ms (2.5%)

prune478.0ms (12.9%)

localize8.0ms (0.2%)

rewrite64.0ms (1.7%)

series339.0ms (9.1%)

simplify94.0ms (2.5%)

prune176.0ms (4.8%)

regimes67.0ms (1.8%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample653.0ms (17.6%)

Profiling