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)

sample19.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

prune2.0ms (0%)

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

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`sqrt-prod_binary64`
6×	`associate-/r*_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 71

Calls

3 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series184.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

126.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
31.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify58.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5024	1543

prune171.0ms (3.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 0b

Counts

81 → 4

Compiler

Compiled 2689 to 2104 computations (21.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite66.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`*-un-lft-identity_binary64`
92×	`add-sqr-sqrt_binary64`
79×	`sqrt-prod_binary64`
76×	`times-frac_binary64`
57×	`distribute-lft-out_binary64`
47×	`add-cube-cbrt_binary64`
42×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l_binary64` `unswap-sqr_binary64` `associate-/l_binary64`
4×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 160

Calls

4 calls:

28.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
11.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(sqrt.f64 (+.f64 x 1))

series357.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
118.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
32.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4950	3818
1	4950	3818

prune329.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	172	4	176

Merged error: 0b

Counts

176 → 4

Compiler

Compiled 3674 to 2333 computations (36.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.3b	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.3b	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
0.4b	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))

rewrite218.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

730×	`sqrt-prod_binary64`
540×	`*-un-lft-identity_binary64`
530×	`add-sqr-sqrt_binary64`
496×	`times-frac_binary64`
236×	`distribute-lft-out_binary64`
229×	`add-cube-cbrt_binary64`
126×	`swap-sqr_binary64`
60×	`associate-r_binary64` `associate-l_binary64`
25×	`unswap-sqr_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-/r*_binary64`
14×	`sqrt-div_binary64`
12×	`pow1_binary64` `associate-/r/_binary64` `associate-/l*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`cbrt-undiv_binary64` `sqrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `pow-prod-up_binary64` `rem-square-sqrt_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 483

Calls

4 calls:

90.0ms	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
16.0ms	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
12.0ms	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
7.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series857.0ms (16.6%)

Counts

4 → 12

Calls

4 calls:

340.0ms	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
332.0ms	(/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
115.0ms	(*.f64 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))) (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))))
70.0ms	(sqrt.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))))

simplify218.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

495 → 495

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4962	16980
1	4962	16980

prune1.1s (22.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	495	0	495
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	495	4	499

Merged error: 0b

Counts

499 → 4

Compiler

Compiled 15004 to 10894 computations (27.4% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
0.2b	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
29.9b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))

rewrite65.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`*-un-lft-identity_binary64`
91×	`add-sqr-sqrt_binary64`
90×	`times-frac_binary64`
68×	`distribute-lft-out_binary64`
57×	`add-cube-cbrt_binary64`
54×	`cbrt-prod_binary64`
48×	`unpow-prod-down_binary64` `cube-prod_binary64`
34×	`sqrt-prod_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `add-log-exp_binary64` `flip-+_binary64`
5×	`pow1_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`cbrt-undiv_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 187

Calls

4 calls:

14.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
13.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
10.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series541.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

269.0ms	(pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3)
130.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1)))) 3))
115.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
27.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify94.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5037	4793

prune225.0ms (4.4%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	199	0	199
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	199	4	203

Merged error: 0b

Counts

203 → 4

Compiler

Compiled 3820 to 2925 computations (23.4% saved)

regimes24.0ms (0.5%)

Compiler: Compiled 122 to 102 computations (16.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	9	12

end0.0ms (0%)

sample426.0ms (8.2%)

Algorithm

1×

intervals

Results

228.0ms	7996×	body	128	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 69 to 59 computations (14.5% saved)

Details

analyze3.0ms (0.1%)

sample19.0ms (0.4%)

simplify8.0ms (0.2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite25.0ms (0.5%)

series184.0ms (3.6%)

simplify58.0ms (1.1%)

prune171.0ms (3.3%)

localize7.0ms (0.1%)

rewrite66.0ms (1.3%)

series357.0ms (6.9%)

simplify94.0ms (1.8%)

prune329.0ms (6.4%)

localize9.0ms (0.2%)

rewrite218.0ms (4.2%)

series857.0ms (16.6%)

simplify218.0ms (4.2%)

prune1.1s (22.2%)

localize8.0ms (0.2%)

rewrite65.0ms (1.3%)

series541.0ms (10.5%)

simplify94.0ms (1.8%)

prune225.0ms (4.4%)

regimes24.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample426.0ms (8.2%)

Profiling