Details

analyze802.0ms (14.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

Compiler

Compiled 22 to 18 computations (18.2% saved)

sample44.0ms (0.8%)

Algorithm

1×

intervals

Results

11.0ms	189×	body	80	valid
10.0ms	29×	body	2560	valid
5.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
3.0ms	14×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	39	26
1	39	26

prune7.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 13.5b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.2b	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
13.1b	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 29

Calls

2 calls:

16.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
7.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

series140.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

86.0ms	(+.f64 1 (/.f64 x (sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))))
54.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 4 p) p) (*.f64 x x)))

simplify183.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	5243	691

prune58.0ms (1.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	29	6	35
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	7	36

Merged error: 13.2b

Counts

36 → 7

Compiler

Compiled 921 to 635 computations (31.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
6.3b	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite60.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`sqrt-prod_binary64`
50×	`add-sqr-sqrt_binary64`
34×	`sqrt-pow1_binary64`
29×	`pow1_binary64`
28×	`sqrt-div_binary64`
20×	`*-un-lft-identity_binary64`
18×	`pow1/2_binary64` `add-cube-cbrt_binary64`
15×	`swap-sqr_binary64`
9×	`flip3-+_binary64` `associate-r_binary64` `pow-prod-up_binary64` `associate-l_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-down_binary64` `pow-sqr_binary64`
4×	`insert-posit16` `frac-times_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 129

Calls

4 calls:

27.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
13.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series267.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

96.0ms	(+.f64 1 (/.f64 x (.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
61.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))
57.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
53.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify163.0ms (3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4988	2889
1	4988	2889

prune241.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	139	9	148

Merged error: 13.2b

Counts

148 → 9

Compiler

Compiled 4410 to 2933 computations (33.5% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
13.8b	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
13.8b	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
13.8b	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow1/3_binary64` `sqrt-prod_binary64`
2×	`sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
7.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
7.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series569.0ms (10.3%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
170.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))
168.0ms	(cbrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
55.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 p 4)) (*.f64 x x)))

simplify233.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (207.0ms)

Iter	Nodes	Cost
0	5496	1432

prune214.0ms (3.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	67	12	79

Merged error: 13.2b

Counts

79 → 12

Compiler

Compiled 4708 to 3018 computations (35.9% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

10.7b	(+.f64 1 (/.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
13.1b	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3-+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip-+_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`distribute-lft-out_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 61

Calls

4 calls:

20.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
7.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

series248.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(+.f64 1 (/.f64 x (.f64 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x)))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (.f64 x x))))) (cbrt.f64 (sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))))))
53.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
52.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))
49.0ms	(sqrt.f64 (+.f64 (.f64 p (.f64 4 p)) (*.f64 x x)))

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5064	1287

prune140.0ms (2.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	2	6	8
Picked	1	0	1
Done	0	3	3
Total	74	11	85

Merged error: 13.2b

Counts

85 → 11

Compiler

Compiled 3056 to 1949 computations (36.2% saved)

regimes238.0ms (4.3%)

Compiler: Compiled 3611 to 2604 computations (27.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	26
1	22	26

end0.0ms (0%)

sample1.6s (29.2%)

Algorithm

1×

intervals

Results

335.0ms	6009×	body	80	valid
258.0ms	816×	body	2560	valid
162.0ms	621×	body	1280	valid
156.0ms	8000×	pre	80	true
64.0ms	310×	body	640	valid
24.0ms	158×	body	320	valid
9.0ms	86×	body	160	valid

Compiler

Compiled 550 to 403 computations (26.7% saved)

Details

analyze802.0ms (14.6%)

sample44.0ms (0.8%)

simplify22.0ms (0.4%)

prune7.0ms (0.1%)

localize12.0ms (0.2%)

rewrite24.0ms (0.4%)

series140.0ms (2.5%)

simplify183.0ms (3.3%)

prune58.0ms (1.1%)

localize13.0ms (0.2%)

rewrite60.0ms (1.1%)

series267.0ms (4.9%)

simplify163.0ms (3%)

prune241.0ms (4.4%)

localize30.0ms (0.5%)

rewrite30.0ms (0.5%)

series569.0ms (10.3%)

simplify233.0ms (4.2%)

prune214.0ms (3.9%)

localize16.0ms (0.3%)

rewrite43.0ms (0.8%)

series248.0ms (4.5%)

simplify96.0ms (1.7%)

prune140.0ms (2.5%)

regimes238.0ms (4.3%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.6s (29.2%)

Profiling