Details

analyze609.0ms (10.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample40.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	36×	body	2048	valid
8.0ms	172×	body	128	valid
6.0ms	11×	body	4096	valid
4.0ms	22×	body	1024	valid
1.0ms	11×	body	512	valid
1.0ms	24×	body	128	nan
0.0ms	4×	body	256	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify193.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 32.4b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series494.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
120.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
56.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify69.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4975	2155
1	4975	2155

prune106.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	9	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	9	95

Merged error: 5.6b

Counts

95 → 9

Compiler

Compiled 2047 to 426 computations (79.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

16.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series483.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
58.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify100.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4895	1889
1	4895	1889

prune83.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	94	10	104

Merged error: 5.6b

Counts

104 → 10

Compiler

Compiled 2035 to 594 computations (70.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series502.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
120.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
119.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
100.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify63.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4965	1324
1	4965	1324

prune73.0ms (1.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	70	10	80

Merged error: 5.6b

Counts

80 → 10

Compiler

Compiled 2304 to 434 computations (81.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.9b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.2b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
12.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series890.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

369.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
285.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
121.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify111.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5322	8155

prune197.0ms (3.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	229	10	239

Merged error: 5.6b

Counts

239 → 10

Compiler

Compiled 6523 to 812 computations (87.6% saved)

regimes153.0ms (2.7%)

Compiler: Compiled 537 to 354 computations (34.1% saved)

bsearch84.0ms (1.5%)

Steps

Iters	Range	Point
6	1.7970418206640836e+48	1.3661902469412723e+49	1.3393452413162394e+49
8	-1.9231846378125796e-175	-1.9752681808694755e-179	-2.015156662498609e-179
9	-7.799907689180803e+153	-1.140147330439728e+149	-4.889385504355394e+152

Iters

Range

Point

1.7970418206640836e+48

1.3661902469412723e+49

1.3393452413162394e+49

-1.9231846378125796e-175

-1.9752681808694755e-179

-2.015156662498609e-179

-7.799907689180803e+153

-1.140147330439728e+149

-4.889385504355394e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	88
1	101	88

end0.0ms (0%)

sample1.2s (21.5%)

Algorithm

1×

intervals

Results

240.0ms	5204×	body	128	valid
233.0ms	1115×	body	2048	valid
129.0ms	768×	body	1024	valid
108.0ms	408×	body	4096	valid
42.0ms	339×	body	512	valid
37.0ms	841×	body	128	nan
14.0ms	166×	body	256	valid
13.0ms	281×	body	128	invalid

Compiler

Compiled 250 to 162 computations (35.2% saved)

Details

analyze609.0ms (10.6%)

sample40.0ms (0.7%)

simplify193.0ms (3.4%)

prune6.0ms (0.1%)

localize16.0ms (0.3%)

rewrite41.0ms (0.7%)

series494.0ms (8.6%)

simplify69.0ms (1.2%)

prune106.0ms (1.8%)

localize9.0ms (0.2%)

rewrite42.0ms (0.7%)

series483.0ms (8.4%)

simplify100.0ms (1.8%)

prune83.0ms (1.5%)

localize11.0ms (0.2%)

rewrite32.0ms (0.6%)

series502.0ms (8.8%)

simplify63.0ms (1.1%)

prune73.0ms (1.3%)

localize10.0ms (0.2%)

rewrite69.0ms (1.2%)

series890.0ms (15.6%)

simplify111.0ms (1.9%)

prune197.0ms (3.4%)

regimes153.0ms (2.7%)

bsearch84.0ms (1.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.5%)

Profiling