Details

analyze996.0ms (12%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1992	72
1	1992	72
0	3	3
1	3	3

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 (0.5%)

Algorithm

1×

intervals

Results

7.0ms	172×	body	128	valid
7.0ms	32×	body	2048	valid
4.0ms	23×	body	1024	valid
3.0ms	13×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	15×	body	128	invalid
0.0ms	5×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	714	18
1	714	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

Error

31.5b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (0.1%)

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)
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite131.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

31.3b

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`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` `cancel-sign-sub-inv_binary64`
3×	`associate-/r*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

13.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
10.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2014 to 333 computations (83.5% saved)

series661.0ms (8%)

Error

6.1b

Counts

4 → 70

Calls

4 calls:

184.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
148.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
146.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
126.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2738 to 1906 computations (30.4% saved)

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5251	3035

prune125.0ms (1.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	145	11	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	11	157

Error

6.0b

Counts

157 → 11

Compiler

Compiled 2836 to 635 computations (77.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.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)
1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite198.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

144×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `flip--_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `pow-flip_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 164

Calls

4 calls:

14.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
10.0ms	(-.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))

Compiler

Compiled 4825 to 1174 computations (75.7% saved)

series630.0ms (7.6%)

Error

6.0b

Counts

4 → 70

Calls

4 calls:

183.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
142.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
132.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
127.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3006 to 2177 computations (27.6% saved)

simplify114.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4963	6026
1	4963	6026

prune182.0ms (2.2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	233	1	234
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	233	12	245

Error

6.0b

Counts

245 → 12

Compiler

Compiled 5310 to 1227 computations (76.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite109.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

30×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `associate-r_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×	`cancel-sign-sub-inv_binary64` `difference-of-squares_binary64` `prod-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `cbrt-unprod_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64` `cbrt-undiv_binary64` `un-div-inv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
7.0ms	(-.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))

Compiler

Compiled 2156 to 599 computations (72.2% saved)

series639.0ms (7.7%)

Error

6.0b

Counts

4 → 70

Calls

4 calls:

188.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
138.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
138.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
123.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 3006 to 2186 computations (27.3% saved)

simplify86.0ms (1%)

Algorithm

1×	egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4962	2787
1	4962	2787

prune120.0ms (1.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	157	0	157
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	157	12	169

Error

6.0b

Counts

169 → 12

Compiler

Compiled 2952 to 923 computations (68.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
1.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
20.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite69.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

6.0b

Rules

12×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64` `cancel-sign-sub-inv_binary64`
3×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
2×	`sqrt-div_binary64` `diff-log_binary64` `sub-neg_binary64` `difference-of-squares_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `pow1/3_binary64`

Counts

4 → 55

Calls

4 calls:

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))
1.0ms	(cbrt.f64 a)

Compiler

Compiled 1518 to 297 computations (80.4% saved)

series533.0ms (6.4%)

Error

6.0b

Counts

4 → 57

Calls

4 calls:

144.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
137.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
125.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
78.0ms	(cbrt.f64 a)

Compiler

Compiled 3227 to 1847 computations (42.8% saved)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4916	1594
1	4916	1594

prune87.0ms (1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	6	9
Picked	0	1	1
Done	0	2	2
Total	112	12	124

Error

6.0b

Counts

124 → 12

Compiler

Compiled 2512 to 475 computations (81.1% saved)

regimes1.0s (12.3%)

Accuracy

Total 3.2b remaining (37.6%)

Threshold costs 0b (0%)

Compiler

Compiled 5520 to 3398 computations (38.4% saved)

bsearch116.0ms (1.4%)

Steps

Iters	Range		Point
11	970439.7667140847	4.823276898905944e+26	2101650834768822.8
10	4.9991337409591946e-132	2.2819827125566793e-122	1.496397647743439e-129
9	-9.798057463869279e+160	-2.583958821678533e+153	-1.1611459299322468e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	99	91
1	99	91

end0.0ms (0%)

sample2.2s (26.2%)

Algorithm

1×

intervals

Results

235.0ms	1156×	body	2048	valid
235.0ms	5189×	body	128	valid
131.0ms	782×	body	1024	valid
90.0ms	354×	body	4096	valid
43.0ms	338×	body	512	valid
30.0ms	756×	body	128	nan
14.0ms	181×	body	256	valid
11.0ms	266×	body	128	invalid

Compiler

Compiled 1446 to 886 computations (38.7% saved)

Details

analyze996.0ms (12%)

sample40.0ms (0.5%)

simplify72.0ms (0.9%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite131.0ms (1.6%)

series661.0ms (8%)

simplify75.0ms (0.9%)

prune125.0ms (1.5%)

localize10.0ms (0.1%)

rewrite198.0ms (2.4%)

series630.0ms (7.6%)

simplify114.0ms (1.4%)

prune182.0ms (2.2%)

localize11.0ms (0.1%)

rewrite109.0ms (1.3%)

series639.0ms (7.7%)

simplify86.0ms (1%)

prune120.0ms (1.4%)

localize12.0ms (0.1%)

rewrite69.0ms (0.8%)

series533.0ms (6.4%)

simplify74.0ms (0.9%)

prune87.0ms (1%)

regimes1.0s (12.3%)

bsearch116.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.2s (26.2%)

Profiling