Details

analyze605.0ms (9.8%)

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)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

8.0ms	39×	body	2048	valid
8.0ms	167×	body	128	valid
4.0ms	15×	body	4096	valid
3.0ms	19×	body	1024	valid
1.0ms	9×	body	512	valid
1.0ms	22×	body	128	nan
1.0ms	7×	body	256	valid
1.0ms	12×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify189.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune8.0ms (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: 31.3b

Counts

2 → 1

Compiler

Compiled 49 to 37 computations (24.5% saved)

localize10.0ms (0.2%)

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))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

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` `cancel-sign-sub-inv_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 → 86

Calls

4 calls:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series490.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
124.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
60.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4877	2170
1	4877	2170

prune387.0ms (6.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	88	10	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Merged error: 5.1b

Counts

99 → 11

Compiler

Compiled 7591 to 3775 computations (50.3% saved)

localize10.0ms (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))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
13×	`associate-r_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×	`cancel-sign-sub-inv_binary64` `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 → 87

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
11.0ms	(-.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))

series459.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
118.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5038	1904

prune128.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	98	12	110

Merged error: 5.1b

Counts

110 → 12

Compiler

Compiled 2843 to 1141 computations (59.9% saved)

localize10.0ms (0.2%)

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)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

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` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 164

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series495.0ms (8%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
97.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
50.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify104.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5062	5163

prune179.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	2	8	10
Picked	1	0	1
Done	0	1	1
Total	176	12	188

Merged error: 5.1b

Counts

188 → 12

Compiler

Compiled 4998 to 1321 computations (73.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite124.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

789×	`times-frac_binary64`
494×	`add-sqr-sqrt_binary64`
407×	`*-un-lft-identity_binary64`
321×	`add-cube-cbrt_binary64`
86×	`difference-of-squares_binary64`
46×	`sqrt-prod_binary64`
44×	`add-exp-log_binary64`
43×	`distribute-lft-out--_binary64`
40×	`div-inv_binary64`
32×	`div-exp_binary64`
29×	`associate-/r/_binary64`
24×	`associate-/r*_binary64`
17×	`flip3--_binary64` `flip--_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64`
5×	`pow1_binary64`
4×	`cancel-sign-sub-inv_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 425

Calls

4 calls:

26.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
9.0ms	(-.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))

series498.0ms (8%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
100.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify195.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

437 → 437

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5050	17791

prune456.0ms (7.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	437	0	437
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	437	12	449

Merged error: 5.1b

Counts

449 → 12

Compiler

Compiled 12779 to 3245 computations (74.6% saved)

regimes213.0ms (3.4%)

Compiler: Compiled 492 to 375 computations (23.8% saved)

bsearch94.0ms (1.5%)

Steps

Iters	Range	Point
8	1.8173103053317733e+102	3.268093057783e+106	2.7099763392697605e+106
8	4.906681521097057e-200	3.115477367038795e-197	4.525283768938065e-198
10	-9.016554096635856e+165	-6.078197847532872e+152	-1.3450496563396583e+154

Iters

Range

Point

1.8173103053317733e+102

3.268093057783e+106

2.7099763392697605e+106

4.906681521097057e-200

3.115477367038795e-197

4.525283768938065e-198

-9.016554096635856e+165

-6.078197847532872e+152

-1.3450496563396583e+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	110	85
1	110	85

end0.0ms (0%)

sample1.2s (19.4%)

Algorithm

1×

intervals

Results

233.0ms	1138×	body	2048	valid
223.0ms	5229×	body	128	valid
111.0ms	689×	body	1024	valid
103.0ms	388×	body	4096	valid
42.0ms	360×	body	512	valid
31.0ms	767×	body	128	nan
16.0ms	196×	body	256	valid
12.0ms	271×	body	128	invalid

Compiler

Compiled 233 to 164 computations (29.6% saved)

Details

analyze605.0ms (9.8%)

sample37.0ms (0.6%)

simplify189.0ms (3.1%)

prune8.0ms (0.1%)

localize10.0ms (0.2%)

rewrite47.0ms (0.8%)

series490.0ms (7.9%)

simplify70.0ms (1.1%)

prune387.0ms (6.3%)

localize10.0ms (0.2%)

rewrite44.0ms (0.7%)

series459.0ms (7.4%)

simplify69.0ms (1.1%)

prune128.0ms (2.1%)

localize10.0ms (0.2%)

rewrite56.0ms (0.9%)

series495.0ms (8%)

simplify104.0ms (1.7%)

prune179.0ms (2.9%)

localize11.0ms (0.2%)

rewrite124.0ms (2%)

series498.0ms (8%)

simplify195.0ms (3.2%)

prune456.0ms (7.4%)

regimes213.0ms (3.4%)

bsearch94.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (19.4%)

Profiling