Details

analyze1.3s (13.5%)

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)

sample68.0ms (0.7%)

Algorithm

1×

intervals

Results

14.0ms	43×	body	2048	valid
12.0ms	162×	body	128	valid
9.0ms	36×	body	1024	valid
9.0ms	9×	body	4096	valid
1.0ms	5×	body	512	valid
1.0ms	16×	body	128	nan
0.0ms	1×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify92.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune7.0ms (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

35.5b

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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite138.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

35.4b

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:

11.0ms	(/.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 2014 to 333 computations (83.5% saved)

series728.0ms (7.6%)

Error

6.6b

Counts

4 → 65

Calls

4 calls:

229.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
194.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
138.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
117.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2415 to 1700 computations (29.6% saved)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5044	2832

prune143.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	142	9	151
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	10	152

Error

6.5b

Counts

152 → 10

Compiler

Compiled 2674 to 554 computations (79.3% 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)))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite242.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

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:

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

Compiler

Compiled 4825 to 1174 computations (75.7% saved)

series750.0ms (7.9%)

Error

6.5b

Counts

4 → 65

Calls

4 calls:

244.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
173.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
161.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
118.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 2665 to 1953 computations (26.7% saved)

simplify130.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4960	5823
1	4960	5823

prune203.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	229	10	239

Error

6.5b

Counts

239 → 10

Compiler

Compiled 5102 to 1122 computations (78% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
23.8b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite91.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

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

Counts

4 → 64

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

Compiler

Compiled 2248 to 296 computations (86.8% saved)

series777.0ms (8.1%)

Error

6.5b

Counts

4 → 68

Calls

4 calls:

189.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
184.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
160.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
156.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 5210 to 2890 computations (44.5% saved)

simplify113.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4932	2184
1	4932	2184

prune167.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	132	10	142

Error

6.5b

Counts

142 → 10

Compiler

Compiled 3899 to 693 computations (82.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 c b_2))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

6.5b

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-l_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `div-exp_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

1 → 32

Calls

1 calls:

7.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 373 to 195 computations (47.7% saved)

series81.0ms (0.9%)

Error

6.5b

Counts

1 → 6

Calls

1 calls:

78.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 90 to 88 computations (2.2% saved)

simplify112.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5015	369

prune40.0ms (0.4%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	33	5	38
Fresh	0	6	6
Picked	1	0	1
Done	0	3	3
Total	34	14	48

Error

6.5b

Counts

48 → 14

Compiler

Compiled 356 to 175 computations (50.8% saved)

regimes1.2s (12.8%)

Accuracy

Total 4.3b remaining (43.4%)

Threshold costs 0b (0%)

Compiler

Compiled 6484 to 3702 computations (42.9% saved)

bsearch44.0ms (0.5%)

Steps

Iters	Range		Point
2	8.958792135215151e-83	9.81985712365668e-83	9.712224000101489e-83
9	-5.2076508682082046e+160	-3.538530979810466e+152	-3.816390652545122e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	68	47
1	68	47

end0.0ms (0%)

sample2.9s (30.8%)

Algorithm

1×

intervals

Results

285.0ms	1095×	body	2048	valid
281.0ms	5269×	body	128	valid
144.0ms	698×	body	1024	valid
122.0ms	378×	body	4096	valid
63.0ms	393×	body	512	valid
39.0ms	741×	body	128	nan
22.0ms	167×	body	256	valid
17.0ms	240×	body	128	invalid

Compiler

Compiled 1659 to 952 computations (42.6% saved)

Details

analyze1.3s (13.5%)

sample68.0ms (0.7%)

simplify92.0ms (1%)

prune7.0ms (0.1%)

localize10.0ms (0.1%)

rewrite138.0ms (1.4%)

series728.0ms (7.6%)

simplify94.0ms (1%)

prune143.0ms (1.5%)

localize10.0ms (0.1%)

rewrite242.0ms (2.5%)

series750.0ms (7.9%)

simplify130.0ms (1.4%)

prune203.0ms (2.1%)

localize11.0ms (0.1%)

rewrite91.0ms (1%)

series777.0ms (8.1%)

simplify113.0ms (1.2%)

prune167.0ms (1.7%)

localize4.0ms (0%)

rewrite35.0ms (0.4%)

series81.0ms (0.9%)

simplify112.0ms (1.2%)

prune40.0ms (0.4%)

regimes1.2s (12.8%)

bsearch44.0ms (0.5%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (30.8%)

Profiling