Details

analyze1.0s (8.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample46.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	45×	body	2048	valid
8.0ms	160×	body	128	valid
5.0ms	14×	body	4096	valid
4.0ms	19×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	21×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify384.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (375.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune5.0ms (0%)

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

36.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a))
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite176.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

36.4b

Rules

22×	`*-un-lft-identity_binary64_760`
20×	`add-sqr-sqrt_binary64_782`
16×	`associate-r_binary64_700`
14×	`add-cube-cbrt_binary64_795`
13×	`times-frac_binary64_766`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`pow1_binary64_821`
4×	`distribute-lft-out_binary64_711`
3×	`sqrt-prod_binary64_776` `associate-l_binary64_701`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `pow-prod-down_binary64_831` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-r/_binary64_702` `div-inv_binary64_757` `-commutative_binary64_691`

Counts

4 → 74

Calls

4 calls:

13.0ms	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2115 to 1105 computations (47.8% saved)

series898.0ms (7.7%)

Error

6.8b

Counts

4 → 76

Calls

4 calls:

267.0ms	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) a))
190.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
170.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
161.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3383 to 2540 computations (24.9% saved)

simplify114.0ms (1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4936	2958
1	4936	2958

prune186.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	142	8	150
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	8	151

Error

6.6b

Counts

151 → 8

Compiler

Compiled 3127 to 1645 computations (47.4% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
10.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite328.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

66×	`times-frac_binary64_766`
59×	`add-sqr-sqrt_binary64_782`
44×	`*-un-lft-identity_binary64_760`
30×	`add-cube-cbrt_binary64_795`
27×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
14×	`difference-of-squares_binary64_729`
13×	`sqrt-prod_binary64_776` `associate-/l*_binary64_705`
10×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/r/_binary64_706`
9×	`associate-/r*_binary64_704`
7×	`flip3--_binary64_764` `flip--_binary64_735` `distribute-lft-out--_binary64_712`
6×	`add-log-exp_binary64_799` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `div-inv_binary64_757` `cancel-sign-sub-inv_binary64_726`
5×	`pow1_binary64_821`
2×	`sqrt-div_binary64_777` `frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-/l/_binary64_707` `diff-log_binary64_852` `sub-neg_binary64_753`

Counts

4 → 136

Calls

4 calls:

25.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
14.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5265 to 2649 computations (49.7% saved)

series1.3s (11.5%)

Error

6.6b

Counts

4 → 73

Calls

4 calls:

464.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
410.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
176.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
172.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 4600 to 3295 computations (28.4% saved)

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4942	6184
1	4942	6184

prune293.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	209	8	217

Error

6.6b

Counts

217 → 8

Compiler

Compiled 6009 to 3119 computations (48.1% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.8b	(-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
10.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite195.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Rules

13×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `add-sqr-sqrt_binary64_782`
8×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`pow1_binary64_821` `add-log-exp_binary64_799` `sqrt-prod_binary64_776`
4×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `times-frac_binary64_766` `associate-/r*_binary64_704`
3×	`prod-exp_binary64_809` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `cbrt-unprod_binary64_793` `difference-of-squares_binary64_729`
2×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `associate-/r/_binary64_706`
1×	`frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-/l*_binary64_705` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726`

Counts

4 → 70

Calls

4 calls:

8.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
3.0ms	(-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))

Compiler

Compiled 3776 to 1975 computations (47.7% saved)

series1.1s (9.7%)

Error

6.6b

Counts

4 → 75

Calls

4 calls:

422.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))))
214.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
200.0ms	(-.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
188.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 6185 to 4195 computations (32.2% saved)

simplify75.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5236	3195

prune231.0ms (2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	145	8	153

Error

6.6b

Counts

153 → 8

Compiler

Compiled 4918 to 2556 computations (48% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Error

6.6b

Counts

0 → 0

Compiler

Compiled 0 to 0 computations (0% saved)

series0.0ms (0%)

Error: 6.6b
Counts: 0 → 0
Compiler: Compiled 0 to 0 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune1.0ms (0%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	5	5
Picked	1	1
Done	2	2
Total	8	8

Error

6.6b

Counts

8 → 8

Compiler

Compiled 0 to 0 computations (0% saved)

regimes1.5s (12.8%)

Accuracy

Total 3.5b remaining (36.4%)

Threshold costs 0b (0%)

Compiler

Compiled 7704 to 5654 computations (26.6% saved)

bsearch126.0ms (1.1%)

Steps

Iters	Range	Point
9	1.1935307154283341e+95	4.0136306422491975e+100	5.559837845063527e+97
7	-4.189671040625987e-222	-1.3438807303379218e-223	-2.5936672057451206e-222
9	-5.7837835545064236e-15	-9.00223585802719e-21	-1.0628887340948368e-15

Iters

Range

Point

1.1935307154283341e+95

4.0136306422491975e+100

5.559837845063527e+97

-4.189671040625987e-222

-1.3438807303379218e-223

-2.5936672057451206e-222

-5.7837835545064236e-15

-9.00223585802719e-21

-1.0628887340948368e-15

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	109	91
1	109	91

end0.0ms (0%)

sample3.4s (29.3%)

Algorithm

1×

intervals

Results

362.0ms	1159×	body	2048	valid
333.0ms	5195×	body	128	valid
165.0ms	680×	body	1024	valid
159.0ms	419×	body	4096	valid
64.0ms	362×	body	512	valid
44.0ms	680×	body	128	nan
24.0ms	396×	body	128	invalid
22.0ms	185×	body	256	valid

Compiler

Compiled 2037 to 1484 computations (27.1% saved)

Details

analyze1.0s (8.7%)

sample46.0ms (0.4%)

simplify384.0ms (3.3%)

prune5.0ms (0%)

localize18.0ms (0.2%)

rewrite176.0ms (1.5%)

series898.0ms (7.7%)

simplify114.0ms (1%)

prune186.0ms (1.6%)

localize12.0ms (0.1%)

rewrite328.0ms (2.8%)

series1.3s (11.5%)

simplify126.0ms (1.1%)

prune293.0ms (2.5%)

localize25.0ms (0.2%)

rewrite195.0ms (1.7%)

series1.1s (9.7%)

simplify75.0ms (0.6%)

prune231.0ms (2%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune1.0ms (0%)

regimes1.5s (12.8%)

bsearch126.0ms (1.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.4s (29.3%)

Profiling