Details

analyze1.6s (11.9%)

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)

sample82.0ms (0.6%)

Algorithm

1×

intervals

Results

17.0ms	169×	body	128	valid
15.0ms	30×	body	2048	valid
11.0ms	17×	body	4096	valid
11.0ms	28×	body	1024	valid
3.0ms	11×	body	512	valid
3.0ms	29×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify633.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (622.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune11.0ms (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

32.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_760`
15×	`add-sqr-sqrt_binary64_782`
14×	`add-cube-cbrt_binary64_795`
12×	`times-frac_binary64_766`
8×	`add-log-exp_binary64_799`
6×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
5×	`distribute-lft-out_binary64_711` `pow1_binary64_821`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3-+_binary64_763` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `flip-+_binary64_734` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

4 → 72

Calls

4 calls:

17.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series811.0ms (6.1%)

Counts

4 → 51

Calls

4 calls:

272.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
223.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
165.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
151.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 1398 to 1214 computations (13.2% saved)

simplify109.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5261	2325

prune259.0ms (1.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Error

4.0b

Counts

124 → 8

Compiler

Compiled 2561 to 1369 computations (46.5% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.4b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
6.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite89.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 128

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)
21.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.2s (9.3%)

Counts

4 → 55

Calls

4 calls:

396.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
354.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
293.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
196.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2130 to 1667 computations (21.7% saved)

simplify139.0ms (1%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4974	5197
1	4974	5197

prune394.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	185	6	191

Error

4.0b

Counts

191 → 6

Compiler

Compiled 5230 to 2756 computations (47.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.2b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_782`
28×	`*-un-lft-identity_binary64_760`
18×	`add-cube-cbrt_binary64_795` `times-frac_binary64_766`
11×	`sqrt-prod_binary64_776`
10×	`difference-of-squares_binary64_729`
8×	`add-log-exp_binary64_799`
7×	`cancel-sign-sub-inv_binary64_726`
6×	`add-exp-log_binary64_798` `associate-/r*_binary64_704` `add-cbrt-cube_binary64_796`
5×	`distribute-lft-out--_binary64_712` `pow1_binary64_821`
4×	`flip--_binary64_735` `flip3--_binary64_764`
3×	`associate-/l*_binary64_705`
2×	`diff-log_binary64_852` `associate-/r/_binary64_706` `sqrt-div_binary64_777` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `pow1/2_binary64_840` `div-exp_binary64_811` `clear-num_binary64_759`

Counts

4 → 88

Calls

4 calls:

16.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
13.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.0s (7.6%)

Counts

4 → 56

Calls

4 calls:

312.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
289.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
217.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
202.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2035 to 1768 computations (13.1% saved)

simplify133.0ms (1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4984	3010
1	4984	3010

prune281.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	144	6	150

Error

4.0b

Counts

150 → 6

Compiler

Compiled 3604 to 2142 computations (40.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite81.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_766`
82×	`*-un-lft-identity_binary64_760`
57×	`add-sqr-sqrt_binary64_782`
56×	`add-cube-cbrt_binary64_795`
18×	`associate-/r*_binary64_704`
15×	`add-exp-log_binary64_798`
13×	`distribute-lft-out_binary64_711`
9×	`associate-/r/_binary64_706` `add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799`
7×	`div-exp_binary64_811`
6×	`pow1_binary64_821`
5×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734`
3×	`cbrt-undiv_binary64_794` `sqrt-prod_binary64_776` `associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `rec-exp_binary64_810` `1-exp_binary64_804` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `cancel-sign-sub-inv_binary64_726` `sqrt-pow1_binary64_778` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `pow1/2_binary64_840` `clear-num_binary64_759` `sub-neg_binary64_753` `pow-flip_binary64_834`

Counts

4 → 135

Calls

4 calls:

22.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
11.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series807.0ms (6%)

Counts

4 → 51

Calls

4 calls:

287.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
220.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
157.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
143.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1532 to 1348 computations (12% saved)

simplify207.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4944	4811
1	4944	4811

prune365.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Error

4.0b

Counts

192 → 7

Compiler

Compiled 4601 to 2533 computations (44.9% saved)

regimes998.0ms (7.5%)

Accuracy

Total 1.5b remaining (21.6%)

Threshold costs 0b (0%)

Compiler

Compiled 3348 to 2590 computations (22.6% saved)

bsearch158.0ms (1.2%)

Steps

Iters	Range	Point
5	2.1185936279355515e+57	5.720434717612344e+57	4.492769536356283e+57
9	2.8546213422044465e-125	2.2818203321252932e-116	2.9229233280338277e-125
7	-1.7965637555557037e+135	-1.6589745466350036e+133	-8.25042444002418e+133

Iters

Range

Point

2.1185936279355515e+57

5.720434717612344e+57

4.492769536356283e+57

2.8546213422044465e-125

2.2818203321252932e-116

2.9229233280338277e-125

-1.7965637555557037e+135

-1.6589745466350036e+133

-8.25042444002418e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	120	91
1	120	91

end0.0ms (0%)

sample3.8s (28.1%)

Algorithm

1×

intervals

Results

543.0ms	1146×	body	2048	valid
501.0ms	5149×	body	128	valid
288.0ms	745×	body	1024	valid
254.0ms	419×	body	4096	valid
109.0ms	367×	body	512	valid
67.0ms	661×	body	128	nan
36.0ms	373×	body	128	invalid
33.0ms	174×	body	256	valid

Compiler

Compiled 948 to 723 computations (23.7% saved)

Details

analyze1.6s (11.9%)

sample82.0ms (0.6%)

simplify633.0ms (4.7%)

prune11.0ms (0.1%)

localize21.0ms (0.2%)

rewrite58.0ms (0.4%)

series811.0ms (6.1%)

simplify109.0ms (0.8%)

prune259.0ms (1.9%)

localize24.0ms (0.2%)

rewrite89.0ms (0.7%)

series1.2s (9.3%)

simplify139.0ms (1%)

prune394.0ms (2.9%)

localize25.0ms (0.2%)

rewrite62.0ms (0.5%)

series1.0s (7.6%)

simplify133.0ms (1%)

prune281.0ms (2.1%)

localize23.0ms (0.2%)

rewrite81.0ms (0.6%)

series807.0ms (6%)

simplify207.0ms (1.6%)

prune365.0ms (2.7%)

regimes998.0ms (7.5%)

bsearch158.0ms (1.2%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample3.8s (28.1%)

Profiling