Details

analyze467.0ms (6.7%)

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
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)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	39×	body	2048	valid
8.0ms	163×	body	128	valid
4.0ms	22×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	29×	body	128	nan
1.0ms	7×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify420.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (327.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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: 31.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (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)
1.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms (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:

8.0ms	(/.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)))

series233.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4970	2025
1	4970	2025

prune127.0ms (1.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	74	10	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 4.9b

Counts

85 → 10

Compiler

Compiled 2222 to 1215 computations (45.3% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.5b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
9.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite53.0ms (0.8%)

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:

17.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series464.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
164.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify101.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4949	4742
1	4949	4742

prune204.0ms (2.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	134	6	140
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Merged error: 4.9b

Counts

150 → 9

Compiler

Compiled 4644 to 2492 computations (46.3% saved)

localize16.0ms (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))))))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms (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:

9.0ms	(/.f64 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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series340.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
63.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
34.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify79.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4882	2580
1	4882	2580

prune129.0ms (1.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 4.9b

Counts

109 → 10

Compiler

Compiled 3038 to 1820 computations (40.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
0.8b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64_782`
27×	`*-un-lft-identity_binary64_760`
24×	`associate-r_binary64_700`
20×	`times-frac_binary64_766`
18×	`add-cube-cbrt_binary64_795`
13×	`add-exp-log_binary64_798`
10×	`sqrt-prod_binary64_776`
9×	`add-cbrt-cube_binary64_796`
8×	`add-log-exp_binary64_799` `difference-of-squares_binary64_729`
7×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
4×	`prod-exp_binary64_809` `distribute-lft-out--_binary64_712` `flip--_binary64_735` `flip3--_binary64_764`
3×	`unswap-sqr_binary64_728` `associate-l_binary64_701`
2×	`diff-log_binary64_852` `associate-/r/_binary64_706` `sqrt-div_binary64_777` `cbrt-unprod_binary64_793` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `associate-r/_binary64_702` `rec-exp_binary64_810` `pow1/2_binary64_840` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `1-exp_binary64_804` `-commutative_binary64_691`

Counts

4 → 94

Calls

4 calls:

16.0ms	(.f64 c (/.f64 1 (-.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))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series334.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(.f64 c (/.f64 1 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))))
66.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
55.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
31.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4904	2312
1	4904	2312

prune135.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	106	10	116

Merged error: 4.9b

Counts

116 → 10

Compiler

Compiled 3133 to 1950 computations (37.8% saved)

regimes985.0ms (14.1%)

Compiler: Compiled 6250 to 4550 computations (27.2% saved)

bsearch106.0ms (1.5%)

Steps

Iters	Range	Point
7	1.936749611573707e+19	8.152720514590401e+20	3.032635602239435e+20
10	-7.368854685223572e-308	3.6907232803257034e-294	6.340718814578958e-296
8	-1.3912480923785817e+149	-3.187310626829432e+145	-9.661125962095032e+146

Iters

Range

Point

1.936749611573707e+19

8.152720514590401e+20

3.032635602239435e+20

-7.368854685223572e-308

3.6907232803257034e-294

6.340718814578958e-296

-1.3912480923785817e+149

-3.187310626829432e+145

-9.661125962095032e+146

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	108	95
1	108	95

end0.0ms (0%)

sample2.4s (35%)

Algorithm

1×

intervals

Results

306.0ms	1186×	body	2048	valid
276.0ms	5175×	body	128	valid
143.0ms	704×	body	1024	valid
119.0ms	391×	body	4096	valid
55.0ms	361×	body	512	valid
34.0ms	687×	body	128	nan
19.0ms	367×	body	128	invalid
18.0ms	183×	body	256	valid

Compiler

Compiled 1663 to 1202 computations (27.7% saved)

Details

analyze467.0ms (6.7%)

sample40.0ms (0.6%)

simplify420.0ms (6%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite29.0ms (0.4%)

series233.0ms (3.3%)

simplify89.0ms (1.3%)

prune127.0ms (1.8%)

localize12.0ms (0.2%)

rewrite53.0ms (0.8%)

series464.0ms (6.6%)

simplify101.0ms (1.4%)

prune204.0ms (2.9%)

localize16.0ms (0.2%)

rewrite33.0ms (0.5%)

series340.0ms (4.9%)

simplify79.0ms (1.1%)

prune129.0ms (1.8%)

localize18.0ms (0.3%)

rewrite41.0ms (0.6%)

series334.0ms (4.8%)

simplify76.0ms (1.1%)

prune135.0ms (1.9%)

regimes985.0ms (14.1%)

bsearch106.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.4s (35%)

Profiling