Details

analyze465.0ms (4.8%)

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
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)

sample43.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	35×	body	2048	valid
8.0ms	164×	body	128	valid
4.0ms	23×	body	1024	valid
4.0ms	13×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	13×	body	128	invalid
1.0ms	12×	body	128	nan

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify420.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (323.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

37.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.1%)

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)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite136.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

36.9b

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×	`pow1_binary64_821` `distribute-lft-out_binary64_711`
4×	`associate-/l*_binary64_705`
3×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l/_binary64_707`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811` `cbrt-undiv_binary64_794` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757`

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)))

Compiler

Compiled 2053 to 1050 computations (48.9% saved)

series526.0ms (5.5%)

Error

7.0b

Counts

4 → 52

Calls

4 calls:

163.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
125.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
99.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
97.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2061 to 1601 computations (22.3% saved)

simplify94.0ms (1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4947	2356
1	4947	2356

prune130.0ms (1.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	118	7	125

Error

6.9b

Counts

125 → 7

Compiler

Compiled 2539 to 1349 computations (46.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(-.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)
11.0b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite248.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

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×	`div-exp_binary64_811` `cbrt-undiv_binary64_794` `associate-/r/_binary64_706`
9×	`sqrt-prod_binary64_776` `associate-/r*_binary64_704`
7×	`flip3--_binary64_764` `flip--_binary64_735`
6×	`add-log-exp_binary64_799` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `distribute-lft-out--_binary64_712` `div-inv_binary64_757`
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` `cancel-sign-sub-inv_binary64_726`

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

Compiler

Compiled 4938 to 2474 computations (49.9% saved)

series810.0ms (8.4%)

Error

6.9b

Counts

4 → 58

Calls

4 calls:

232.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
218.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
162.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3323 to 2372 computations (28.6% saved)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5103	5281

prune234.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	187	6	193

Error

6.9b

Counts

193 → 6

Compiler

Compiled 5337 to 2797 computations (47.6% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

8.3b	(-.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)))))))
10.8b	(/.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))))))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite173.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

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))))))))
5.0ms	(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)

series775.0ms (8.1%)

Error

6.9b

Counts

4 → 62

Calls

4 calls:

236.0ms	(/.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))))))))
164.0ms	(-.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)))))))
156.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
147.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 5139 to 3459 computations (32.7% saved)

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5461	2667

prune185.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	132	6	138

Error

6.9b

Counts

138 → 6

Compiler

Compiled 4398 to 2258 computations (48.7% saved)

localize12.0ms (0.1%)

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)))))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
26.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite244.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

6.9b

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×	`add-cbrt-cube_binary64_796` `associate-/r/_binary64_706`
8×	`add-log-exp_binary64_799`
7×	`div-exp_binary64_811`
6×	`pow1_binary64_821`
5×	`flip3-+_binary64_763` `flip-+_binary64_734` `div-inv_binary64_757`
3×	`sqrt-prod_binary64_776` `cbrt-undiv_binary64_794` `associate-/l*_binary64_705`
2×	`flip3--_binary64_764` `sqrt-div_binary64_777` `flip--_binary64_735` `1-exp_binary64_804` `rec-exp_binary64_810`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `sum-log_binary64_851` `+-commutative_binary64_690` `diff-log_binary64_852` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `inv-pow_binary64_845` `pow-flip_binary64_834` `frac-2neg_binary64_771` `clear-num_binary64_759`

Counts

4 → 135

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
6.0ms	(+.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))))

Compiler

Compiled 4590 to 2591 computations (43.6% saved)

series498.0ms (5.2%)

Error

6.9b

Counts

4 → 52

Calls

4 calls:

161.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
119.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
91.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
90.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))

Compiler

Compiled 2279 to 1821 computations (20.1% saved)

simplify114.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4914	4842
1	4914	4842

prune204.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	187	6	193

Error

6.9b

Counts

193 → 6

Compiler

Compiled 4630 to 2550 computations (44.9% saved)

regimes1.4s (14.4%)

Accuracy

Total 4.5b remaining (44%)

Threshold costs 0b (0%)

Compiler

Compiled 6864 to 5026 computations (26.8% saved)

bsearch70.0ms (0.7%)

Steps

Iters	Range		Point
8	3.491779748544258e+102	7.975797880991267e+105	2.2091409533552714e+105
10	-6.384695991916974e-27	-1.716379672332725e-41	-2.0515509085142014e-38

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	106	58
1	106	58

end0.0ms (0%)

sample2.6s (27.5%)

Algorithm

1×

intervals

Results

277.0ms	1117×	body	2048	valid
266.0ms	5207×	body	128	valid
152.0ms	729×	body	1024	valid
118.0ms	369×	body	4096	valid
59.0ms	373×	body	512	valid
31.0ms	653×	body	128	nan
20.0ms	205×	body	256	valid
19.0ms	334×	body	128	invalid

Compiler

Compiled 1805 to 1319 computations (26.9% saved)

Details

analyze465.0ms (4.8%)

sample43.0ms (0.4%)

simplify420.0ms (4.4%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite136.0ms (1.4%)

series526.0ms (5.5%)

simplify94.0ms (1%)

prune130.0ms (1.4%)

localize12.0ms (0.1%)

rewrite248.0ms (2.6%)

series810.0ms (8.4%)

simplify77.0ms (0.8%)

prune234.0ms (2.4%)

localize18.0ms (0.2%)

rewrite173.0ms (1.8%)

series775.0ms (8.1%)

simplify72.0ms (0.7%)

prune185.0ms (1.9%)

localize12.0ms (0.1%)

rewrite244.0ms (2.5%)

series498.0ms (5.2%)

simplify114.0ms (1.2%)

prune204.0ms (2.1%)

regimes1.4s (14.4%)

bsearch70.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (27.5%)

Profiling