Details

analyze992.0ms (7.8%)

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)

sample43.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	45×	body	2048	valid
8.0ms	159×	body	128	valid
5.0ms	28×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	11×	body	512	valid
1.0ms	20×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	2×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify335.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (330.0ms)

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

33.7b

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)
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite139.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

33.5b

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:

9.0ms	(/.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)

series721.0ms (5.7%)

Error

4.2b

Counts

4 → 75

Calls

4 calls:

182.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
160.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
159.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
149.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 3407 to 2579 computations (24.3% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4961	2990
1	4961	2990

prune159.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	137	10	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	10	148

Error

4.1b

Counts

148 → 10

Compiler

Compiled 3108 to 1645 computations (47.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.6b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
8.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite241.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

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:

15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.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 4938 to 2474 computations (49.9% saved)

series1.0s (8.2%)

Error

4.1b

Counts

4 → 74

Calls

4 calls:

349.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
323.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
153.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
151.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 4400 to 3157 computations (28.3% saved)

simplify100.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4944	5781
1	4944	5781

prune260.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	199	3	202
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Error

4.1b

Counts

212 → 8

Compiler

Compiled 5782 to 3034 computations (47.5% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.3b	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite132.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

18×	`add-exp-log_binary64_798`
14×	`add-sqr-sqrt_binary64_782`
13×	`add-cbrt-cube_binary64_796`
11×	`*-un-lft-identity_binary64_760`
9×	`add-cube-cbrt_binary64_795`
8×	`add-log-exp_binary64_799`
7×	`sqrt-prod_binary64_776` `cancel-sign-sub-inv_binary64_726` `div-exp_binary64_811`
5×	`pow1_binary64_821`
4×	`prod-exp_binary64_809` `cbrt-undiv_binary64_794`
3×	`flip3--_binary64_764` `flip--_binary64_735` `times-frac_binary64_766` `associate-/l*_binary64_705`
2×	`sqrt-div_binary64_777` `diff-log_binary64_852` `sub-neg_binary64_753` `1-exp_binary64_804` `cbrt-unprod_binary64_793` `difference-of-squares_binary64_729`
1×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `clear-num_binary64_759` `div-inv_binary64_757` `associate-r/_binary64_702` `associate-/r/_binary64_706` `associate-/r_binary64_704` `distribute-lft-out--_binary64_712`

Counts

4 → 73

Calls

4 calls:

12.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
7.0ms	(-.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))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 2450 to 1516 computations (38.1% saved)

series885.0ms (6.9%)

Error

4.1b

Counts

4 → 73

Calls

4 calls:

319.0ms	(/.f64 4 (.f64 1 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) c)))
171.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
165.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
155.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 4431 to 3562 computations (19.6% saved)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4936	2897
1	4936	2897

prune175.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	145	9	154

Error

4.1b

Counts

154 → 9

Compiler

Compiled 3659 to 2337 computations (36.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.8b	(cbrt.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
22.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite514.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

4.1b

Rules

120×	`times-frac_binary64_766`
99×	`add-sqr-sqrt_binary64_782`
78×	`*-un-lft-identity_binary64_760`
71×	`cbrt-prod_binary64_791`
60×	`add-cube-cbrt_binary64_795`
18×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729`
9×	`distribute-lft-out--_binary64_712`
7×	`pow1_binary64_821`
6×	`sqrt-div_binary64_777`
4×	`add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `div-inv_binary64_757`
3×	`pow1/2_binary64_840` `sqrt-pow1_binary64_778` `flip3--_binary64_764` `flip--_binary64_735` `rem-sqrt-square_binary64_773`
1×	`pow1/3_binary64_842` `cbrt-div_binary64_792` `associate-/r/_binary64_706`

Counts

4 → 125

Calls

4 calls:

13.0ms	(cbrt.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 9292 to 5412 computations (41.8% saved)

series1.3s (10.4%)

Error

4.1b

Counts

4 → 68

Calls

4 calls:

617.0ms	(cbrt.f64 (/.f64 4 (/.f64 (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c)))
186.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
184.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
183.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 11291 to 7603 computations (32.7% saved)

simplify96.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

193 → 193

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4965	6367
1	4965	6367

prune647.0ms (5.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	190	3	193
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	191	11	202

Error

4.1b

Counts

202 → 11

Compiler

Compiled 12842 to 7447 computations (42% saved)

regimes1.4s (11.2%)

Accuracy

Total 1.3b remaining (18.4%)

Threshold costs 0b (0%)

Compiler

Compiled 10120 to 7546 computations (25.4% saved)

bsearch87.0ms (0.7%)

Steps

Iters	Range	Point
8	3.829728770174236e+61	1.6247499196176657e+66	3.89202438398013e+65
7	3.7970626220724793e-249	3.952910155327441e-247	1.061124783334026e-248
5	-1.6779014389528192e+106	-7.383458365950772e+105	-1.0312054881735746e+106

Iters

Range

Point

3.829728770174236e+61

1.6247499196176657e+66

3.89202438398013e+65

3.7970626220724793e-249

3.952910155327441e-247

1.061124783334026e-248

-1.6779014389528192e+106

-7.383458365950772e+105

-1.0312054881735746e+106

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	95
1	109	95

end0.0ms (0%)

sample3.2s (25.1%)

Algorithm

1×

intervals

Results

291.0ms	1187×	body	2048	valid
265.0ms	5178×	body	128	valid
131.0ms	693×	body	1024	valid
121.0ms	406×	body	4096	valid
52.0ms	358×	body	512	valid
31.0ms	663×	body	128	nan
25.0ms	390×	body	128	invalid
17.0ms	178×	body	256	valid

Compiler

Compiled 2644 to 1963 computations (25.8% saved)

Details

analyze992.0ms (7.8%)

sample43.0ms (0.3%)

simplify335.0ms (2.6%)

prune4.0ms (0%)

localize14.0ms (0.1%)

rewrite139.0ms (1.1%)

series721.0ms (5.7%)

simplify65.0ms (0.5%)

prune159.0ms (1.2%)

localize12.0ms (0.1%)

rewrite241.0ms (1.9%)

series1.0s (8.2%)

simplify100.0ms (0.8%)

prune260.0ms (2%)

localize15.0ms (0.1%)

rewrite132.0ms (1%)

series885.0ms (6.9%)

simplify85.0ms (0.7%)

prune175.0ms (1.4%)

localize20.0ms (0.2%)

rewrite514.0ms (4%)

series1.3s (10.4%)

simplify96.0ms (0.8%)

prune647.0ms (5.1%)

regimes1.4s (11.2%)

bsearch87.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.2s (25.1%)

Profiling