Details

analyze452.0ms (5.8%)

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 (0.5%)

Algorithm

1×

intervals

Results

9.0ms	38×	body	2048	valid
8.0ms	154×	body	128	valid
5.0ms	17×	body	4096	valid
5.0ms	23×	body	1024	valid
2.0ms	17×	body	512	valid
1.0ms	18×	body	128	invalid
1.0ms	15×	body	128	nan
1.0ms	7×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify401.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (305.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune5.0ms (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

37.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.0b	(.f64 4 (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
3×	`distribute-lft-out--_binary64_712`
2×	`diff-log_binary64_852` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `div-inv_binary64_757` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 74

Calls

8 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
0.0ms	(.f64 4 (.f64 a c))

series546.0ms (7%)

Counts

4 → 60

Calls

4 calls:

170.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
147.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1765 to 1508 computations (14.6% saved)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5451	2545

prune209.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	126	8	134
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Error

5.7b

Counts

135 → 8

Compiler

Compiled 2725 to 1430 computations (47.5% saved)

localize3.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune9.0ms (0.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	7	7
Picked	1	1
Done	0	0
Total	8	8

Error

5.7b

Counts

8 → 8

Compiler

Compiled 140 to 98 computations (30% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.0b	(.f64 4 (.f64 a c))
0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`associate-r_binary64_700`
10×	`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`
6×	`associate-l_binary64_701`
5×	`sqrt-prod_binary64_776` `flip--_binary64_735` `flip3--_binary64_764`
4×	`cancel-sign-sub-inv_binary64_726` `difference-of-squares_binary64_729`
2×	`diff-log_binary64_852` `unswap-sqr_binary64_728` `associate-*l/_binary64_703` `prod-exp_binary64_809` `sqrt-div_binary64_777` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `cbrt-unprod_binary64_793` `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` `pow1/2_binary64_840` `div-exp_binary64_811` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 83

Calls

8 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.0ms	(.f64 4 (.f64 a c))

series545.0ms (7%)

Counts

4 → 60

Calls

4 calls:

167.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
145.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1765 to 1508 computations (14.6% saved)

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	2791
1	4954	2791

prune138.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	143	8	151

Error

5.7b

Counts

151 → 8

Compiler

Compiled 2953 to 1555 computations (47.3% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

24.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
1.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
0.2b	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))
0.2b	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))
0.8b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.5b	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
24.6b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite42.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_782`
18×	`*-un-lft-identity_binary64_760`
14×	`add-cube-cbrt_binary64_795`
13×	`associate-r_binary64_700`
10×	`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`
6×	`associate-l_binary64_701`
5×	`sqrt-prod_binary64_776`
4×	`difference-of-squares_binary64_729`
3×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
2×	`unswap-sqr_binary64_728` `associate-*l/_binary64_703` `prod-exp_binary64_809` `flip3-+_binary64_763` `sqrt-div_binary64_777` `flip-+_binary64_734` `distribute-lft-out--_binary64_712` `frac-times_binary64_770` `cbrt-unprod_binary64_793`
1×	`diff-log_binary64_852` `rem-sqrt-square_binary64_773` `cbrt-undiv_binary64_794` `sqrt-pow1_binary64_778` `div-inv_binary64_757` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-r/_binary64_702` `pow1/2_binary64_840` `div-exp_binary64_811` `sub-neg_binary64_753` `pow-prod-down_binary64_831` `-commutative_binary64_691`

Counts

4 → 82

Calls

8 calls:

15.0ms	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))
10.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
4.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
4.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))
0.0ms	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))

series557.0ms (7.2%)

Counts

4 → 60

Calls

4 calls:

163.0ms	(.f64 (-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (.f64 c -4)))) b) (/.f64 1/2 a))
156.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
121.0ms	(-.f64 (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))) b)
116.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

Compiler

Compiled 1765 to 1508 computations (14.6% saved)

simplify97.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4933	2750
1	4933	2750

prune136.0ms (1.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	139	3	142
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	141	9	150

Error

5.7b

Counts

150 → 9

Compiler

Compiled 2779 to 1574 computations (43.4% saved)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	369	1481
1	369	1481

regimes654.0ms (8.4%)

Compiler: Compiled 2883 to 2190 computations (24% saved)

bsearch60.0ms (0.8%)

Steps

Iters	Range		Point
8	1.838515329808274e-64	1.504646891257893e-60	9.908180707161701e-62
8	-7.239199173592704e-32	-3.8108211360075656e-36	-7.102439644234899e-32

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes182.0ms (2.3%)

Compiler: Compiled 318 to 348 computations (-9.4% saved)

bsearch57.0ms (0.7%)

Steps

Iters	Range		Point
8	1.838515329808274e-64	1.504646891257893e-60	1.227805983638796e-61
8	-7.239199173592704e-32	-3.8108211360075656e-36	-7.102439644234899e-32

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes157.0ms (2%)

Compiler: Compiled 270 to 309 computations (-14.4% saved)

bsearch58.0ms (0.8%)

Steps

Iters	Range		Point
8	1.838515329808274e-64	1.504646891257893e-60	1.8770875812605243e-64
8	-3.02850562265381e-46	-6.956855420995776e-50	-4.398136104036632e-48

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes140.0ms (1.8%)

Compiler: Compiled 198 to 243 computations (-22.7% saved)

bsearch62.0ms (0.8%)

Steps

Iters	Range		Point
8	1.838515329808274e-64	1.504646891257893e-60	2.2988954179358907e-63
9	-5.781806328546769e-124	-5.723434478968476e-129	-5.476283559993845e-124

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes344.0ms (4.4%)

Compiler: Compiled 168 to 213 computations (-26.8% saved)

bsearch63.0ms (0.8%)

Steps

Iters	Range		Point
8	1.838515329808274e-64	1.504646891257893e-60	1.011243506933701e-60
9	-5.781806328546769e-124	-5.723434478968476e-129	-4.7430289154668276e-124

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes106.0ms (1.4%)

Compiler: Compiled 138 to 183 computations (-32.6% saved)

bsearch31.0ms (0.4%)

Steps

Iters	Range		Point
8	2.6873089196522764e-280	6.026491473597822e-277	1.2380567347774514e-278

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes33.0ms (0.4%)

Compiler: Compiled 27 to 69 computations (-155.6% saved)

bsearch34.0ms (0.4%)

Steps

Iters	Range		Point
10	-1.5265595284484798e-299	9.048194046201865e-304	5.7901680992929e-312

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes25.0ms (0.3%)

Accuracy

Total 5.5b remaining (50.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 167 to 134 computations (19.8% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	249
1	136	249

end0.0ms (0%)

sample2.3s (29.2%)

Algorithm

1×

intervals

Results

291.0ms	1139×	body	2048	valid
271.0ms	5137×	body	128	valid
155.0ms	766×	body	1024	valid
136.0ms	397×	body	4096	valid
54.0ms	374×	body	512	valid
31.0ms	637×	body	128	nan
20.0ms	374×	body	128	invalid
18.0ms	187×	body	256	valid

Compiler

Compiled 1186 to 903 computations (23.9% saved)

Pareto

0.37265634987076424

Details

analyze452.0ms (5.8%)

sample43.0ms (0.5%)

simplify401.0ms (5.2%)

prune5.0ms (0.1%)

localize11.0ms (0.1%)

rewrite35.0ms (0.5%)

series546.0ms (7%)

simplify68.0ms (0.9%)

prune209.0ms (2.7%)

localize3.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.1%)

prune9.0ms (0.1%)

localize11.0ms (0.1%)

rewrite38.0ms (0.5%)

series545.0ms (7%)

simplify85.0ms (1.1%)

prune138.0ms (1.8%)

localize11.0ms (0.1%)

rewrite42.0ms (0.5%)

series557.0ms (7.2%)

simplify97.0ms (1.3%)

prune136.0ms (1.7%)

simplify22.0ms (0.3%)

regimes654.0ms (8.4%)

bsearch60.0ms (0.8%)

regimes182.0ms (2.3%)

bsearch57.0ms (0.7%)

regimes157.0ms (2%)

bsearch58.0ms (0.8%)

regimes140.0ms (1.8%)

bsearch62.0ms (0.8%)

regimes344.0ms (4.4%)

bsearch63.0ms (0.8%)

regimes106.0ms (1.4%)

bsearch31.0ms (0.4%)

regimes33.0ms (0.4%)

bsearch34.0ms (0.4%)

regimes25.0ms (0.3%)

bsearch8.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.3s (29.2%)

Profiling