Details

analyze1.1s (6.3%)

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample71.0ms (0.4%)

Algorithm

1×

intervals

Results

14.0ms	39×	body	2048	valid
14.0ms	170×	body	128	valid
6.0ms	12×	body	256	valid
6.0ms	13×	body	4096	valid
4.0ms	15×	body	1024	valid
2.0ms	25×	body	128	nan
2.0ms	7×	body	512	valid
0.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify298.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune13.0ms (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

34.8b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize29.0ms (0.2%)

Local error

Found 8 expressions with local error:

24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

8 calls:

18.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
10.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)

series935.0ms (5.5%)

Counts

4 → 69

Calls

4 calls:

275.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
239.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
215.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
204.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

Compiler

Compiled 1684 to 1373 computations (18.5% saved)

simplify133.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5274	3056

prune409.0ms (2.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	145	10	155
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	146	10	156

Error

6.2b

Counts

156 → 10

Compiler

Compiled 2828 to 644 computations (77.2% saved)

localize20.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.1b	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.2b	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite95.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

144×	`times-frac_binary64`
124×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
71×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
24×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
4×	`cancel-sign-sub-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 164

Calls

8 calls:

26.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
7.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series983.0ms (5.8%)

Counts

4 → 69

Calls

4 calls:

309.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
247.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
231.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
195.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

Compiler

Compiled 1838 to 1527 computations (16.9% saved)

simplify157.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5157	6047

prune358.0ms (2.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	232	1	233
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	233	10	243

Error

6.2b

Counts

243 → 10

Compiler

Compiled 5276 to 1222 computations (76.8% saved)

localize24.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)) (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))))
0.2b	(/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.1b	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
24.4b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite65.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `cancel-sign-sub-inv_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 64

Calls

8 calls:

21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
0.0ms	(sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))

series1.1s (6.3%)

Counts

4 → 76

Calls

4 calls:

279.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
268.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
263.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
261.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)

Compiler

Compiled 3552 to 2496 computations (29.7% saved)

simplify166.0ms (1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4961	2620
1	4961	2620

prune247.0ms (1.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	140	10	150

Error

6.2b

Counts

150 → 10

Compiler

Compiled 4319 to 848 computations (80.4% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.0b	(*.f64 -1/2 (/.f64 c b_2))
0.0b	(*.f64 -1/2 (/.f64 c b_2))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
10×	`times-frac_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-l_binary64`
2×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
1×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

1 → 32

Calls

2 calls:

14.0ms	(*.f64 -1/2 (/.f64 c b_2))
0.0ms	(*.f64 -1/2 (/.f64 c b_2))

series110.0ms (0.7%)

Counts

1 → 6

Calls

1 calls:

110.0ms

(*.f64 -1/2 (/.f64 c b_2))

Compiler

Compiled 60 to 72 computations (-20% saved)

simplify183.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	5015	369

prune52.0ms (0.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	33	5	38
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	34	14	48

Error

6.2b

Counts

48 → 14

Compiler

Compiled 356 to 175 computations (50.8% saved)

simplify58.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	461	1766
1	461	1766

regimes1.1s (6.7%)

Accuracy

Total 4.6b remaining (47.3%)

Threshold costs 0b (0%)

Compiler

Compiled 3420 to 2136 computations (37.5% saved)

bsearch123.0ms (0.7%)

Steps

Iters	Range		Point
9	2.5782589075849317e-38	2.2163939757815603e-33	3.891425723699142e-38
10	-1.8174596109715902e+163	-1.3809609627569115e+149	-3.423389220310686e+150

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	73	46
1	73	46

end0.0ms (0%)

sample9.0s (53.2%)

Algorithm

1×

intervals

Results

457.0ms	1152×	body	2048	valid
436.0ms	5198×	body	128	valid
226.0ms	717×	body	1024	valid
194.0ms	401×	body	4096	valid
86.0ms	365×	body	512	valid
61.0ms	794×	body	128	nan
26.0ms	167×	body	256	valid
21.0ms	259×	body	128	invalid

Compiler

Compiled 3490 to 2174 computations (37.7% saved)

Pareto

-0.2292515076044825

Details

analyze1.1s (6.3%)

sample71.0ms (0.4%)

simplify298.0ms (1.8%)

prune13.0ms (0.1%)

localize29.0ms (0.2%)

rewrite65.0ms (0.4%)

series935.0ms (5.5%)

simplify133.0ms (0.8%)

prune409.0ms (2.4%)

localize20.0ms (0.1%)

rewrite95.0ms (0.6%)

series983.0ms (5.8%)

simplify157.0ms (0.9%)

prune358.0ms (2.1%)

localize24.0ms (0.1%)

rewrite65.0ms (0.4%)

series1.1s (6.3%)

simplify166.0ms (1%)

prune247.0ms (1.5%)

localize7.0ms (0%)

rewrite19.0ms (0.1%)

series110.0ms (0.7%)

simplify183.0ms (1.1%)

prune52.0ms (0.3%)

simplify58.0ms (0.3%)

regimes1.1s (6.7%)

bsearch123.0ms (0.7%)

simplify5.0ms (0%)

end0.0ms (0%)

sample9.0s (53.2%)

Profiling