Details

analyze1.1s (11.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
26.2%	73.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample24.0ms (0.2%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	26×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify369.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (274.0ms)

Iter	Nodes	Cost
0	5599	16

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

1.5b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

1.9b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
1.9b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64_16468`
71×	`*-un-lft-identity_binary64_16446`
51×	`times-frac_binary64_16452`
31×	`associate-r_binary64_16386`
27×	`add-cube-cbrt_binary64_16481`
22×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
10×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
5×	`pow1_binary64_16507` `add-log-exp_binary64_16485` `associate-/l_binary64_16391` `associate-/r_binary64_16390`
4×	`associate-/r/_binary64_16392`
3×	`flip3--_binary64_16450` `associate-l_binary64_16387` `flip--_binary64_16421`
2×	`cbrt-undiv_binary64_16480` `unswap-sqr_binary64_16414` `associate-/l/_binary64_16393` `cbrt-unprod_binary64_16479` `div-inv_binary64_16443` `prod-exp_binary64_16495` `div-exp_binary64_16497`
1×	`associate-r/_binary64_16388` `div-sub_binary64_16451` `+-commutative_binary64_16376` `clear-num_binary64_16445` `pow-prod-down_binary64_16517` `-commutative_binary64_16377` `flip3-+_binary64_16449` `sum-log_binary64_16537` `flip-+_binary64_16420` `frac-2neg_binary64_16457`

Counts

3 → 113

Calls

6 calls:

15.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
3.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
0.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
0.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

series937.0ms (9.2%)

Counts

3 → 94

Calls

3 calls:

474.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
277.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
186.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

Compiler

Compiled 2837 to 2130 computations (24.9% saved)

simplify107.0ms (1%)

Algorithm

1×	egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4956	4531
1	4956	4531

prune188.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	203	4	207
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	203	5	208

Error

Counts

208 → 5

Compiler

Compiled 4094 to 775 computations (81.1% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

1.9b	(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)))
0.2b	(pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)
0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
0.0b	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))
0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
0.2b	(pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)
1.9b	(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)))
17.8b	(cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))

rewrite109.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

246×	`add-sqr-sqrt_binary64_16468`
231×	`*-un-lft-identity_binary64_16446`
177×	`times-frac_binary64_16452`
142×	`cbrt-prod_binary64_16477`
95×	`cube-prod_binary64_16474` `unpow-prod-down_binary64_16525`
87×	`add-cube-cbrt_binary64_16481`
72×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
71×	`associate-r_binary64_16386`
14×	`associate-/r/_binary64_16392`
11×	`add-exp-log_binary64_16484`
10×	`add-cbrt-cube_binary64_16482`
8×	`flip3--_binary64_16450` `flip--_binary64_16421`
7×	`unswap-sqr_binary64_16414` `pow1_binary64_16507` `div-inv_binary64_16443`
5×	`associate-/l_binary64_16391` `associate-/r_binary64_16390`
4×	`add-log-exp_binary64_16485` `sqr-pow_binary64_16418`
3×	`cube-div_binary64_16475` `cube-mult_binary64_16476` `pow-unpow_binary64_16523` `unpow3_binary64_16512` `associate-l_binary64_16387`
2×	`pow-exp_binary64_16514` `cbrt-undiv_binary64_16480` `rem-cube-cbrt_binary64_16469` `associate-/l/_binary64_16393` `cbrt-div_binary64_16478` `div-exp_binary64_16497`
1×	`associate-r/_binary64_16388` `div-sub_binary64_16451` `clear-num_binary64_16445` `rem-cbrt-cube_binary64_16470` `pow1/3_binary64_16528` `pow-prod-down_binary64_16517` `cbrt-unprod_binary64_16479` `-commutative_binary64_16377` `prod-exp_binary64_16495` `pow-to-exp_binary64_16515` `pow-pow_binary64_16518` `frac-2neg_binary64_16457`

Counts

4 → 305

Calls

8 calls:

35.0ms	(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)))
13.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))
11.0ms	(pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)
9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))

series983.0ms (9.6%)

Counts

4 → 105

Calls

4 calls:

297.0ms	(pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)
283.0ms	(*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3)))
217.0ms	(cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))
186.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

Compiler

Compiled 4196 to 3368 computations (19.7% saved)

simplify116.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

410 → 410

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5013	9916

prune377.0ms (3.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	410	0	410
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	410	5	415

Error

Counts

415 → 5

Compiler

Compiled 9751 to 3126 computations (67.9% saved)

localize9.0ms (0.1%)

Local error

Found 6 expressions with local error:

12.6b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
0.0b	(*.f64 y (-.f64 z t))
0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
0.0b	(*.f64 y (-.f64 z t))
12.6b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

rewrite31.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64_16446` `add-sqr-sqrt_binary64_16468`
10×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
9×	`add-cube-cbrt_binary64_16481`
6×	`cancel-sign-sub-inv_binary64_16412`
5×	`times-frac_binary64_16452` `pow1_binary64_16507` `add-log-exp_binary64_16485` `associate-r_binary64_16386` `associate-/r*_binary64_16390`
4×	`associate-*r/_binary64_16388` `distribute-rgt-in_binary64_16396` `distribute-lft-in_binary64_16395`
3×	`distribute-lft-out--_binary64_16398` `flip3--_binary64_16450` `associate-l_binary64_16387` `flip--_binary64_16421` `difference-of-squares_binary64_16415`
2×	`cbrt-undiv_binary64_16480` `associate-/l/_binary64_16393` `cbrt-unprod_binary64_16479` `prod-exp_binary64_16495` `sub-neg_binary64_16439` `associate-/r/_binary64_16392` `div-exp_binary64_16497`
1×	`+-commutative_binary64_16376` `clear-num_binary64_16445` `unswap-sqr_binary64_16414` `distribute-lft-out_binary64_16397` `pow-prod-down_binary64_16517` `-commutative_binary64_16377` `div-inv_binary64_16443` `flip3-+_binary64_16449` `associate-/l_binary64_16391` `sum-log_binary64_16537` `flip-+_binary64_16420` `frac-2neg_binary64_16457`

Counts

3 → 71

Calls

6 calls:

10.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
8.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
7.0ms	(*.f64 y (-.f64 z t))
0.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
0.0ms	(*.f64 y (-.f64 z t))

series842.0ms (8.2%)

Counts

3 → 82

Calls

3 calls:

477.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
269.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
96.0ms	(*.f64 y (-.f64 z t))

Compiler

Compiled 2278 to 1714 computations (24.8% saved)

simplify80.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5108	2763

prune101.0ms (1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	153	5	158

Error

Counts

158 → 5

Compiler

Compiled 2534 to 524 computations (79.3% saved)

localize11.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 y (sqrt.f64 (-.f64 a t)))
0.0b	(sqrt.f64 (-.f64 a t))
0.0b	(sqrt.f64 (-.f64 a t))
0.0b	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))
0.0b	(sqrt.f64 (-.f64 a t))
0.1b	(/.f64 y (sqrt.f64 (-.f64 a t)))
0.2b	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))
2.6b	(*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))))

rewrite96.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

180×	`add-sqr-sqrt_binary64_16468`
149×	`*-un-lft-identity_binary64_16446`
140×	`times-frac_binary64_16452`
101×	`sqrt-prod_binary64_16462`
77×	`add-cube-cbrt_binary64_16481`
46×	`associate-r_binary64_16386`
36×	`distribute-lft-out--_binary64_16398` `difference-of-squares_binary64_16415`
30×	`associate-l_binary64_16387`
20×	`add-exp-log_binary64_16484` `add-cbrt-cube_binary64_16482`
16×	`associate-/r*_binary64_16390`
10×	`sqrt-div_binary64_16463`
9×	`unswap-sqr_binary64_16414`
8×	`associate-/l*_binary64_16391` `associate-/r/_binary64_16392`
7×	`pow1_binary64_16507`
6×	`cbrt-undiv_binary64_16480` `flip3--_binary64_16450` `div-exp_binary64_16497` `flip--_binary64_16421`
4×	`cbrt-unprod_binary64_16479` `div-inv_binary64_16443` `add-log-exp_binary64_16485` `prod-exp_binary64_16495`
2×	`clear-num_binary64_16445` `associate-/l/_binary64_16393` `frac-2neg_binary64_16457`
1×	`associate-r/_binary64_16388` `rem-sqrt-square_binary64_16459` `div-sub_binary64_16451` `sqrt-pow1_binary64_16464` `pow-prod-down_binary64_16517` `-commutative_binary64_16377` `associate-*l/_binary64_16389` `pow1/2_binary64_16526` `frac-times_binary64_16456`

Counts

4 → 241

Calls

8 calls:

46.0ms	(*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))))
10.0ms	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))
6.0ms	(/.f64 y (sqrt.f64 (-.f64 a t)))
3.0ms	(sqrt.f64 (-.f64 a t))
0.0ms	(+.f64 x (*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))))

series726.0ms (7.1%)

Counts

4 → 65

Calls

4 calls:

269.0ms	(*.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t))))
247.0ms	(/.f64 (-.f64 z t) (sqrt.f64 (-.f64 a t)))
162.0ms	(/.f64 y (sqrt.f64 (-.f64 a t)))
48.0ms	(sqrt.f64 (-.f64 a t))

Compiler

Compiled 2778 to 2148 computations (22.7% saved)

simplify110.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

306 → 306

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5162	7253

prune244.0ms (2.4%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	306	0	306
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	306	5	311

Error

Counts

311 → 5

Compiler

Compiled 7910 to 1522 computations (80.8% saved)

simplify62.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	1612	711
1	1612	711

regimes417.0ms (4.1%)

Compiler: Compiled 3880 to 3104 computations (20% saved)

bsearch0.0ms (0%)

regimes391.0ms (3.8%)

Compiler: Compiled 677 to 937 computations (-38.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 7 to 8 computations (-14.3% saved)

regimes229.0ms (2.2%)

Compiler: Compiled 330 to 495 computations (-50% saved)

bsearch48.0ms (0.5%)

Steps

Iters	Range		Point
10	8.023213073299017e+32	5.3947937367390775e+45	2.0868173352952202e+43
10	-4.588217078307544e+59	-3.6549870192704525e+44	-1.2953388124349229e+47

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes305.0ms (3%)

Compiler: Compiled 285 to 450 computations (-57.9% saved)

bsearch41.0ms (0.4%)

Steps

Iters	Range		Point
8	6.7143694085476615e-46	6.203413676126031e-43	2.3859125965592656e-43
9	-3.6549870192704525e+44	-3.629330705732401e+35	-1.813655537906052e+38

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes251.0ms (2.5%)

Compiler: Compiled 195 to 360 computations (-84.6% saved)

bsearch41.0ms (0.4%)

Steps

Iters	Range		Point
8	2.8276989333864617e-33	2.1699858849173584e-29	1.502996282001404e-29
9	-3.6549870192704525e+44	-3.629330705732401e+35	-1.8517502828614007e+41

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes208.0ms (2%)

Compiler: Compiled 150 to 315 computations (-110% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
8	2.8276989333864617e-33	2.1699858849173584e-29	5.364226396298406e-32
10	-4.588217078307544e+59	-3.6549870192704525e+44	-1.1525003590229609e+45

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes69.0ms (0.7%)

Compiler: Compiled 45 to 195 computations (-333.3% saved)

bsearch42.0ms (0.4%)

Steps

Iters	Range		Point
9	6.1888626972177146e-99	6.646102186518714e-90	1.906926088687382e-98
8	-3.516913723027717e-23	-1.4843507820148314e-27	-2.1304546780209903e-27

Compiler

Compiled 1 to 5 computations (-400% saved)

regimes50.0ms (0.5%)

Compiler: Compiled 30 to 165 computations (-450% saved)

bsearch0.0ms (0%)

regimes48.0ms (0.5%)

Accuracy

Total 1.3b remaining (99.5%)

Threshold costs 0b (0%)

Compiler

Compiled 25 to 140 computations (-460% saved)

bsearch9.0ms (0.1%)

Compiler: Compiled 184 to 122 computations (33.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	255
1	131	255

end0.0ms (0%)

sample1.3s (12.7%)

Algorithm

1×

intervals

Results

322.0ms	7998×	body	128	valid
31.0ms	727×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 706 to 539 computations (23.7% saved)

Pareto

0.5809728431073087

Details

analyze1.1s (11.2%)

sample24.0ms (0.2%)

simplify369.0ms (3.6%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite38.0ms (0.4%)

series937.0ms (9.2%)

simplify107.0ms (1%)

prune188.0ms (1.8%)

localize11.0ms (0.1%)

rewrite109.0ms (1.1%)

series983.0ms (9.6%)

simplify116.0ms (1.1%)

prune377.0ms (3.7%)

localize9.0ms (0.1%)

rewrite31.0ms (0.3%)

series842.0ms (8.2%)

simplify80.0ms (0.8%)

prune101.0ms (1%)

localize11.0ms (0.1%)

rewrite96.0ms (0.9%)

series726.0ms (7.1%)

simplify110.0ms (1.1%)

prune244.0ms (2.4%)

simplify62.0ms (0.6%)

regimes417.0ms (4.1%)

bsearch0.0ms (0%)

regimes391.0ms (3.8%)

bsearch1.0ms (0%)

regimes229.0ms (2.2%)

bsearch48.0ms (0.5%)

regimes305.0ms (3%)

bsearch41.0ms (0.4%)

regimes251.0ms (2.5%)

bsearch41.0ms (0.4%)

regimes208.0ms (2%)

bsearch42.0ms (0.4%)

regimes69.0ms (0.7%)

bsearch42.0ms (0.4%)

regimes50.0ms (0.5%)

bsearch0.0ms (0%)

regimes48.0ms (0.5%)

bsearch9.0ms (0.1%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (12.7%)

Profiling