Details

analyze753.0ms (8.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample57.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	175×	body	128	valid
9.0ms	37×	body	1024	nan
9.0ms	35×	body	1024	valid
5.0ms	26×	body	512	valid
4.0ms	59×	body	128	nan
2.0ms	19×	body	256	valid
2.0ms	13×	body	512	nan
1.0ms	11×	body	256	nan
0.0ms	1×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify165.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5192	41

prune3.0ms (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

Merged error: 44.0b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
13.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.3b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite66.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
7×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `associate--l+_binary64_15` `unswap-sqr_binary64_46` `associate-/r/_binary64_24`
1×	`distribute-lft-in_binary64_27` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `pow-prod-down_binary64_149` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 80

Calls

4 calls:

23.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
15.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
14.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

series1.4s (16.9%)

Counts

4 → 12

Calls

4 calls:

814.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
411.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
179.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
23.0ms	(*.f64 (sqrt.f64 2) t)

simplify56.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5269	3058

prune183.0ms (2.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 6.5b

Counts

93 → 5

Compiler

Compiled 3598 to 2111 computations (41.3% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
5.1b	(/.f64 (*.f64 l l) x)
9.7b	(/.f64 (*.f64 t t) x)
29.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
8×	`associate-*r/_binary64_20`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`frac-add_binary64_86` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `sqrt-div_binary64_95` `flip3-+_binary64_81`
3×	`sqrt-prod_binary64_94`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-+r+_binary64_10` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `pow1/2_binary64_158` `sum-log_binary64_169`

Counts

4 → 74

Calls

4 calls:

8.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
5.0ms	(/.f64 (*.f64 t t) x)
4.0ms	(/.f64 (*.f64 l l) x)

series161.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
45.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
13.0ms	(/.f64 (*.f64 t t) x)
12.0ms	(/.f64 (*.f64 l l) x)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4990	1973
1	4990	1973

prune124.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 4.8b

Counts

91 → 10

Compiler

Compiled 3204 to 1473 computations (54% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
9.7b	(/.f64 (*.f64 t t) x)
29.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-+r+_binary64_10` `sum-log_binary64_169`
1×	`distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
4.0ms	(/.f64 (*.f64 t t) x)
4.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))

series182.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

94.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
46.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
30.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
12.0ms	(/.f64 (*.f64 t t) x)

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4966	2011
1	4966	2011

prune108.0ms (1.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	76	10	86

Merged error: 4.8b

Counts

86 → 10

Compiler

Compiled 2945 to 1330 computations (54.8% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
3.2b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
9.7b	(/.f64 (*.f64 t t) x)
29.6b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

rewrite33.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `associate-*r/_binary64_20`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`flip-+_binary64_52` `pow1_binary64_139` `flip3-+_binary64_81`
4×	`frac-add_binary64_86` `sqrt-div_binary64_95`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-+r+_binary64_10` `sum-log_binary64_169`
1×	`distribute-lft-in_binary64_27` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l*_binary64_23` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 64

Calls

4 calls:

8.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
5.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
5.0ms	(/.f64 (*.f64 t t) x)

series236.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
59.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
48.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
16.0ms	(/.f64 (*.f64 t t) x)

simplify49.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5048	2016

prune95.0ms (1.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	76	10	86

Merged error: 4.8b

Counts

86 → 10

Compiler

Compiled 2807 to 1073 computations (61.8% saved)

regimes1.3s (15.2%)

Compiler: Compiled 12251 to 8610 computations (29.7% saved)

bsearch320.0ms (3.8%)

Steps

Iters	Range		Point
6	4.2574098318715486e+99	3.7144923047798485e+100	3.6293279203079994e+100
9	-6.578433623800053e-208	-3.910842502118582e-214	-6.499970412284675e-208
9	-3.4009149964612336e-158	-1.0130014446784761e-165	-1.02625065655815e-165
7	-6.075593162476744e+128	-1.901138092331567e+127	-2.774724760257283e+128

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	189	244
1	189	244

end0.0ms (0%)

sample2.8s (33.7%)

Algorithm

1×

intervals

Results

365.0ms	5307×	body	128	valid
298.0ms	1158×	body	1024	valid
203.0ms	802×	body	1024	nan
183.0ms	949×	body	512	valid
93.0ms	1467×	body	128	nan
93.0ms	482×	body	512	nan
69.0ms	521×	body	256	valid
36.0ms	277×	body	256	nan
22.0ms	65×	body	2048	valid

Compiler

Compiled 1823 to 1264 computations (30.7% saved)

Details

analyze753.0ms (8.9%)

sample57.0ms (0.7%)

simplify165.0ms (2%)

prune3.0ms (0%)

localize15.0ms (0.2%)

rewrite66.0ms (0.8%)

series1.4s (16.9%)

simplify56.0ms (0.7%)

prune183.0ms (2.2%)

localize14.0ms (0.2%)

rewrite34.0ms (0.4%)

series161.0ms (1.9%)

simplify67.0ms (0.8%)

prune124.0ms (1.5%)

localize14.0ms (0.2%)

rewrite31.0ms (0.4%)

series182.0ms (2.2%)

simplify83.0ms (1%)

prune108.0ms (1.3%)

localize21.0ms (0.3%)

rewrite33.0ms (0.4%)

series236.0ms (2.8%)

simplify49.0ms (0.6%)

prune95.0ms (1.1%)

regimes1.3s (15.2%)

bsearch320.0ms (3.8%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.8s (33.7%)

Profiling