Details

analyze239.0ms (3.8%)

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
0%	99.9%	0.1%	5
0%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms	256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify255.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	1363	18
1	1363	18

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-log-exp_binary64_10223`
16×	`*-un-lft-identity_binary64_10187`
11×	`add-sqr-sqrt_binary64_10208`
7×	`add-cube-cbrt_binary64_10219`
6×	`log-prod_binary64_10270` `pow1_binary64_10245`
5×	`add-exp-log_binary64_10222` `add-cbrt-cube_binary64_10220` `diff-log_binary64_10276`
4×	`associate-l_binary64_10130` `associate-r_binary64_10129` `sum-log_binary64_10275`
3×	`distribute-lft-out_binary64_10140` `distribute-rgt-in_binary64_10139` `distribute-lft-in_binary64_10138`
2×	`sub-neg_binary64_10180` `associate-+l-_binary64_10124` `flip3-+_binary64_10190` `flip-+_binary64_10161` `distribute-lft-out--_binary64_10141` `associate-*l/_binary64_10132`
1×	`associate-+l+_binary64_10122` `flip--_binary64_10162` `+-commutative_binary64_10119` `pow-prod-down_binary64_10255` `flip3--_binary64_10191` `log-pow_binary64_10273` `*-commutative_binary64_10120` `associate--l+_binary64_10126` `unswap-sqr_binary64_10155` `associate--l-_binary64_10127` `prod-exp_binary64_10233` `cbrt-unprod_binary64_10217` `difference-of-squares_binary64_10156`

Counts

3 → 61

Calls

3 calls:

9.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
6.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)

series352.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

181.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
98.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
73.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)

simplify57.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5091	1270

prune77.0ms (1.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	65	6	71

Merged error: 0.0b

Counts

71 → 6

Compiler

Compiled 1356 to 773 computations (43% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod_binary64_10270`
36×	`distribute-rgt-in_binary64_10139` `distribute-lft-in_binary64_10138`
30×	`cbrt-prod_binary64_10215`
26×	`add-sqr-sqrt_binary64_10208` `*-un-lft-identity_binary64_10187`
24×	`associate-+l+_binary64_10122` `add-cube-cbrt_binary64_10219`
12×	`associate-+r+_binary64_10121`
10×	`associate-*l/_binary64_10132`
7×	`pow1_binary64_10245`
6×	`flip3-+_binary64_10190` `add-exp-log_binary64_10222` `flip-+_binary64_10161` `add-cbrt-cube_binary64_10220` `add-log-exp_binary64_10223`
5×	`associate-r_binary64_10129`
4×	`associate-l_binary64_10130` `frac-add_binary64_10195`
3×	`pow1/3_binary64_10266`
2×	`distribute-lft-out_binary64_10140` `log-pow_binary64_10273`
1×	`+-commutative_binary64_10119` `pow-prod-down_binary64_10255` `sum-log_binary64_10275` `*-commutative_binary64_10120` `unswap-sqr_binary64_10155` `prod-exp_binary64_10233` `cbrt-unprod_binary64_10217`

Counts

4 → 109

Calls

4 calls:

16.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.5s (23%)

Counts

4 → 12

Calls

4 calls:

734.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
407.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
174.0ms	(cbrt.f64 y)
147.0ms	(cbrt.f64 y)

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4933	1851
1	4933	1851

prune161.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	119	2	121
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	120	7	127

Merged error: 0.0b

Counts

127 → 7

Compiler

Compiled 3428 to 1945 computations (43.3% saved)

localize22.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3))))
0.6b	(cbrt.f64 y)
5.0b	(pow.f64 y 1/3)

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`log-prod_binary64_10270`
38×	`distribute-rgt-in_binary64_10139` `distribute-lft-in_binary64_10138`
27×	`add-sqr-sqrt_binary64_10208` `*-un-lft-identity_binary64_10187`
25×	`add-cube-cbrt_binary64_10219`
24×	`associate-+l+_binary64_10122`
15×	`cbrt-prod_binary64_10215` `unpow-prod-down_binary64_10263`
14×	`associate-+r+_binary64_10121`
10×	`associate-*l/_binary64_10132`
7×	`add-exp-log_binary64_10222` `pow1_binary64_10245`
6×	`flip3-+_binary64_10190` `flip-+_binary64_10161` `add-cbrt-cube_binary64_10220` `add-log-exp_binary64_10223`
5×	`sqr-pow_binary64_10159`
4×	`associate-l_binary64_10130` `frac-add_binary64_10195` `associate-r_binary64_10129`
3×	`pow-unpow_binary64_10261`
2×	`distribute-lft-out_binary64_10140`
1×	`pow1/3_binary64_10266` `unpow1/3_binary64_10251` `+-commutative_binary64_10119` `pow-prod-down_binary64_10255` `sum-log_binary64_10275` `pow-to-exp_binary64_10253` `log-pow_binary64_10273` `*-commutative_binary64_10120` `unswap-sqr_binary64_10155` `prod-exp_binary64_10233` `pow-exp_binary64_10252` `cbrt-unprod_binary64_10217` `pow-pow_binary64_10256`

Counts

4 → 119

Calls

4 calls:

16.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3))))
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3)))
2.0ms	(pow.f64 y 1/3)
1.0ms	(cbrt.f64 y)

series1.7s (27.1%)

Counts

4 → 12

Calls

4 calls:

1.0s	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3))))
415.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (pow.f64 y 1/3)))
148.0ms	(pow.f64 y 1/3)
145.0ms	(cbrt.f64 y)

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4906	1899
1	4906	1899

prune176.0ms (2.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	131	7	138

Merged error: 0.0b

Counts

138 → 7

Compiler

Compiled 3696 to 2244 computations (39.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y) z)
0.1b	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)
0.4b	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))
0.5b	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))

rewrite49.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_10187`
18×	`add-log-exp_binary64_10223`
15×	`add-sqr-sqrt_binary64_10208`
14×	`sqrt-div_binary64_10203`
12×	`pow1_binary64_10245`
11×	`associate-l_binary64_10130` `add-exp-log_binary64_10222` `add-cbrt-cube_binary64_10220`
10×	`associate-*r/_binary64_10131`
9×	`sqrt-prod_binary64_10202` `add-cube-cbrt_binary64_10219`
8×	`flip3-+_binary64_10190` `associate-r_binary64_10129` `flip-+_binary64_10161`
5×	`diff-log_binary64_10276`
4×	`distribute-lft-out_binary64_10140` `frac-times_binary64_10197` `pow-prod-down_binary64_10255` `sum-log_binary64_10275` `prod-exp_binary64_10233` `cbrt-unprod_binary64_10217`
2×	`sub-neg_binary64_10180` `associate-+l-_binary64_10124` `-commutative_binary64_10120` `unswap-sqr_binary64_10155` `distribute-lft-out--_binary64_10141` `associate-l/_binary64_10132`
1×	`associate-+l+_binary64_10122` `flip--_binary64_10162` `+-commutative_binary64_10119` `flip3--_binary64_10191` `log-pow_binary64_10273` `associate--l+_binary64_10126` `associate--l-_binary64_10127` `difference-of-squares_binary64_10156`

Counts

4 → 89

Calls

4 calls:

13.0ms	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))
11.0ms	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))
9.0ms	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y) z)
6.0ms	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)

series424.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))
100.0ms	(-.f64 (+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y) z)
83.0ms	(+.f64 (-.f64 x (.f64 (sqrt.f64 (+.f64 y 1/2)) (.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2))))) y)
76.0ms	(*.f64 (log.f64 y) (sqrt.f64 (+.f64 y 1/2)))

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4993	2011
1	4993	2011

prune111.0ms (1.8%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	102	6	108

Merged error: 0.0b

Counts

108 → 6

Compiler

Compiled 2248 to 1373 computations (38.9% saved)

regimes86.0ms (1.4%)

Compiler: Compiled 635 to 526 computations (17.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	117	37
1	117	37

end0.0ms (0%)

sample762.0ms (12%)

Algorithm

1×

intervals

Results

382.0ms	8000×	body	128	valid
1.0ms	32×	body	128	invalid

Compiler

Compiled 166 to 138 computations (16.9% saved)

Details

analyze239.0ms (3.8%)

sample20.0ms (0.3%)

simplify255.0ms (4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite27.0ms (0.4%)

series352.0ms (5.5%)

simplify57.0ms (0.9%)

prune77.0ms (1.2%)

localize15.0ms (0.2%)

rewrite41.0ms (0.6%)

series1.5s (23%)

simplify88.0ms (1.4%)

prune161.0ms (2.5%)

localize22.0ms (0.3%)

rewrite44.0ms (0.7%)

series1.7s (27.1%)

simplify76.0ms (1.2%)

prune176.0ms (2.8%)

localize11.0ms (0.2%)

rewrite49.0ms (0.8%)

series424.0ms (6.7%)

simplify70.0ms (1.1%)

prune111.0ms (1.8%)

regimes86.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample762.0ms (12%)

Profiling