Details

analyze4.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample20.0ms (0.9%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

valid

Compiler

Compiled 35 to 30 computations (14.3% saved)

simplify251.0ms (11.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (242.0ms)

Iter	Nodes	Cost
0	4596	25
1	4596	25

prune3.0ms (0.2%)

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: 0.0b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
0.0b	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
17.4b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite29.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`
10×	`times-frac_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 78

Calls

4 calls:

11.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

series25.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))) x)
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
4.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))

simplify104.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4999	2132
1	4999	2132

prune96.0ms (4.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Merged error: 0b

Counts

91 → 3

Compiler

Compiled 2348 to 1841 computations (21.6% saved)

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
0.1b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
17.3b	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
17.3b	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

rewrite47.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

288×	`times-frac_binary64`
164×	`add-sqr-sqrt_binary64`
162×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
156×	`sqrt-prod_binary64`
27×	`associate-/l*_binary64`
22×	`sqrt-div_binary64`
18×	`associate-/r/_binary64`
12×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`div-inv_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 264

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

series24.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
5.0ms	(/.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
5.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
5.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify233.0ms (11.1%)

Algorithm

1×	egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5007	14708

prune694.0ms (32.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	276	3	279

Merged error: 0b

Counts

279 → 3

Compiler

Compiled 12443 to 10174 computations (18.2% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
0.0b	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.5b	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

rewrite37.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`
16×	`times-frac_binary64`
11×	`pow1_binary64`
8×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-log-exp_binary64` `log-pow_binary64`
5×	`associate-/r*_binary64` `log-prod_binary64`
3×	`flip3-+_binary64` `associate-r_binary64` `associate-l_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `associate-/r/_binary64` `distribute-rgt-in_binary64` `exp-sum_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

13.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
12.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
2.0ms	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

series26.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

8.0ms	(-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))) x)
7.0ms	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
7.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
5.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))

simplify111.0ms (5.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4920	2444
1	4920	2444

prune106.0ms (5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	103	3	106

Merged error: 0b

Counts

106 → 3

Compiler

Compiled 2676 to 2113 computations (21% saved)

localize13.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.9b	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
5.1b	(.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))

rewrite38.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
32×	`sqrt-prod_binary64`
27×	`associate-r_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`pow1_binary64` `associate-l_binary64`
8×	`sqrt-div_binary64`
7×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64`
3×	`associate-/r_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 134

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
7.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
3.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

series29.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

12.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
6.0ms	(.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
5.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

simplify94.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5294	4405

Details

analyze4.0ms (0.2%)

sample20.0ms (0.9%)

simplify251.0ms (11.9%)

prune3.0ms (0.2%)

localize10.0ms (0.5%)

rewrite29.0ms (1.4%)

series25.0ms (1.2%)

simplify104.0ms (4.9%)

prune96.0ms (4.6%)

localize16.0ms (0.8%)

rewrite47.0ms (2.2%)

series24.0ms (1.2%)

simplify233.0ms (11.1%)

prune694.0ms (32.9%)

localize12.0ms (0.6%)

rewrite37.0ms (1.8%)

series26.0ms (1.2%)

simplify111.0ms (5.3%)

prune106.0ms (5%)

localize13.0ms (0.6%)

rewrite38.0ms (1.8%)

series29.0ms (1.4%)

simplify94.0ms (4.4%)

prune85.0ms (4%)

Profiling