Details

analyze4.0ms

Algorithm

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

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify240.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4940	25
1	4940	25

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.0b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2485`
16×	`*-un-lft-identity_binary64_2500`
14×	`add-cube-cbrt_binary64_2471`
10×	`times-frac_binary64_2495`
8×	`add-log-exp_binary64_2465` `add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
6×	`pow1_binary64_2446`
4×	`flip3-+_binary64_2498` `flip-+_binary64_2525`
3×	`associate-l_binary64_2560` `associate-/l_binary64_2564` `associate-/r_binary64_2563` `associate-r_binary64_2559`
2×	`associate-*l/_binary64_2562` `associate-/l/_binary64_2566` `associate-/r/_binary64_2565` `difference-of-squares_binary64_2529`
1×	`diff-log_binary64_2416` `distribute-lft-out--_binary64_2545` `+-commutative_binary64_2567` `div-exp_binary64_2453` `frac-2neg_binary64_2493` `sub-neg_binary64_2504` `div-inv_binary64_2501` `cbrt-undiv_binary64_2470` `sum-log_binary64_2415` `pow-prod-down_binary64_2427` `prod-exp_binary64_2451` `unswap-sqr_binary64_2528` `*-commutative_binary64_2568` `clear-num_binary64_2503` `flip--_binary64_2526` `cbrt-unprod_binary64_2469` `flip3--_binary64_2499`

Counts

4 → 76

Calls

4 calls:

3.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
10.0ms	(-.f64 x (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x))))
6.0ms	(.f64 (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)) x)
7.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x)))

series107.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))
25.0ms	(-.f64 x (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x))))
37.0ms	(.f64 (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)) x)
25.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x)))

simplify77.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4938	2129
1	4938	2129

prune395.0ms

Filtered

71 candidates to 88 candidates (-23.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	3	89

Merged error: 0b

Counts

89 → 3

localize31.0ms

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 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x))))
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 (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)) x)))
17.3b	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64_2495`
164×	`add-sqr-sqrt_binary64_2485`
162×	`add-cube-cbrt_binary64_2471` `*-un-lft-identity_binary64_2500`
156×	`sqrt-prod_binary64_2479`
27×	`associate-/l*_binary64_2564`
22×	`sqrt-div_binary64_2480`
18×	`associate-/r/_binary64_2565`
12×	`flip3-+_binary64_2498` `associate-/r*_binary64_2563` `flip-+_binary64_2525`
11×	`add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
9×	`div-inv_binary64_2501`
6×	`pow1_binary64_2446`
4×	`div-exp_binary64_2453` `add-log-exp_binary64_2465` `cbrt-undiv_binary64_2470`
3×	`associate-/l/_binary64_2566`
2×	`pow1/2_binary64_2436` `frac-2neg_binary64_2493` `sqrt-pow1_binary64_2481` `rem-sqrt-square_binary64_2488` `clear-num_binary64_2503`

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 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x))))
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 (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)) x)))
3.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.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 (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)) x))))
37.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))
20.0ms	(sqrt.f64 (+.f64 1 (.f64 (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)) x)))
23.0ms	(sqrt.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify200.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4988	15642
1	4988	15642

prune1.2s

Filtered

151 candidates to 276 candidates (-82.8%)

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

localize21.0ms

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 x (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))))
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)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_2500`
24×	`add-sqr-sqrt_binary64_2485`
17×	`add-cube-cbrt_binary64_2471`
16×	`times-frac_binary64_2495`
11×	`pow1_binary64_2446`
8×	`add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472` `distribute-lft-out_binary64_2544`
7×	`log-pow_binary64_2421` `add-log-exp_binary64_2465`
5×	`associate-/r*_binary64_2563` `log-prod_binary64_2418`
3×	`flip3-+_binary64_2498` `associate-l_binary64_2560` `associate-/l_binary64_2564` `associate-r*_binary64_2559` `flip-+_binary64_2525`
2×	`associate-/l/_binary64_2566` `associate-/r/_binary64_2565` `distribute-rgt-in_binary64_2543` `difference-of-squares_binary64_2529` `exp-sum_binary64_2459` `distribute-lft-in_binary64_2542` `associate-*r/_binary64_2561`
1×	`diff-log_binary64_2416` `distribute-lft-out--_binary64_2545` `div-exp_binary64_2453` `frac-2neg_binary64_2493` `sub-neg_binary64_2504` `exp-prod_binary64_2454` `div-inv_binary64_2501` `exp-to-pow_binary64_2440` `cbrt-undiv_binary64_2470` `pow-prod-down_binary64_2427` `prod-exp_binary64_2451` `unswap-sqr_binary64_2528` `rem-log-exp_binary64_2463` `*-commutative_binary64_2568` `clear-num_binary64_2503` `flip--_binary64_2526` `cbrt-unprod_binary64_2469` `flip3--_binary64_2499`

Counts

4 → 91

Calls

4 calls:

8.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
12.0ms	(-.f64 x (/.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)))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))))
26.0ms	(-.f64 x (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936))))))))
39.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
41.0ms	(log.f64 (exp.f64 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4966	2463
1	4966	2463

prune390.0ms

Filtered

73 candidates to 103 candidates (-41.1%)

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

localize20.0ms

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 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
4.7b	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac_binary64_2495`
166×	`add-sqr-sqrt_binary64_2485`
163×	`add-cube-cbrt_binary64_2471` `*-un-lft-identity_binary64_2500`
153×	`sqrt-prod_binary64_2479`
30×	`associate-/r*_binary64_2563`
20×	`sqrt-div_binary64_2480`
17×	`associate-/r/_binary64_2565`
13×	`add-exp-log_binary64_2464` `add-cbrt-cube_binary64_2472`
12×	`flip3-+_binary64_2498` `flip-+_binary64_2525`
9×	`div-inv_binary64_2501` `associate-/l*_binary64_2564`
7×	`pow1_binary64_2446`
4×	`associate-/l/_binary64_2566` `div-exp_binary64_2453` `add-log-exp_binary64_2465` `cbrt-undiv_binary64_2470`
3×	`associate-l_binary64_2560` `associate-r_binary64_2559`
2×	`frac-2neg_binary64_2493` `clear-num_binary64_2503` `associate-*r/_binary64_2561`
1×	`distribute-rgt-in_binary64_2543` `pow1/2_binary64_2436` `distribute-lft-in_binary64_2542` `sqrt-pow1_binary64_2481` `pow-prod-down_binary64_2427` `rem-sqrt-square_binary64_2488` `prod-exp_binary64_2451` `unswap-sqr_binary64_2528` `*-commutative_binary64_2568` `cbrt-unprod_binary64_2469`

Counts

4 → 271

Calls

4 calls:

3.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
6.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
12.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
15.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))
41.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
42.0ms	(/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))))
23.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (/.f64 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))) (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)))))

simplify195.0ms

Algorithm

egg-herbie

Counts

283 → 283

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4924	14036
1	4924	14036

prune195.0ms

Filtered: 157 candidates to 283 candidates (-80.3%)

Details

analyze4.0ms

sample21.0ms

simplify240.0ms

prune12.0ms

localize16.0ms

rewrite28.0ms

series107.0ms

simplify77.0ms

prune395.0ms

localize31.0ms

rewrite45.0ms

series101.0ms

simplify200.0ms

prune1.2s

localize21.0ms

rewrite30.0ms

series126.0ms

simplify81.0ms

prune390.0ms

localize20.0ms

rewrite52.0ms

series126.0ms

simplify195.0ms

prune195.0ms

Profiling