Details

analyze9.0ms (0.1%)

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 20 to 17 computations (15% saved)

sample30.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms

256×

body

128

valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify483.0ms (7.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	1225	28
1	1225	28

prune5.0ms (0.1%)

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 38 to 32 computations (15.8% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
0.0b	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
13.7b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

rewrite83.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2120`
18×	`*-un-lft-identity_binary64_2099`
16×	`add-cube-cbrt_binary64_2131`
10×	`add-cbrt-cube_binary64_2132` `times-frac_binary64_2105` `add-exp-log_binary64_2134`
9×	`associate-r_binary64_2041`
8×	`pow1_binary64_2157`
6×	`associate-l_binary64_2042` `add-log-exp_binary64_2135`
4×	`associate-*r/_binary64_2043` `flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`associate-/r_binary64_2045` `associate-/l_binary64_2046`
2×	`difference-of-squares_binary64_2068` `sub-neg_binary64_2092` `distribute-rgt-in_binary64_2051` `*-commutative_binary64_2032` `distribute-lft-in_binary64_2050` `associate-/l/_binary64_2048` `associate-/r/_binary64_2047` `prod-exp_binary64_2145` `pow-prod-down_binary64_2167` `unswap-sqr_binary64_2067` `cbrt-unprod_binary64_2129`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `flip3--_binary64_2103` `flip--_binary64_2074` `clear-num_binary64_2098` `div-inv_binary64_2096` `distribute-lft-out--_binary64_2053`

Counts

4 → 89

Calls

4 calls:

30.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
15.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
12.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
6.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))

series398.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
97.0ms	(.f64 6369080665019903/9007199254740992 (-.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
80.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
73.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))

simplify173.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	5121	2363

prune283.0ms (4.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	4	102

Merged error: 0b

Counts

102 → 4

Compiler

Compiled 2894 to 2317 computations (19.9% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))
0.1b	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
0.8b	(/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
12.8b	(.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))))

rewrite78.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_2120`
23×	`*-un-lft-identity_binary64_2099`
22×	`add-cube-cbrt_binary64_2131`
20×	`times-frac_binary64_2105`
19×	`add-exp-log_binary64_2134`
18×	`associate-r_binary64_2041`
13×	`add-cbrt-cube_binary64_2132`
9×	`pow1_binary64_2157`
6×	`associate-l_binary64_2042` `flip3-+_binary64_2102` `add-log-exp_binary64_2135` `flip-+_binary64_2073`
5×	`prod-exp_binary64_2145`
4×	`div-exp_binary64_2147` `associate-/r/_binary64_2047` `unswap-sqr_binary64_2067`
3×	`associate-r/_binary64_2043` `associate-/r_binary64_2045` `associate-/l*_binary64_2046` `cbrt-unprod_binary64_2129`
2×	`cbrt-undiv_binary64_2130` `1-exp_binary64_2140` `-commutative_binary64_2032` `rec-exp_binary64_2146` `associate-l/_binary64_2044` `pow-prod-down_binary64_2167` `frac-times_binary64_2109` `div-inv_binary64_2096`
1×	`pow-flip_binary64_2170` `un-div-inv_binary64_2097` `distribute-rgt-in_binary64_2051` `inv-pow_binary64_2181` `distribute-lft-in_binary64_2050` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `clear-num_binary64_2098`

Counts

4 → 108

Calls

4 calls:

25.0ms	(.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))))
12.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
11.0ms	(/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))
6.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))

series373.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
83.0ms	(+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248))
78.0ms	(.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))))
55.0ms	(/.f64 1 (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))

simplify176.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4899	2440
1	4899	2440

prune315.0ms (4.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	120	4	124

Merged error: 0b

Counts

124 → 4

Compiler

Compiled 3467 to 2827 computations (18.5% saved)

localize39.0ms (0.6%)

Local error

Found 4 expressions with local error:

13.7b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
13.7b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
13.7b	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
13.7b	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (.f64 x x))) (+.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))

rewrite148.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_2099`
31×	`times-frac_binary64_2105`
30×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131`
15×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
13×	`associate-/r*_binary64_2045`
10×	`associate-/l*_binary64_2046`
8×	`associate-/l/_binary64_2048` `associate-/r/_binary64_2047`
7×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
5×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
4×	`pow1_binary64_2157` `frac-2neg_binary64_2110` `add-log-exp_binary64_2135` `clear-num_binary64_2098` `div-inv_binary64_2096`
2×	`distribute-lft-out_binary64_2052` `associate-*r/_binary64_2043`
1×	`prod-exp_binary64_2145` `flip3--_binary64_2103` `flip--_binary64_2074` `cbrt-unprod_binary64_2129`

Counts

4 → 120

Calls

4 calls:

59.0ms	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (.f64 x x))) (+.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
15.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
14.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
14.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

series463.0ms (7%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(/.f64 (.f64 6369080665019903/9007199254740992 (-.f64 (.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))))) (.f64 x x))) (+.f64 (/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936))))) x))
81.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
65.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
61.0ms	(/.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248)) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))

simplify183.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5158	4494

prune864.0ms (13.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

Compiler

Compiled 8079 to 6277 computations (22.3% saved)

localize30.0ms (0.5%)

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)))
3.5b	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
4.0b	(.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))))))

rewrite100.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64_2120`
40×	`times-frac_binary64_2105`
37×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
32×	`sqrt-prod_binary64_2114`
27×	`associate-r_binary64_2041`
13×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
9×	`associate-l_binary64_2042` `pow1_binary64_2157`
8×	`sqrt-div_binary64_2115`
7×	`flip3-+_binary64_2102` `unswap-sqr_binary64_2067` `flip-+_binary64_2073`
6×	`associate-/l*_binary64_2046`
4×	`associate-/r/_binary64_2047` `add-log-exp_binary64_2135`
3×	`associate-r/_binary64_2043` `prod-exp_binary64_2145` `associate-/r_binary64_2045` `cbrt-unprod_binary64_2129`
2×	`cbrt-undiv_binary64_2130` `-commutative_binary64_2032` `div-exp_binary64_2147` `associate-/l/_binary64_2048` `associate-l/_binary64_2044` `pow-prod-down_binary64_2167` `frac-times_binary64_2109` `div-inv_binary64_2096`
1×	`distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `frac-2neg_binary64_2110` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `clear-num_binary64_2098` `sqrt-pow1_binary64_2116`

Counts

4 → 134

Calls

4 calls:

34.0ms	(.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))))))
14.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
11.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
10.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

series422.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(/.f64 (sqrt.f64 (+.f64 162377988252285/70368744177664 (.f64 x 609359547581365/2251799813685248))) (+.f64 1 (.f64 x (+.f64 8937753748486939/9007199254740992 (*.f64 x 3228900788839551/72057594037927936)))))
140.0ms	(.f64 x (+.f64 8937753748486939/9007199254740992 (.f64 x 3228900788839551/72057594037927936)))
71.0ms	(.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))))))
68.0ms	(sqrt.f64 (+.f64 162377988252285/70368744177664 (*.f64 x 609359547581365/2251799813685248)))

simplify178.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4974	4362
1	4974	4362

prune536.0ms (8.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	146	4	150

Merged error: 0b

Counts

150 → 4

Compiler

Compiled 5434 to 4443 computations (18.2% saved)

regimes29.0ms (0.4%)

Compiler: Compiled 114 to 95 computations (16.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	31
1	36	31

end0.0ms (0%)

sample1.1s (17%)

Algorithm

1×

intervals

Results

675.0ms

8000×

body

128

valid

Compiler

Compiled 153 to 129 computations (15.7% saved)

Details

analyze9.0ms (0.1%)

sample30.0ms (0.5%)

simplify483.0ms (7.3%)

prune5.0ms (0.1%)

localize26.0ms (0.4%)

rewrite83.0ms (1.3%)

series398.0ms (6.1%)

simplify173.0ms (2.6%)

prune283.0ms (4.3%)

localize27.0ms (0.4%)

rewrite78.0ms (1.2%)

series373.0ms (5.7%)

simplify176.0ms (2.7%)

prune315.0ms (4.8%)

localize39.0ms (0.6%)

rewrite148.0ms (2.2%)

series463.0ms (7%)

simplify183.0ms (2.8%)

prune864.0ms (13.1%)

localize30.0ms (0.5%)

rewrite100.0ms (1.5%)

series422.0ms (6.4%)

simplify178.0ms (2.7%)

prune536.0ms (8.1%)

regimes29.0ms (0.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (17%)

Profiling