Details

analyze1.7s (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
0%	74.9%	25.1%	2
18.7%	56.2%	25.1%	3
37.5%	37.5%	25.1%	4
42.1%	32.8%	25.1%	5
46.8%	28.1%	25.1%	6
48%	26.9%	25.1%	7
49.2%	25.8%	25.1%	8
49.5%	25.5%	25.1%	9
49.8%	25.2%	25.1%	10
49.8%	25.2%	25.1%	11
49.8%	25.1%	25.1%	12
49.9%	25%	25.1%	13
49.9%	25%	25.1%	14

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample2.4s (2.4%)

Algorithm

1×

intervals

Results

2.3s	107×	body	8192	exit
82.0ms	256×	body	128	valid
8.0ms	368×	pre	128	true
2.0ms	5×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify209.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	115

prune24.0ms (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: 1.8b

Counts

2 → 2

Compiler

Compiled 468 to 403 computations (13.9% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_2143`
28×	`add-sqr-sqrt_binary64_2165`
24×	`add-log-exp_binary64_2182` `cancel-sign-sub-inv_binary64_2109`
16×	`associate--l+_binary64_2080`
12×	`diff-log_binary64_2235` `distribute-lft-out--_binary64_2095` `add-cube-cbrt_binary64_2178`
8×	`sub-neg_binary64_2136` `difference-of-squares_binary64_2112`
4×	`pow1_binary64_2204` `flip--_binary64_2118` `associate--l-_binary64_2081` `add-exp-log_binary64_2181` `flip3--_binary64_2147` `difference-of-sqr-1_binary64_2113` `add-cbrt-cube_binary64_2179`

Counts

4 → 100

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)

series74.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (-.f64 1 z) 1)
18.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4806	704
1	4806	704

prune1.2s (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	2	114

Merged error: 1.8b

Counts

114 → 2

Compiler

Compiled 14747 to 12487 computations (15.3% saved)

localize65.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(-.f64 (-.f64 1 z) 1)
6.9b	(log.f64 (exp.f64 (neg.f64 z)))

rewrite67.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64_2143`
26×	`add-sqr-sqrt_binary64_2165`
19×	`add-log-exp_binary64_2182`
18×	`cancel-sign-sub-inv_binary64_2109`
14×	`add-cube-cbrt_binary64_2178`
12×	`associate--l+_binary64_2080`
11×	`log-pow_binary64_2232`
10×	`exp-prod_binary64_2195`
9×	`diff-log_binary64_2235` `distribute-lft-out--_binary64_2095`
6×	`sub-neg_binary64_2136` `difference-of-squares_binary64_2112`
5×	`pow1_binary64_2204`
4×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`flip--_binary64_2118` `distribute-rgt-neg-in_binary64_2101` `distribute-lft-neg-in_binary64_2100` `log-prod_binary64_2229` `associate--l-_binary64_2081` `flip3--_binary64_2147` `difference-of-sqr-1_binary64_2113`
2×	`log-div_binary64_2230` `exp-neg_binary64_2190`
1×	`log-rec_binary64_2231` `rem-log-exp_binary64_2184` `neg-sub0_binary64_2138` `neg-mul-1_binary64_2139` `exp-diff_binary64_2191`

Counts

4 → 100

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 z) 1)
10.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
4.0ms	(log.f64 (exp.f64 (neg.f64 z)))

series186.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

136.0ms	(log.f64 (exp.f64 (neg.f64 z)))
17.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)
16.0ms	(-.f64 (-.f64 1 z) 1)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4915	670
1	4915	670

prune1.2s (1.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	112	2	114

Merged error: 1.8b

Counts

114 → 2

Compiler

Compiled 14195 to 11692 computations (17.6% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
1.0b	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite181.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_2143`
44×	`add-log-exp_binary64_2182` `frac-add_binary64_2151`
31×	`sum-log_binary64_2234` `distribute-lft-out_binary64_2094`
10×	`add-exp-log_binary64_2181`
9×	`pow1_binary64_2204` `flip3-+_binary64_2146` `flip-+_binary64_2117` `add-cbrt-cube_binary64_2179`
7×	`prod-exp_binary64_2192`
5×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178`
4×	`associate-r_binary64_2083`
3×	`cbrt-unprod_binary64_2176`
2×	`+-commutative_binary64_2073` `associate-+l+_binary64_2076` `pow-prod-down_binary64_2214` `sqrt-pow1_binary64_2161`
1×	`pow1/2_binary64_2223` `exp-sum_binary64_2189` `pow-to-exp_binary64_2212` `sqrt-prod_binary64_2159` `pow-sub_binary64_2219` `associate-l_binary64_2084` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `*-commutative_binary64_2074` `pow-exp_binary64_2211`

Counts

4 → 86

Calls

4 calls:

110.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
24.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
18.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series305.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

180.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
95.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z))) (/.f64 -6214088902520669/35184372088832 (-.f64 4 z))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
29.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4951	7992
1	4951	7992

prune1.2s (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	88	8	96
Fresh	0	0	0
Picked	1	0	1
Done	1	0	1
Total	90	8	98

Merged error: 0.2b

Counts

98 → 8

Compiler

Compiled 21998 to 17824 computations (19% saved)

localize102.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.6b	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

rewrite369.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-log-exp_binary64_2182` `*-un-lft-identity_binary64_2143`
12×	`sum-log_binary64_2234` `distribute-lft-out_binary64_2094`
8×	`flip3-+_binary64_2146` `flip-+_binary64_2117` `frac-add_binary64_2151`
4×	`pow1_binary64_2204` `+-commutative_binary64_2073` `add-sqr-sqrt_binary64_2165` `add-exp-log_binary64_2181` `associate-+r+_binary64_2075` `add-cube-cbrt_binary64_2178` `add-cbrt-cube_binary64_2179`

Counts

4 → 68

Calls

4 calls:

230.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series135.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

35.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
34.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
33.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
33.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5020	2204

prune3.8s (3.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 0.2b

Counts

88 → 8

Compiler

Compiled 31904 to 26358 computations (17.4% saved)

regimes117.0ms (0.1%)

Compiler: Compiled 1113 to 921 computations (17.3% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	205	589
1	205	589

end0.0ms (0%)

sample1.4min (86%)

Algorithm

1×

intervals

Results

1.3min	3873×	body	8192	exit
2.5s	8000×	body	128	valid
232.0ms	11974×	pre	128	true
33.0ms	101×	body	128	invalid

Compiler

Compiled 1627 to 1359 computations (16.5% saved)

Details

analyze1.7s (1.7%)

sample2.4s (2.4%)

simplify209.0ms (0.2%)

prune24.0ms (0%)

localize57.0ms (0.1%)

rewrite67.0ms (0.1%)

series74.0ms (0.1%)

simplify74.0ms (0.1%)

prune1.2s (1.2%)

localize65.0ms (0.1%)

rewrite67.0ms (0.1%)

series186.0ms (0.2%)

simplify79.0ms (0.1%)

prune1.2s (1.2%)

localize58.0ms (0.1%)

rewrite181.0ms (0.2%)

series305.0ms (0.3%)

simplify110.0ms (0.1%)

prune1.2s (1.2%)

localize102.0ms (0.1%)

rewrite369.0ms (0.4%)

series135.0ms (0.1%)

simplify81.0ms (0.1%)

prune3.8s (3.8%)

regimes117.0ms (0.1%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample1.4min (86%)

Profiling