Details

analyze1.9s (2.2%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115
0	1	1
1	1	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)

sample1.5s (1.8%)

Algorithm

1×

intervals

Results

1.4s	124×	body	8192	exit
78.0ms	256×	body	128	valid
6.0ms	380×	pre	128	true

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify48.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune17.0ms (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

Error

1.8b

Counts

2 → 2

Compiler

Compiled 271 to 232 computations (14.4% saved)

localize57.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.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)))
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	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite944.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

58×	`add-log-exp_binary64_2163` `*-un-lft-identity_binary64_2124`
56×	`frac-add_binary64_2132`
41×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075`
13×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
7×	`pow1_binary64_2185`
4×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
3×	`associate-+l+_binary64_2057` `+-commutative_binary64_2054`
2×	`sqrt-pow1_binary64_2142`
1×	`pow1/2_binary64_2204` `pow-prod-down_binary64_2195` `sqrt-prod_binary64_2140`

Counts

4 → 90

Calls

4 calls:

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)))
52.0ms	(+.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)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9977 to 7937 computations (20.4% saved)

series236.0ms (0.3%)

Error

0.3b

Counts

4 → 18

Calls

4 calls:

73.0ms	(+.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)))
58.0ms	(+.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)))
48.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 2088 to 1638 computations (21.6% saved)

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5000	9017

prune820.0ms (1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	5	110

Error

0.2b

Counts

110 → 5

Compiler

Compiled 10193 to 8056 computations (21% saved)

localize85.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 4 z) (+.f64 (.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) (-.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 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite3.4s (4.1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

36×	`frac-times_binary64_2134`
34×	`associate-*r/_binary64_2066`
30×	`associate-*l/_binary64_2067`
27×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
25×	`frac-add_binary64_2132`
24×	`flip3--_binary64_2128` `flip--_binary64_2099`
16×	`pow1_binary64_2185`
15×	`add-log-exp_binary64_2163`
14×	`*-un-lft-identity_binary64_2124`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`sum-log_binary64_2215` `pow-prod-down_binary64_2195`
6×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `distribute-lft-out_binary64_2075`
5×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
3×	`associate-+l+_binary64_2057` `associate-l_binary64_2065`
2×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-+r+_binary64_2056` `+-commutative_binary64_2054` `sqrt-pow1_binary64_2142`
1×	`pow1/2_binary64_2204` `sqrt-prod_binary64_2140` `associate-r_binary64_2064` `*-commutative_binary64_2055`

Counts

4 → 111

Calls

4 calls:

173.0ms	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 4 z) (+.f64 (.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) (-.f64 4 z))))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
33.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
17.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 25089 to 20550 computations (18.1% saved)

series742.0ms (0.9%)

Error

0.2b

Counts

4 → 18

Calls

4 calls:

451.0ms	(+.f64 (+.f64 (+.f64 (/.f64 (+.f64 (.f64 (-.f64 4 z) (+.f64 (.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z)) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) 848079078717083/1099511627776)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))) (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) (-.f64 4 z))))) (/.f64 7041008316161153/562949953421312 (-.f64 5 z))) (/.f64 -4992549864024149/36028797018963968 (-.f64 6 z))) (/.f64 5893731530977871/590295810358705651712 (-.f64 7 z)))
104.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
94.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 4222 to 3426 computations (18.9% saved)

simplify174.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5208	16341

prune3.2s (3.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	130	4	134

Error

0.2b

Counts

134 → 4

Compiler

Compiled 24731 to 20149 computations (18.5% saved)

localize78.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 (*.f64 PI.f64 2))
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))))

rewrite835.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

19×	`add-log-exp_binary64_2163` `*-un-lft-identity_binary64_2124`
9×	`sum-log_binary64_2215` `distribute-lft-out_binary64_2075`
7×	`pow1_binary64_2185`
6×	`flip3-+_binary64_2127` `frac-add_binary64_2132` `flip-+_binary64_2098`
4×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
3×	`associate-+r+_binary64_2056` `+-commutative_binary64_2054`
2×	`sqrt-pow1_binary64_2142`
1×	`pow1/2_binary64_2204` `pow-prod-down_binary64_2195` `sqrt-prod_binary64_2140`

Counts

4 → 62

Calls

4 calls:

27.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
24.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
24.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9866 to 8013 computations (18.8% saved)

series367.0ms (0.4%)

Error

0.2b

Counts

4 → 18

Calls

4 calls:

78.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
78.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
78.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6183 to 5096 computations (17.6% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4995	1728
1	4995	1728

prune997.0ms (1.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	80	4	84

Error

0.2b

Counts

84 → 4

Compiler

Compiled 11297 to 9146 computations (19% saved)

localize113.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
1.0b	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))
2.6b	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))

rewrite8.7s (10.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

96×	`associate-*r/_binary64_2066` `frac-times_binary64_2134`
69×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
64×	`frac-add_binary64_2132`
61×	`flip3--_binary64_2128` `flip--_binary64_2099`
60×	`associate-*l/_binary64_2067`
18×	`pow1_binary64_2185`
15×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
13×	`add-sqr-sqrt_binary64_2146`
11×	`*-un-lft-identity_binary64_2124`
9×	`add-cube-cbrt_binary64_2159`
8×	`pow-prod-down_binary64_2195`
7×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
6×	`add-log-exp_binary64_2163` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-l_binary64_2065` `associate-r_binary64_2064` `cancel-sign-sub-inv_binary64_2090`
2×	`associate-+l+_binary64_2057` `associate-+r+_binary64_2056` `sqrt-pow1_binary64_2142` `*-commutative_binary64_2055` `sub-neg_binary64_2117`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sqrt-prod_binary64_2140` `unswap-sqr_binary64_2092` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`

Counts

4 → 173

Calls

4 calls:

41.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
30.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
18.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 56461 to 46026 computations (18.5% saved)

series646.0ms (0.8%)

Error

0.2b

Counts

4 → 18

Calls

4 calls:

146.0ms	(.f64 (+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))))) (-.f64 3 z))
144.0ms	(+.f64 (.f64 (-.f64 2 z) (+.f64 178405961588143256171617450107358831776190125/178405961588244985132285746181186892047843328 (pow.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) 3))) (.f64 -5537752839100187/4398046511104 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (*.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312)))))
129.0ms	(.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 2 z) (.f64 (-.f64 3 z) -6214088902520669/35184372088832)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 9724 to 7896 computations (18.8% saved)

simplify234.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4903	17581
1	4903	17581

prune7.6s (9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	189	2	191
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	190	5	195

Error

0.2b

Counts

195 → 5

Compiler

Compiled 52664 to 42712 computations (18.9% saved)

regimes4.4s (5.3%)

Accuracy

Total 0.2b remaining (37.4%)

Threshold costs 0.2b (37.4%)

Compiler

Compiled 60180 to 49842 computations (17.2% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	239	508
1	239	508

end15.0ms (0%)

Compiler: Compiled 336 to 280 computations (16.7% saved)

sample46.8s (55.6%)

Algorithm

1×

intervals

Results

42.2s	3856×	body	8192	exit
2.4s	8000×	body	128	valid
198.0ms	11938×	pre	128	true
27.0ms	82×	body	128	invalid

Compiler

Compiled 1633 to 1371 computations (16% saved)

Details

analyze1.9s (2.2%)

sample1.5s (1.8%)

simplify48.0ms (0.1%)

prune17.0ms (0%)

localize57.0ms (0.1%)

rewrite944.0ms (1.1%)

series236.0ms (0.3%)

simplify110.0ms (0.1%)

prune820.0ms (1%)

localize85.0ms (0.1%)

rewrite3.4s (4.1%)

series742.0ms (0.9%)

simplify174.0ms (0.2%)

prune3.2s (3.8%)

localize78.0ms (0.1%)

rewrite835.0ms (1%)

series367.0ms (0.4%)

simplify72.0ms (0.1%)

prune997.0ms (1.2%)

localize113.0ms (0.1%)

rewrite8.7s (10.3%)

series646.0ms (0.8%)

simplify234.0ms (0.3%)

prune7.6s (9%)

regimes4.4s (5.3%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end15.0ms (0%)

sample46.8s (55.6%)

Profiling