Details

analyze3.6s (2.9%)

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)

sample2.8s (2.3%)

Algorithm

1×

intervals

Results

2.6s	116×	body	8192	exit
154.0ms	256×	body	128	valid
11.0ms	372×	pre	128	true

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify259.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune23.0ms (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)

localize116.0ms (0.1%)

Local error

Found 4 expressions with local error:

7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)
7.0b	(-.f64 (-.f64 1 z) 1)

rewrite1.9s (1.5%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64_1783`
28×	`add-sqr-sqrt_binary64_1805`
24×	`add-log-exp_binary64_1822` `cancel-sign-sub-inv_binary64_1749`
16×	`associate--l+_binary64_1720`
12×	`diff-log_binary64_1875` `add-cube-cbrt_binary64_1818` `distribute-lft-out--_binary64_1735`
8×	`sub-neg_binary64_1776` `difference-of-squares_binary64_1752`
4×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `flip3--_binary64_1787` `flip--_binary64_1758` `difference-of-sqr-1_binary64_1753` `associate--l-_binary64_1721`

Counts

4 → 100

Calls

4 calls:

23.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)
15.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 12896 to 10998 computations (14.7% saved)

series408.0ms (0.3%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

75.0ms	(-.f64 (-.f64 1 z) 1)
75.0ms	(-.f64 (-.f64 1 z) 1)
73.0ms	(-.f64 (-.f64 1 z) 1)
72.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 4356 to 3833 computations (12% saved)

simplify142.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5392	704

prune2.3s (1.9%)

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

Error

1.8b

Counts

114 → 2

Compiler

Compiled 13990 to 11821 computations (15.5% saved)

localize112.0ms (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)))

rewrite1.6s (1.3%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

45×	`*-un-lft-identity_binary64_1783`
44×	`add-log-exp_binary64_1822` `frac-add_binary64_1791`
31×	`sum-log_binary64_1874` `distribute-lft-out_binary64_1734`
10×	`add-exp-log_binary64_1821`
9×	`pow1_binary64_1844` `add-cbrt-cube_binary64_1819` `flip3-+_binary64_1786` `flip-+_binary64_1757`
7×	`prod-exp_binary64_1832`
5×	`add-cube-cbrt_binary64_1818` `add-sqr-sqrt_binary64_1805`
4×	`associate-r_binary64_1723`
3×	`cbrt-unprod_binary64_1816`
2×	`associate-+l+_binary64_1716` `+-commutative_binary64_1713` `pow-prod-down_binary64_1854` `sqrt-pow1_binary64_1801`
1×	`pow1/2_binary64_1863` `sqrt-prod_binary64_1799` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `pow-sub_binary64_1859` `associate-r/_binary64_1725` `associate-l/_binary64_1726` `associate-l_binary64_1724` `exp-sum_binary64_1829` `*-commutative_binary64_1714`

Counts

4 → 86

Calls

4 calls:

186.0ms	(+.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)))
43.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
31.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
4.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 10066 to 7936 computations (21.2% saved)

series731.0ms (0.6%)

Error

0.3b

Counts

4 → 22

Calls

4 calls:

361.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
170.0ms	(+.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)))
67.0ms	(+.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 3444 to 2750 computations (20.2% saved)

simplify177.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5189	8306

prune1.5s (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Error

0.2b

Counts

110 → 5

Compiler

Compiled 11605 to 9071 computations (21.8% saved)

localize66.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 PI.f64 z)
0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 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))

rewrite397.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64_1805`
15×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
14×	`add-exp-log_binary64_1821`
13×	`add-cbrt-cube_binary64_1819`
11×	`pow1_binary64_1844`
9×	`times-frac_binary64_1789`
8×	`prod-exp_binary64_1832`
7×	`associate-r_binary64_1723`
4×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
3×	`pow-prod-down_binary64_1854` `associate-/l_binary64_1728` `associate-/r_binary64_1727`
2×	`sqrt-pow1_binary64_1801` `*-commutative_binary64_1714`
1×	`pow1/2_binary64_1863` `sqrt-prod_binary64_1799` `pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `pow-sub_binary64_1859` `associate-r/_binary64_1725` `associate-l/_binary64_1726` `exp-sum_binary64_1829` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `div-inv_binary64_1780` `unswap-sqr_binary64_1751`

Counts

4 → 77

Calls

4 calls:

32.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
7.0ms	(*.f64 PI.f64 z)
7.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
4.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3790 to 2463 computations (35% saved)

series519.0ms (0.4%)

Error

0.1b

Counts

4 → 12

Calls

4 calls:

331.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
78.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
52.0ms	(*.f64 PI.f64 z)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1811 to 1407 computations (22.3% saved)

simplify207.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (169.0ms)

Iter	Nodes	Cost
0	4947	1639
1	4947	1639

prune451.0ms (0.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	81	13	94

Error

0.0b

Counts

94 → 13

Compiler

Compiled 5169 to 3491 computations (32.5% saved)

localize127.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
1.0b	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))

rewrite1.2s (1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

26×	`add-sqr-sqrt_binary64_1805`
19×	`add-exp-log_binary64_1821`
16×	`sqrt-prod_binary64_1799`
12×	`add-cube-cbrt_binary64_1818` `-un-lft-identity_binary64_1783` `associate-l*_binary64_1724`
11×	`add-cbrt-cube_binary64_1819`
10×	`prod-exp_binary64_1832` `associate-r_binary64_1723`
9×	`pow1_binary64_1844`
8×	`unswap-sqr_binary64_1751`
6×	`unpow-prod-down_binary64_1862`
4×	`add-log-exp_binary64_1822` `cbrt-unprod_binary64_1816`
3×	`unpow2_binary64_1848` `sqr-pow_binary64_1755`
2×	`pow-to-exp_binary64_1852` `pow-exp_binary64_1851` `*-commutative_binary64_1714` `pow1/2_binary64_1863` `sqrt-pow1_binary64_1801` `rem-sqrt-square_binary64_1796`
1×	`pow-prod-down_binary64_1854` `log-pow_binary64_1872`

Counts

4 → 83

Calls

4 calls:

22.0ms	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))
18.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
3.0ms	(sqrt.f64 PI.f64)
3.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 9652 to 7528 computations (22% saved)

series1.0ms (0%)

Error

0.0b

Counts

4 → 0

Calls

4 calls:

0.0ms	(.f64 (sqrt.f64 15/2) (.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(*.f64 (sqrt.f64 2) (pow.f64 (log.f64 15/2) 2))
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 0 to 0 computations (0% saved)

simplify128.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5087	1014

prune1.1s (0.9%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	83	13	96

Error

0.0b

Counts

96 → 13

Compiler

Compiled 9467 to 7359 computations (22.3% saved)

regimes1.9s (1.6%)

Accuracy

Total 0.4b remaining (96.5%)

Threshold costs 0.4b (96.5%)

Compiler

Compiled 12140 to 9776 computations (19.5% saved)

bsearch0.0ms (0%)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	113	133
1	113	133

end0.0ms (0%)

sample1.7min (82.3%)

Algorithm

1×

intervals

Results

1.4min	3938×	body	8192	exit
4.7s	8000×	body	128	valid
376.0ms	12030×	pre	128	true
59.0ms	92×	body	128	invalid

Compiler

Compiled 6155 to 4960 computations (19.4% saved)

Details

analyze3.6s (2.9%)

sample2.8s (2.3%)

simplify259.0ms (0.2%)

prune23.0ms (0%)

localize116.0ms (0.1%)

rewrite1.9s (1.5%)

series408.0ms (0.3%)

simplify142.0ms (0.1%)

prune2.3s (1.9%)

localize112.0ms (0.1%)

rewrite1.6s (1.3%)

series731.0ms (0.6%)

simplify177.0ms (0.1%)

prune1.5s (1.2%)

localize66.0ms (0.1%)

rewrite397.0ms (0.3%)

series519.0ms (0.4%)

simplify207.0ms (0.2%)

prune451.0ms (0.4%)

localize127.0ms (0.1%)

rewrite1.2s (1%)

series1.0ms (0%)

simplify128.0ms (0.1%)

prune1.1s (0.9%)

regimes1.9s (1.6%)

bsearch0.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample1.7min (82.3%)

Profiling