Details

analyze1.8s (3%)

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

Symmetry

Compiler

Compiled 126 to 112 computations (11.1% saved)

sample1.5s (2.4%)

Algorithm

1×

intervals

Results

1.4s	124×	body	8192	exit
73.0ms	256×	body	128	valid
7.0ms	380×	pre	128	true

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify52.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4804	115
1	4804	115

prune8.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.8b

Counts

2 → 1

Compiler

Compiled 148 to 122 computations (17.6% saved)

localize58.0ms (0.1%)

Local error

Found 4 expressions with local error:

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	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 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)))

rewrite454.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

1.1b

Rules

19×	`*-un-lft-identity_binary64_2806`
18×	`add-log-exp_binary64_2845`
10×	`add-exp-log_binary64_2844`
9×	`sum-log_binary64_2897` `pow1_binary64_2867` `add-cbrt-cube_binary64_2842` `distribute-lft-out_binary64_2757`
8×	`frac-add_binary64_2814`
7×	`prod-exp_binary64_2855`
5×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `flip3-+_binary64_2809` `flip-+_binary64_2780`
4×	`associate-r_binary64_2746`
3×	`cbrt-unprod_binary64_2839`
2×	`associate-+l+_binary64_2739` `+-commutative_binary64_2736` `pow-prod-down_binary64_2877` `sqrt-pow1_binary64_2824`
1×	`pow1/2_binary64_2886` `sqrt-prod_binary64_2822` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `pow-sub_binary64_2882` `associate-r/_binary64_2748` `associate-l/_binary64_2749` `associate-l_binary64_2747` `exp-sum_binary64_2852` `*-commutative_binary64_2737`

Counts

4 → 70

Calls

4 calls:

38.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
22.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
16.0ms	(.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))

Compiler

Compiled 6200 to 4800 computations (22.6% saved)

series356.0ms (0.6%)

Error

1.1b

Counts

4 → 20

Calls

4 calls:

191.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
51.0ms	(+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
38.0ms	(+.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 3676 to 2954 computations (19.6% saved)

simplify63.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5563	2799

prune520.0ms (0.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	5	91

Error

1.1b

Counts

91 → 5

Compiler

Compiled 7849 to 6052 computations (22.9% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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	(+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
1.0b	(sqrt.f64 (*.f64 PI.f64 2))

rewrite896.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

49×	`*-un-lft-identity_binary64_2806`
48×	`add-log-exp_binary64_2845`
34×	`sum-log_binary64_2897` `distribute-lft-out_binary64_2757`
32×	`frac-add_binary64_2814`
10×	`add-exp-log_binary64_2844`
9×	`pow1_binary64_2867` `add-cbrt-cube_binary64_2842`
8×	`flip3-+_binary64_2809` `flip-+_binary64_2780`
7×	`prod-exp_binary64_2855`
5×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828`
4×	`associate-r_binary64_2746`
3×	`cbrt-unprod_binary64_2839`
2×	`pow-prod-down_binary64_2877` `sqrt-pow1_binary64_2824` `associate-+l+_binary64_2739` `+-commutative_binary64_2736`
1×	`pow1/2_binary64_2886` `sqrt-prod_binary64_2822` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `pow-sub_binary64_2882` `associate-r/_binary64_2748` `associate-l/_binary64_2749` `associate-l_binary64_2747` `exp-sum_binary64_2852` `*-commutative_binary64_2737`

Counts

4 → 86

Calls

4 calls:

105.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
16.0ms	(.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))

Compiler

Compiled 9783 to 7705 computations (21.2% saved)

series411.0ms (0.7%)

Error

0.3b

Counts

4 → 24

Calls

4 calls:

192.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
90.0ms	(+.f64 (+.f64 (+.f64 (+.f64 (+.f64 (+.f64 562949953421205/562949953421312 (+.f64 (/.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 562949953421205/562949953421312 (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))) (/.f64 848079078717083/1099511627776 (-.f64 3 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3624 to 2888 computations (20.3% saved)

simplify111.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4957	7930
1	4957	7930

prune844.0ms (1.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	108	7	115

Error

0.3b

Counts

115 → 7

Compiler

Compiled 11329 to 8839 computations (22% saved)

localize30.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite222.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-exp-log_binary64_2844`
16×	`add-cbrt-cube_binary64_2842`
15×	`add-sqr-sqrt_binary64_2828`
14×	`pow1_binary64_2867` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
10×	`prod-exp_binary64_2855`
9×	`times-frac_binary64_2812`
7×	`associate-r_binary64_2746`
6×	`cbrt-unprod_binary64_2839`
5×	`pow-prod-down_binary64_2877`
4×	`add-log-exp_binary64_2845`
3×	`associate-/l_binary64_2751` `associate-/r_binary64_2750`
2×	`sqrt-pow1_binary64_2824` `associate-l_binary64_2747` `*-commutative_binary64_2737`
1×	`pow1/2_binary64_2886` `sqrt-prod_binary64_2822` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `pow-sub_binary64_2882` `associate-r/_binary64_2748` `associate-l/_binary64_2749` `exp-sum_binary64_2852` `unswap-sqr_binary64_2774` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 78

Calls

4 calls:

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)))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
3.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
2.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 3848 to 2484 computations (35.4% saved)

series487.0ms (0.8%)

Error

0.2b

Counts

4 → 12

Calls

4 calls:

228.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
181.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
46.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 1811 to 1419 computations (21.6% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4951	1669
1	4951	1669

prune235.0ms (0.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	3	2	5
Picked	1	0	1
Done	0	1	1
Total	84	13	97

Error

0.0b

Counts

97 → 13

Compiler

Compiled 4947 to 3288 computations (33.5% saved)

localize31.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
0.4b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
1.0b	(.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2))
1.0b	(sqrt.f64 (*.f64 2 PI.f64))

rewrite225.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

20×	`add-cbrt-cube_binary64_2842`
18×	`add-exp-log_binary64_2844`
17×	`pow1_binary64_2867`
15×	`add-sqr-sqrt_binary64_2828` `prod-exp_binary64_2855`
14×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
9×	`cbrt-unprod_binary64_2839` `times-frac_binary64_2812`
7×	`pow-prod-down_binary64_2877`
6×	`associate-r_binary64_2746`
4×	`add-log-exp_binary64_2845`
3×	`associate-l/_binary64_2749` `associate-/l_binary64_2751` `associate-/r*_binary64_2750`
2×	`sqrt-pow1_binary64_2824` `associate-l_binary64_2747` `*-commutative_binary64_2737`
1×	`pow1/2_binary64_2886` `sqrt-prod_binary64_2822` `pow-to-exp_binary64_2875` `pow-exp_binary64_2874` `pow-sub_binary64_2882` `unswap-sqr_binary64_2774` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 80

Calls

4 calls:

17.0ms	(.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2))
6.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
4.0ms	(sqrt.f64 (*.f64 2 PI.f64))
3.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))

Compiler

Compiled 4052 to 2565 computations (36.7% saved)

series297.0ms (0.5%)

Error

0.0b

Counts

4 → 12

Calls

4 calls:

194.0ms	(.f64 (.f64 (.f64 (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z)) (sqrt.f64 (.f64 2 PI.f64))) (exp.f64 z)) (exp.f64 -15/2))
40.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
35.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 2 PI.f64))

Compiler

Compiled 1837 to 1437 computations (21.8% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4929	1713
1	4929	1713

prune208.0ms (0.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	1	92
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	92	13	105

Error

0.0b

Counts

105 → 13

Compiler

Compiled 4384 to 2810 computations (35.9% saved)

regimes702.0ms (1.2%)

Accuracy

Total 0.4b remaining (91.7%)

Threshold costs 0.4b (91.7%)

Compiler

Compiled 10570 to 8448 computations (20.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	115
1	104	115

Removed

()

end0.0ms (0%)

sample50.7s (83.9%)

Algorithm

1×

intervals

Results

43.7s	3967×	body	8192	exit
2.4s	8000×	body	128	valid
233.0ms	12058×	pre	128	true
28.0ms	91×	body	128	invalid

Compiler

Compiled 5361 to 4287 computations (20% saved)

Details

analyze1.8s (3%)

sample1.5s (2.4%)

simplify52.0ms (0.1%)

prune8.0ms (0%)

localize58.0ms (0.1%)

rewrite454.0ms (0.8%)

series356.0ms (0.6%)

simplify63.0ms (0.1%)

prune520.0ms (0.9%)

localize59.0ms (0.1%)

rewrite896.0ms (1.5%)

series411.0ms (0.7%)

simplify111.0ms (0.2%)

prune844.0ms (1.4%)

localize30.0ms (0%)

rewrite222.0ms (0.4%)

series487.0ms (0.8%)

simplify81.0ms (0.1%)

prune235.0ms (0.4%)

localize31.0ms (0.1%)

rewrite225.0ms (0.4%)

series297.0ms (0.5%)

simplify85.0ms (0.1%)

prune208.0ms (0.3%)

regimes702.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample50.7s (83.9%)

Profiling