Details

analyze1.7s (1.8%)

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
10.0ms	368×	pre	128	true
2.0ms	5×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify217.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4776	115
1	4776	115

prune20.0ms (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)

localize61.0ms (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)

rewrite71.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_3175`
28×	`add-sqr-sqrt_binary64_3197`
24×	`cancel-sign-sub-inv_binary64_3141` `add-log-exp_binary64_3214`
16×	`associate--l+_binary64_3112`
12×	`diff-log_binary64_3267` `add-cube-cbrt_binary64_3210` `distribute-lft-out--_binary64_3127`
8×	`sub-neg_binary64_3168` `difference-of-squares_binary64_3144`
4×	`flip--_binary64_3150` `difference-of-sqr-1_binary64_3145` `flip3--_binary64_3179` `associate--l-_binary64_3113` `add-cbrt-cube_binary64_3211` `add-exp-log_binary64_3213` `pow1_binary64_3236`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)
9.0ms	(-.f64 (-.f64 1 z) 1)

series72.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

19.0ms	(-.f64 (-.f64 1 z) 1)
19.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)
17.0ms	(-.f64 (-.f64 1 z) 1)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4806	704
1	4806	704

prune1.3s (1.3%)

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 14626 to 12379 computations (15.4% saved)

localize57.0ms (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)))

rewrite178.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64_3175`
44×	`frac-add_binary64_3183` `add-log-exp_binary64_3214`
31×	`distribute-lft-out_binary64_3126` `sum-log_binary64_3266`
10×	`add-exp-log_binary64_3213`
9×	`flip-+_binary64_3149` `add-cbrt-cube_binary64_3211` `flip3-+_binary64_3178` `pow1_binary64_3236`
7×	`prod-exp_binary64_3224`
5×	`add-cube-cbrt_binary64_3210` `add-sqr-sqrt_binary64_3197`
4×	`associate-r_binary64_3115`
3×	`cbrt-unprod_binary64_3208`
2×	`pow-prod-down_binary64_3246` `sqrt-pow1_binary64_3193` `associate-+l+_binary64_3108` `+-commutative_binary64_3105`
1×	`associate-r/_binary64_3117` `pow-exp_binary64_3243` `-commutative_binary64_3106` `exp-sum_binary64_3221` `pow-to-exp_binary64_3244` `associate-l_binary64_3116` `pow1/2_binary64_3255` `associate-*l/_binary64_3118` `pow-sub_binary64_3251` `sqrt-prod_binary64_3191`

Counts

4 → 86

Calls

4 calls:

102.0ms	(+.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)))
24.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series311.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

186.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
94.0ms	(+.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)))
31.0ms	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify111.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (44.0ms)

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 22008 to 17834 computations (19% saved)

localize103.0ms (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))))

rewrite166.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_3175` `add-log-exp_binary64_3214`
12×	`distribute-lft-out_binary64_3126` `sum-log_binary64_3266`
8×	`frac-add_binary64_3183` `flip-+_binary64_3149` `flip3-+_binary64_3178`
4×	`associate-+r+_binary64_3107` `add-cbrt-cube_binary64_3211` `add-cube-cbrt_binary64_3210` `+-commutative_binary64_3105` `add-sqr-sqrt_binary64_3197` `add-exp-log_binary64_3213` `pow1_binary64_3236`

Counts

4 → 68

Calls

4 calls:

30.0ms	(+.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))))
26.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

series150.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
40.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
38.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))
32.0ms	(+.f64 (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)) (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))))

simplify76.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5020	2204

prune3.7s (3.7%)

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 32625 to 26950 computations (17.4% saved)

localize36.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
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))

rewrite43.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-exp-log_binary64_3213`
16×	`add-cbrt-cube_binary64_3211`
15×	`add-sqr-sqrt_binary64_3197`
14×	`*-un-lft-identity_binary64_3175` `add-cube-cbrt_binary64_3210` `pow1_binary64_3236`
10×	`prod-exp_binary64_3224`
9×	`times-frac_binary64_3181`
7×	`associate-r_binary64_3115`
6×	`cbrt-unprod_binary64_3208`
5×	`pow-prod-down_binary64_3246`
4×	`add-log-exp_binary64_3214`
3×	`associate-/l_binary64_3120` `associate-/r_binary64_3119`
2×	`-commutative_binary64_3106` `sqrt-pow1_binary64_3193` `associate-l*_binary64_3116`
1×	`associate-r/_binary64_3117` `pow-exp_binary64_3243` `clear-num_binary64_3174` `div-inv_binary64_3172` `frac-2neg_binary64_3186` `exp-sum_binary64_3221` `pow-to-exp_binary64_3244` `cbrt-undiv_binary64_3209` `unswap-sqr_binary64_3143` `pow1/2_binary64_3255` `associate-l/_binary64_3118` `pow-sub_binary64_3251` `sqrt-prod_binary64_3191` `div-exp_binary64_3226`

Counts

4 → 78

Calls

4 calls:

19.0ms	(.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 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
4.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
3.0ms	(sqrt.f64 (*.f64 PI.f64 2))

series296.0ms (0.3%)

Counts

4 → 10

Calls

4 calls:

206.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
55.0ms	(/.f64 PI.f64 (sin.f64 (*.f64 PI.f64 z)))
35.0ms	(.f64 (.f64 z z) 2533639962396748701166118939/4648579506574807007232000)
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5054	1673

prune1.2s (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	8	88
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

Compiler

Compiled 24665 to 18994 computations (23% saved)

regimes96.0ms (0.1%)

Compiler: Compiled 969 to 769 computations (20.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	69
1	61	69

end0.0ms (0%)

sample1.4min (86.2%)

Algorithm

1×

intervals

Results

1.3min	3873×	body	8192	exit
2.6s	8000×	body	128	valid
244.0ms	11974×	pre	128	true
34.0ms	101×	body	128	invalid

Compiler

Compiled 1136 to 914 computations (19.5% saved)

Details

analyze1.7s (1.8%)

sample2.4s (2.4%)

simplify217.0ms (0.2%)

prune20.0ms (0%)

localize61.0ms (0.1%)

rewrite71.0ms (0.1%)

series72.0ms (0.1%)

simplify71.0ms (0.1%)

prune1.3s (1.3%)

localize57.0ms (0.1%)

rewrite178.0ms (0.2%)

series311.0ms (0.3%)

simplify111.0ms (0.1%)

prune1.2s (1.2%)

localize103.0ms (0.1%)

rewrite166.0ms (0.2%)

series150.0ms (0.2%)

simplify76.0ms (0.1%)

prune3.7s (3.7%)

localize36.0ms (0%)

rewrite43.0ms (0%)

series296.0ms (0.3%)

simplify68.0ms (0.1%)

prune1.2s (1.2%)

regimes96.0ms (0.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4min (86.2%)

Profiling