Details

analyze1.8s (3%)

Algorithm

1×	search
2×	egg-herbie

Rules

388×	`associate-+l+_binary64`
318×	`exp-sum_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
224×	`associate-r_binary64`
209×	`associate-l_binary64`
206×	`associate-/r/_binary64`
167×	`distribute-rgt-out_binary64`
163×	`exp-diff_binary64`
143×	`sub-neg_binary64`
117×	`+-commutative_binary64`
100×	`distribute-lft-out_binary64`
93×	`distribute-neg-in_binary64`
92×	`div-sub_binary64`
86×	`*-commutative_binary64`
57×	`associate-*r/_binary64`
54×	`associate--l+_binary64` `associate-+r-_binary64`
51×	`associate-*l/_binary64` `associate--l-_binary64`
48×	`associate-+l-_binary64`
36×	`associate--r+_binary64`
32×	`associate-/l/_binary64`
30×	`exp-prod_binary64`
24×	`*-rgt-identity_binary64`
22×	`*-lft-identity_binary64`
21×	`associate-/r*_binary64`
19×	`neg-mul-1_binary64` `neg-sub0_binary64`
15×	`associate--r-_binary64`
12×	`times-frac_binary64` `associate-/l*_binary64`
11×	`sqr-pow_binary64`
9×	`unswap-sqr_binary64`
8×	`rec-exp_binary64` `cancel-sign-sub-inv_binary64`
6×	`pow-sqr_binary64`
4×	`div-exp_binary64` `unsub-neg_binary64`
3×	`--rgt-identity_binary64`
2×	`remove-double-neg_binary64` `distribute-lft-neg-in_binary64`
1×	`unpow3_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-unmult_binary64` `/-rgt-identity_binary64` `sub0-neg_binary64` `+-rgt-identity_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-rgt1-in_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	604	119
3	3400	115
4	4793	115
5	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)

sample1.6s (2.6%)

Algorithm

1×

intervals

Results

1.4s	129×	body	8192	exit
81.0ms	256×	body	128	valid
7.0ms	389×	pre	128	true
1.0ms	4×	body	128	invalid

Compiler

Compiled 249 to 223 computations (10.4% saved)

simplify53.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

388×	`associate-+l+_binary64`
318×	`exp-sum_binary64`
296×	`associate-+r+_binary64`
271×	`distribute-rgt-in_binary64`
266×	`distribute-lft-in_binary64`
224×	`associate-r_binary64`
209×	`associate-l_binary64`
206×	`associate-/r/_binary64`
167×	`distribute-rgt-out_binary64`
163×	`exp-diff_binary64`
143×	`sub-neg_binary64`
117×	`+-commutative_binary64`
100×	`distribute-lft-out_binary64`
93×	`distribute-neg-in_binary64`
92×	`div-sub_binary64`
86×	`*-commutative_binary64`
57×	`associate-*r/_binary64`
54×	`associate--l+_binary64` `associate-+r-_binary64`
51×	`associate-*l/_binary64` `associate--l-_binary64`
48×	`associate-+l-_binary64`
36×	`associate--r+_binary64`
32×	`associate-/l/_binary64`
30×	`exp-prod_binary64`
24×	`*-rgt-identity_binary64`
22×	`*-lft-identity_binary64`
21×	`associate-/r*_binary64`
19×	`neg-mul-1_binary64` `neg-sub0_binary64`
15×	`associate--r-_binary64`
12×	`times-frac_binary64` `associate-/l*_binary64`
11×	`sqr-pow_binary64`
9×	`unswap-sqr_binary64`
8×	`rec-exp_binary64` `cancel-sign-sub-inv_binary64`
6×	`pow-sqr_binary64`
4×	`div-exp_binary64` `unsub-neg_binary64`
3×	`--rgt-identity_binary64`
2×	`remove-double-neg_binary64` `distribute-lft-neg-in_binary64`
1×	`unpow3_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-unmult_binary64` `/-rgt-identity_binary64` `sub0-neg_binary64` `+-rgt-identity_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-rgt1-in_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

1 → 1

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	61	156
1	160	147
2	604	119
3	3400	115
4	4793	115
5	4804	115

prune8.0ms (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)

localize68.0ms (0.1%)

Local error

Found 4 expressions with local error:

6.8b	(-.f64 (-.f64 1 z) 1)
6.8b	(-.f64 (-.f64 1 z) 1)
6.8b	(-.f64 (-.f64 1 z) 1)
6.8b	(-.f64 (-.f64 1 z) 1)

rewrite516.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

1.8b

Rules

36×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64`
16×	`associate--l+_binary64`
12×	`diff-log_binary64` `add-cube-cbrt_binary64` `distribute-lft-out--_binary64`
8×	`sub-neg_binary64` `difference-of-squares_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip3--_binary64` `flip--_binary64` `difference-of-sqr-1_binary64` `associate--l-_binary64`

Counts

4 → 100

Calls

4 calls:

9.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)
8.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 11372 to 9694 computations (14.8% saved)

series100.0ms (0.2%)

Error

1.8b

Counts

4 → 12

Calls

4 calls:

21.0ms	(-.f64 (-.f64 1 z) 1)
21.0ms	(-.f64 (-.f64 1 z) 1)
20.0ms	(-.f64 (-.f64 1 z) 1)
19.0ms	(-.f64 (-.f64 1 z) 1)

Compiler

Compiled 3388 to 3009 computations (11.2% saved)

simplify106.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

547×	`distribute-rgt-in_binary64`
455×	`distribute-lft-in_binary64`
385×	`sub-neg_binary64`
314×	`difference-of-squares_binary64`
305×	`associate-+l+_binary64`
241×	`neg-sub0_binary64`
229×	`neg-mul-1_binary64`
219×	`associate-+r+_binary64`
175×	`sqr-pow_binary64`
138×	`exp-sum_binary64`
137×	`associate-+l-_binary64`
132×	`*-commutative_binary64`
114×	`exp-prod_binary64`
106×	`remove-double-neg_binary64`
105×	`div-sub_binary64` `distribute-lft-neg-out_binary64`
104×	`unswap-sqr_binary64`
102×	`times-frac_binary64`
101×	`distribute-rgt-out_binary64`
100×	`distribute-rgt-neg-out_binary64`
86×	`exp-diff_binary64`
85×	`associate-+r-_binary64`
83×	`cube-prod_binary64`
81×	`associate-l_binary64`
79×	`log-prod_binary64`
78×	`unsub-neg_binary64`
77×	`associate-r_binary64`
65×	`distribute-lft-out_binary64` `associate--l+_binary64`
54×	`cancel-sign-sub-inv_binary64`
47×	`associate--r+_binary64`
44×	`pow-sqr_binary64`
39×	`+-commutative_binary64`
36×	`mul0-rgt_binary64` `mul0-lft_binary64`
33×	`distribute-rgt-neg-in_binary64`
32×	`*-rgt-identity_binary64` `distribute-neg-in_binary64`
29×	`swap-sqr_binary64`
27×	`*-lft-identity_binary64`
26×	`associate--l-_binary64`
25×	`distribute-neg-out_binary64`
20×	`difference-of-sqr--1_binary64`
19×	`pow-plus_binary64` `sub0-neg_binary64` `distribute-lft-neg-in_binary64`
16×	`unpow3_binary64` `sqr-neg_binary64`
15×	`div-exp_binary64`
13×	`/-rgt-identity_binary64`
12×	`mul-1-neg_binary64` `associate--r-_binary64`
10×	`cube-unmult_binary64` `cube-mult_binary64` `cancel-sign-sub_binary64` `associate-/l_binary64` `associate-r/_binary64`
9×	`prod-exp_binary64` `distribute-rgt1-in_binary64`
8×	`cube-neg_binary64` `rem-sqrt-square_binary64` `difference-of-sqr-1_binary64`
7×	`associate-/r_binary64` `associate-l/_binary64`
6×	`rec-exp_binary64` `distribute-lft1-in_binary64`
5×	`exp-neg_binary64`
4×	`log-pow_binary64` `associate-/r/_binary64`
3×	`--rgt-identity_binary64` `+-rgt-identity_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate-/l/_binary64`
2×	`unpow1/2_binary64` `cube-div_binary64` `rem-3cbrt-lft_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-cbrt-cube_binary64` `rem-square-sqrt_binary64` `distribute-frac-neg_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `+-lft-identity_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `distribute-neg-frac_binary64` `count-2_binary64`

Counts

112 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	54	1032
1	107	772
2	209	728
3	775	720
4	3390	704
5	4184	704
6	5392	704

prune238.0ms (0.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

1.8b

Counts

102 → 3

Compiler

Compiled 6196 to 5210 computations (15.9% saved)

localize62.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.9b	(+.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 (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))
2.5b	(+.f64 (+.f64 562949953421205/562949953421312 (/.f64 5950736089418501/8796093022208 (-.f64 1 z))) (/.f64 -5537752839100187/4398046511104 (-.f64 2 z)))

rewrite283.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

24×	`*-un-lft-identity_binary64`
23×	`add-log-exp_binary64`
14×	`frac-add_binary64`
13×	`sum-log_binary64` `distribute-lft-out_binary64`
10×	`add-exp-log_binary64`
9×	`pow1_binary64` `add-cbrt-cube_binary64`
7×	`prod-exp_binary64`
6×	`flip3-+_binary64` `flip-+_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`associate-r_binary64`
3×	`cbrt-unprod_binary64`
2×	`associate-+l+_binary64` `+-commutative_binary64` `pow-prod-down_binary64` `sqrt-pow1_binary64`
1×	`pow1/2_binary64` `sqrt-prod_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `pow-sub_binary64` `associate-r/_binary64` `associate-l/_binary64` `associate-l_binary64` `exp-sum_binary64` `*-commutative_binary64`

Counts

4 → 74

Calls

4 calls:

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)))
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 6199 to 4828 computations (22.1% saved)

series169.0ms (0.3%)

Error

1.1b

Counts

4 → 30

Calls

4 calls:

53.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
29.0ms	(+.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)))
28.0ms	(+.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 4228 to 3404 computations (19.5% saved)

simplify158.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-l_binary64`
359×	`associate-r_binary64`
270×	`*-commutative_binary64`
246×	`cancel-sign-sub-inv_binary64`
158×	`distribute-rgt-in_binary64`
142×	`distribute-lft-in_binary64`
129×	`distribute-lft-out_binary64`
125×	`sub-neg_binary64`
124×	`+-commutative_binary64`
118×	`distribute-rgt-neg-in_binary64`
103×	`associate-+l+_binary64`
99×	`distribute-lft-neg-in_binary64`
84×	`associate-+r+_binary64`
73×	`exp-prod_binary64` `distribute-rgt-out_binary64`
67×	`log-prod_binary64`
65×	`sqr-pow_binary64`
62×	`distribute-neg-in_binary64`
59×	`distribute-lft-neg-out_binary64`
53×	`associate-*r/_binary64`
48×	`prod-exp_binary64`
46×	`neg-mul-1_binary64` `neg-sub0_binary64`
41×	`associate-*l/_binary64`
40×	`distribute-rgt-neg-out_binary64`
39×	`associate--l+_binary64`
35×	`unswap-sqr_binary64`
33×	`distribute-neg-frac_binary64`
27×	`unsub-neg_binary64`
26×	`unpow3_binary64`
25×	`distribute-lft-out--_binary64`
22×	`cube-prod_binary64` `swap-sqr_binary64`
21×	`associate--r+_binary64`
20×	`distribute-rgt-out--_binary64`
16×	`exp-sum_binary64`
13×	`cube-mult_binary64`
12×	`associate-/r*_binary64`
11×	`associate-/l*_binary64`
10×	`div-sub_binary64`
9×	`*-rgt-identity_binary64`
8×	`log-pow_binary64` `*-lft-identity_binary64`
7×	`cube-unmult_binary64` `pow-sqr_binary64` `associate-+r-_binary64`
6×	`cube-div_binary64` `associate-+l-_binary64`
5×	`exp-to-pow_binary64`
4×	`log-div_binary64` `unpow1/2_binary64` `exp-diff_binary64` `rem-log-exp_binary64`
3×	`difference-of-squares_binary64`
2×	`unpow2_binary64` `pow-plus_binary64` `unpow1_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

104 → 82

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	333	4211
1	937	3961
2	3465	3729
3	4906	3729
4	4910	3729

prune173.0ms (0.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	78	7	85

Error

0.3b

Counts

85 → 7

Compiler

Compiled 5990 to 4668 computations (22.1% saved)

localize94.0ms (0.2%)

Local error

Found 4 expressions with local error:

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	(.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 (-.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)))))

rewrite1.0s (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

36×	`frac-times_binary64`
35×	`associate-*r/_binary64`
31×	`associate-*l/_binary64`
24×	`flip3-+_binary64` `flip3--_binary64` `flip-+_binary64` `flip--_binary64`
19×	`add-exp-log_binary64`
18×	`pow1_binary64` `add-cbrt-cube_binary64`
16×	`frac-add_binary64`
13×	`prod-exp_binary64`
9×	`cbrt-unprod_binary64`
8×	`pow-prod-down_binary64`
6×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
5×	`associate-r_binary64`
4×	`associate-l_binary64`
2×	`distribute-rgt-in_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-+r+_binary64` `sqrt-pow1_binary64` `*-commutative_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow1/2_binary64` `sqrt-prod_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `pow-sub_binary64` `exp-sum_binary64`

Counts

4 → 110

Calls

4 calls:

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)))
17.0ms	(.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))

Compiler

Compiled 21043 to 17130 computations (18.6% saved)

series218.0ms (0.4%)

Error

0.3b

Counts

4 → 18

Calls

4 calls:

69.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
35.0ms	(.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)))
34.0ms	(+.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)))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 6610 to 5446 computations (17.6% saved)

simplify254.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

646×	`distribute-rgt-in_binary64`
630×	`distribute-lft-in_binary64`
211×	`*-commutative_binary64`
119×	`associate-r_binary64`
80×	`associate-l_binary64`
64×	`+-commutative_binary64`
59×	`cancel-sign-sub-inv_binary64`
43×	`distribute-rgt-neg-in_binary64`
42×	`exp-sum_binary64`
38×	`sub-neg_binary64`
37×	`exp-prod_binary64`
36×	`distribute-lft-neg-in_binary64`
32×	`sqr-pow_binary64` `associate-*r/_binary64`
29×	`associate-*l/_binary64`
24×	`neg-mul-1_binary64` `neg-sub0_binary64` `swap-sqr_binary64`
22×	`log-prod_binary64`
20×	`associate-+r+_binary64`
19×	`distribute-neg-in_binary64` `distribute-rgt-out_binary64`
18×	`prod-exp_binary64`
16×	`unpow3_binary64`
11×	`cube-prod_binary64`
10×	`cube-unmult_binary64` `cube-mult_binary64`
7×	`distribute-lft-neg-out_binary64`
6×	`distribute-rgt-out--_binary64`
5×	`log-pow_binary64` `exp-diff_binary64` `unswap-sqr_binary64`
4×	`log-div_binary64`
3×	`unpow1/2_binary64` `cube-div_binary64` `pow-sqr_binary64` `distribute-neg-frac_binary64` `associate--l+_binary64` `associate-+r-_binary64`
2×	`unpow2_binary64` `unpow1_binary64` `unsub-neg_binary64` `*-rgt-identity_binary64` `associate--r+_binary64` `associate-+l+_binary64`
1×	`exp-to-pow_binary64` `div-exp_binary64` `1-exp_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/l*_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-plus_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/r*_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

128 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	449	8499
1	1492	7946
2	4897	7946
3	4933	7946

prune685.0ms (1.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	96	4	100
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	99	8	107

Error

0.3b

Counts

107 → 8

Compiler

Compiled 18717 to 15209 computations (18.7% saved)

localize106.0ms (0.2%)

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 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 -6214088902520669/35184372088832 (-.f64 27 (pow.f64 z 3))))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.f64 3 z)))))
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)))))

rewrite1.0s (1.7%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

55×	`associate-*r/_binary64`
42×	`add-exp-log_binary64`
41×	`add-cbrt-cube_binary64`
40×	`frac-times_binary64`
30×	`flip3-+_binary64` `flip-+_binary64`
26×	`associate-/l/_binary64`
24×	`flip3--_binary64` `flip--_binary64`
23×	`prod-exp_binary64`
19×	`cbrt-unprod_binary64`
16×	`frac-add_binary64`
15×	`associate-*l/_binary64`
9×	`pow1_binary64`
8×	`div-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64`
6×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
4×	`associate-r_binary64`
2×	`distribute-rgt-in_binary64` `associate-+l+_binary64` `distribute-lft-in_binary64` `associate-+r+_binary64` `pow-prod-down_binary64` `sqrt-pow1_binary64`
1×	`sum-log_binary64` `+-commutative_binary64` `pow1/2_binary64` `sqrt-prod_binary64` `frac-2neg_binary64` `times-frac_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/l_binary64` `associate-/r_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `pow-sub_binary64` `associate-l_binary64` `exp-sum_binary64` `*-commutative_binary64`

Counts

4 → 126

Calls

4 calls:

39.0ms	(/.f64 (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 -6214088902520669/35184372088832 (-.f64 27 (pow.f64 z 3))))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.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)))))
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 27893 to 22146 computations (20.6% saved)

series225.0ms (0.4%)

Error

0.3b

Counts

4 → 18

Calls

4 calls:

70.0ms	(.f64 (.f64 (sqrt.f64 (*.f64 PI.f64 2)) (pow.f64 (-.f64 15/2 z) (-.f64 1/2 z))) (exp.f64 (+.f64 z -15/2)))
36.0ms	(+.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)))))
36.0ms	(/.f64 (.f64 (+.f64 316912650056936879084143652025/316912650057057350374175801344 (.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) (+.f64 (/.f64 5950736089418501/8796093022208 (-.f64 1 z)) -562949953421205/562949953421312))) (.f64 (-.f64 4 (.f64 z z)) (.f64 -6214088902520669/35184372088832 (-.f64 27 (pow.f64 z 3))))) (.f64 (+.f64 2 z) (+.f64 (.f64 3 3) (+.f64 (.f64 z z) (*.f64 3 z)))))
0.0ms	(sqrt.f64 (*.f64 PI.f64 2))

Compiler

Compiled 7150 to 5814 computations (18.7% saved)

simplify321.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

499×	`times-frac_binary64`
253×	`+-commutative_binary64`
221×	`associate-/l*_binary64`
216×	`sub-neg_binary64`
214×	`*-commutative_binary64`
192×	`associate-/r*_binary64`
112×	`associate-l_binary64`
109×	`associate-r_binary64`
102×	`associate-+r+_binary64`
93×	`associate-+l+_binary64`
90×	`neg-mul-1_binary64` `neg-sub0_binary64`
73×	`log-div_binary64`
70×	`cube-prod_binary64`
62×	`cancel-sign-sub-inv_binary64` `associate-*r/_binary64`
61×	`exp-sum_binary64` `cube-div_binary64` `associate-*l/_binary64`
59×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64`
57×	`unpow3_binary64`
56×	`log-prod_binary64`
53×	`cube-mult_binary64` `distribute-rgt-neg-in_binary64`
52×	`div-sub_binary64`
48×	`exp-prod_binary64`
45×	`distribute-lft-neg-in_binary64`
36×	`unsub-neg_binary64` `associate--l+_binary64`
34×	`distribute-neg-in_binary64` `associate--r+_binary64`
33×	`sqr-pow_binary64`
30×	`swap-sqr_binary64`
24×	`prod-exp_binary64` `distribute-rgt-out_binary64`
22×	`associate-/r/_binary64`
18×	`cube-unmult_binary64`
8×	`exp-diff_binary64` `distribute-lft-neg-out_binary64` `associate-+r-_binary64`
7×	`log-pow_binary64`
6×	`unswap-sqr_binary64` `distribute-rgt-out--_binary64`
5×	`rem-log-exp_binary64` `associate-+l-_binary64`
4×	`pow-sqr_binary64`
3×	`unpow1/2_binary64` `div-exp_binary64` `rem-sqrt-square_binary64` `distribute-neg-frac_binary64` `associate-/l/_binary64`
2×	`unpow2_binary64` `exp-to-pow_binary64` `unpow1_binary64` `rem-exp-log_binary64` `*-rgt-identity_binary64`
1×	`pow-plus_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

144 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	508	10372
1	1843	8971
2	4603	8971
3	4556	8969
4	5083	8969

prune1.0s (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	125	8	133

Error

0.3b

Counts

133 → 8

Compiler

Compiled 21248 to 16935 computations (20.3% saved)

regimes3.1s (5.1%)

Accuracy

Total 0.2b remaining (37.5%)

Threshold costs 0.2b (37.5%)

Compiler

Compiled 64716 to 54376 computations (16% saved)

bsearch0.0ms (0%)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`*-commutative_binary64` `+-commutative_binary64`
11×	`sub-neg_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	78	252
1	121	252
2	134	252
3	136	252
4	137	252
5	136	252

end4.0ms (0%)

Compiler: Compiled 165 to 138 computations (16.4% saved)

sample47.3s (77.9%)

Algorithm

1×

intervals

Results

42.6s	3817×	body	8192	exit
2.5s	8000×	body	128	valid
222.0ms	11915×	pre	128	true
33.0ms	98×	body	128	invalid

Compiler

Compiled 1599 to 1354 computations (15.3% saved)

Details

analyze1.8s (3%)

sample1.6s (2.6%)

simplify53.0ms (0.1%)

prune8.0ms (0%)

localize68.0ms (0.1%)

rewrite516.0ms (0.9%)

series100.0ms (0.2%)

simplify106.0ms (0.2%)

prune238.0ms (0.4%)

localize62.0ms (0.1%)

rewrite283.0ms (0.5%)

series169.0ms (0.3%)

simplify158.0ms (0.3%)

prune173.0ms (0.3%)

localize94.0ms (0.2%)

rewrite1.0s (1.7%)

series218.0ms (0.4%)

simplify254.0ms (0.4%)

prune685.0ms (1.1%)

localize106.0ms (0.2%)

rewrite1.0s (1.7%)

series225.0ms (0.4%)

simplify321.0ms (0.5%)

prune1.0s (1.7%)

regimes3.1s (5.1%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end4.0ms (0%)

sample47.3s (77.9%)

Profiling