Details

analyze1.1s (4.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

872×	`unswap-sqr_binary64`
470×	`distribute-rgt-in_binary64`
438×	`distribute-lft-in_binary64`
368×	`*-commutative_binary64`
320×	`associate-l_binary64`
272×	`unsub-neg_binary64`
236×	`associate-r_binary64`
186×	`difference-of-squares_binary64` `distribute-rgt-neg-in_binary64`
170×	`associate-/l/_binary64`
162×	`cancel-sign-sub-inv_binary64`
158×	`distribute-lft-neg-in_binary64`
122×	`neg-sub0_binary64` `associate-/r/_binary64`
114×	`neg-mul-1_binary64`
92×	`sub-neg_binary64` `sqr-pow_binary64`
88×	`associate-+r+_binary64`
72×	`associate-/l*_binary64`
62×	`associate-+l+_binary64`
60×	`distribute-lft-neg-out_binary64`
56×	`pow-sqr_binary64`
54×	`associate-/r*_binary64`
50×	`associate-*r/_binary64`
42×	`mul0-rgt_binary64` `mul0-lft_binary64`
40×	`distribute-rgt-neg-out_binary64`
38×	`associate-*l/_binary64`
34×	`+-commutative_binary64`
24×	`pow-plus_binary64`
22×	`associate-+l-_binary64`
20×	`distribute-neg-in_binary64` `associate--r+_binary64`
18×	`+-lft-identity_binary64`
16×	`cube-unmult_binary64` `cube-prod_binary64` `remove-double-neg_binary64`
14×	`associate-+r-_binary64`
12×	`sub0-neg_binary64` `+-rgt-identity_binary64`
6×	`*-lft-identity_binary64`
4×	`unpow3_binary64` `unpow2_binary64` `cube-mult_binary64` `--rgt-identity_binary64` `distribute-rgt-out_binary64` `distribute-lft-out_binary64`
2×	`associate--r-_binary64` `associate--l+_binary64`
1×	`1-exp_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` `unpow1/2_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` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_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` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_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` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	38
1	33	38
2	72	38
3	179	38
4	435	38
5	1405	38
6	3508	38
7	5242	38
0	2	2
1	2	2

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	62.4%	12.6%	5
25%	56.2%	18.8%	6
28.1%	50%	22%	7
28.1%	46.8%	25.1%	8
29.7%	41.4%	29%	9
29.7%	39.4%	30.9%	10
31.1%	35.8%	33.1%	11
31.1%	34.4%	34.5%	12
31.5%	32.9%	35.6%	13
31.5%	32.1%	36.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample225.0ms (0.8%)

Algorithm

1×

intervals

Results

57.0ms	93×	body	1024	valid
39.0ms	50×	body	1024	nan
35.0ms	58×	body	2048	valid
18.0ms	31×	body	512	nan
16.0ms	87×	body	128	overflowed
14.0ms	36×	body	512	valid
6.0ms	12×	body	512	invalid
5.0ms	55×	body	128	valid
4.0ms	17×	body	256	nan
4.0ms	4×	body	1024	invalid
3.0ms	14×	body	256	valid
2.0ms	6×	body	256	invalid
1.0ms	10×	body	128	invalid
1.0ms	19×	body	128	nan

Compiler

Compiled 27 to 25 computations (7.4% saved)

simplify50.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

673×	`distribute-rgt-neg-in_binary64`
436×	`unswap-sqr_binary64`
309×	`*-commutative_binary64`
248×	`sub-neg_binary64`
235×	`distribute-rgt-in_binary64` `associate-/l/_binary64`
234×	`unsub-neg_binary64`
228×	`associate-/r/_binary64`
219×	`distribute-lft-in_binary64`
205×	`distribute-lft-neg-out_binary64`
204×	`distribute-lft-neg-in_binary64`
196×	`distribute-rgt-neg-out_binary64`
181×	`neg-sub0_binary64`
177×	`neg-mul-1_binary64`
176×	`cancel-sign-sub_binary64`
166×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
118×	`associate-r_binary64`
93×	`difference-of-squares_binary64`
86×	`distribute-neg-out_binary64` `+-commutative_binary64`
83×	`distribute-neg-in_binary64`
73×	`associate-/l*_binary64`
72×	`sqr-pow_binary64`
70×	`associate--r+_binary64`
69×	`associate-*r/_binary64`
66×	`associate-+l-_binary64`
64×	`associate-/r*_binary64`
52×	`sub0-neg_binary64` `associate-*l/_binary64`
44×	`associate-+r+_binary64`
42×	`associate--l+_binary64`
40×	`pow-sqr_binary64` `associate-+r-_binary64`
31×	`associate-+l+_binary64`
26×	`cube-prod_binary64`
23×	`swap-sqr_binary64`
22×	`remove-double-neg_binary64` `--rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
20×	`pow-plus_binary64` `+-lft-identity_binary64`
16×	`+-rgt-identity_binary64`
13×	`cube-unmult_binary64`
8×	`distribute-rgt-out_binary64`
6×	`*-lft-identity_binary64`
4×	`unpow3_binary64` `unpow2_binary64` `cube-mult_binary64` `distribute-lft-out_binary64` `associate--r-_binary64`
2×	`unpow1_binary64`
1×	`1-exp_binary64` `*-rgt-identity_binary64` `distribute-rgt-out--_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-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_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` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_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` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	19
1	20	19
2	40	19
3	96	19
4	228	19
5	723	19
6	1798	19
7	3290	19
8	4831	19

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

30.0b

Counts

1 → 1

Compiler

Compiled 13 to 11 computations (15.4% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(pow.f64 (+.f64 x 1) (/.f64 1 n))
0.0b	(pow.f64 x (/.f64 1 n))
1.3b	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))

rewrite204.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

30.0b

Rules

33×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
26×	`pow-unpow_binary64`
21×	`add-cube-cbrt_binary64`
20×	`unpow-prod-down_binary64`
18×	`times-frac_binary64`
9×	`difference-of-squares_binary64` `sqr-pow_binary64`
7×	`cancel-sign-sub-inv_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64`
3×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `div-inv_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64`

Counts

3 → 85

Calls

3 calls:

10.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
8.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))
3.0ms	(pow.f64 x (/.f64 1 n))

Compiler

Compiled 1801 to 1292 computations (28.3% saved)

series176.0ms (0.6%)

Error

1.0b

Counts

3 → 42

Calls

3 calls:

69.0ms	(-.f64 (pow.f64 (+.f64 x 1) (/.f64 1 n)) (pow.f64 x (/.f64 1 n)))
31.0ms	(pow.f64 x (/.f64 1 n))
27.0ms	(pow.f64 (+.f64 x 1) (/.f64 1 n))

Compiler

Compiled 2478 to 1948 computations (21.4% saved)

simplify126.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

721×	`times-frac_binary64`
379×	`associate-/l*_binary64`
237×	`cancel-sign-sub-inv_binary64`
159×	`sub-neg_binary64`
151×	`sqr-pow_binary64`
124×	`unswap-sqr_binary64`
120×	`associate-/l/_binary64`
109×	`+-commutative_binary64`
107×	`exp-prod_binary64`
105×	`distribute-rgt-in_binary64`
83×	`distribute-lft-in_binary64`
82×	`associate-/r*_binary64`
69×	`associate-+r+_binary64`
68×	`associate-r_binary64`
66×	`associate-+l+_binary64`
64×	`distribute-rgt-neg-in_binary64` `*-commutative_binary64`
62×	`pow-sqr_binary64`
61×	`distribute-neg-in_binary64`
55×	`distribute-lft-neg-in_binary64`
54×	`associate-l_binary64`
48×	`neg-mul-1_binary64` `neg-sub0_binary64` `associate-/r/_binary64`
43×	`log-prod_binary64` `associate--l+_binary64`
34×	`associate--r+_binary64`
32×	`log-pow_binary64` `distribute-neg-frac_binary64` `associate-*r/_binary64`
29×	`associate-*l/_binary64`
27×	`swap-sqr_binary64`
26×	`unsub-neg_binary64`
24×	`unpow3_binary64` `cube-prod_binary64` `distribute-rgt-out_binary64`
22×	`difference-of-squares_binary64`
20×	`distribute-lft-neg-out_binary64`
12×	`pow-plus_binary64` `cube-unmult_binary64`
11×	`associate-+r-_binary64`
10×	`exp-to-pow_binary64` `cube-mult_binary64` `distribute-rgt-out--_binary64`
9×	`distribute-rgt-neg-out_binary64`
8×	`div-sub_binary64` `distribute-lft-out_binary64`
7×	`log-div_binary64` `exp-sum_binary64`
6×	`exp-diff_binary64` `rem-sqrt-square_binary64`
5×	`unpow1/2_binary64` `unpow1_binary64` `mul-1-neg_binary64` `*-rgt-identity_binary64`
4×	`unpow2_binary64` `pow-base-1_binary64` `*-lft-identity_binary64` `+-rgt-identity_binary64` `count-2_binary64`
3×	`log-rec_binary64` `/-rgt-identity_binary64`
2×	`div-exp_binary64` `exp-neg_binary64` `remove-double-neg_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `+-inverses_binary64` `associate--r-_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` `pow-base-0_binary64` `unpow1/3_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_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-neg-out_binary64` `distribute-lft1-in_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

127 → 103

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	3251
1	656	3108
2	1907	2839
3	4871	2827
4	4988	2827

prune110.0ms (0.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Error

1.0b

Counts

104 → 6

Compiler

Compiled 2017 to 1387 computations (31.2% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.7b	(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))
6.6b	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
9.8b	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
12.5b	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))

rewrite723.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

Rules

91×	`add-log-exp_binary64`
52×	`sum-log_binary64`
36×	`frac-add_binary64`
28×	`flip3-+_binary64` `flip-+_binary64`
24×	`frac-sub_binary64`
20×	`associate-*r/_binary64`
17×	`add-exp-log_binary64`
16×	`diff-log_binary64` `*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `times-frac_binary64` `associate-/l*_binary64`
8×	`unpow-prod-down_binary64`
6×	`pow1_binary64` `associate-+r-_binary64` `div-exp_binary64`
4×	`cancel-sign-sub-inv_binary64` `log-div_binary64` `div-sub_binary64` `associate-+l-_binary64`
3×	`prod-exp_binary64`
2×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64` `associate--l-_binary64` `+-commutative_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `unpow2_binary64` `sqr-pow_binary64`
1×	`flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+r+_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `associate-/r*_binary64`

Counts

4 → 124

Calls

4 calls:

59.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
15.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
10.0ms	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
7.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))

Compiler

Compiled 19454 to 12754 computations (34.4% saved)

series805.0ms (3%)

Error

0.2b

Counts

4 → 51

Calls

4 calls:

277.0ms	(-.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (.f64 n n))) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (/.f64 (pow.f64 (log.f64 x) 2) (.f64 n n))) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4))))))
223.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 4)) (+.f64 (/.f64 (log.f64 (+.f64 1 x)) n) (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 1 x)) n) 3))))
143.0ms	(+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)) (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)))
53.0ms	(/.f64 (pow.f64 (log.f64 (+.f64 1 x)) 2) (*.f64 n n))

Compiler

Compiled 9991 to 7560 computations (24.3% saved)

simplify358.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

687×	`distribute-rgt-in_binary64`
368×	`times-frac_binary64`
197×	`*-commutative_binary64`
170×	`sub-neg_binary64`
168×	`cancel-sign-sub-inv_binary64`
155×	`+-commutative_binary64`
122×	`distribute-neg-in_binary64`
118×	`distribute-rgt-neg-in_binary64`
100×	`associate-+r+_binary64`
88×	`sqr-pow_binary64`
84×	`neg-mul-1_binary64` `neg-sub0_binary64`
81×	`distribute-lft-neg-in_binary64`
54×	`distribute-lft-in_binary64` `associate-*r/_binary64`
51×	`associate-l_binary64` `associate-r_binary64`
40×	`associate-/r*_binary64`
39×	`distribute-lft-neg-out_binary64`
37×	`unswap-sqr_binary64`
25×	`unpow3_binary64` `associate--r+_binary64`
24×	`cube-mult_binary64`
21×	`div-sub_binary64`
20×	`associate-/l*_binary64`
19×	`cube-prod_binary64` `distribute-rgt-out_binary64` `associate--l+_binary64`
17×	`swap-sqr_binary64`
14×	`unpow2_binary64` `distribute-frac-neg_binary64`
12×	`exp-prod_binary64`
11×	`unpow1_binary64`
10×	`prod-exp_binary64` `cube-div_binary64`
8×	`difference-of-squares_binary64` `distribute-neg-frac_binary64` `distribute-rgt-out--_binary64`
7×	`distribute-rgt-neg-out_binary64`
6×	`log-prod_binary64` `exp-sum_binary64` `pow-sqr_binary64` `associate-+r-_binary64`
5×	`div-exp_binary64`
4×	`log-div_binary64`
3×	`cube-unmult_binary64` `mul-1-neg_binary64` `distribute-lft-out_binary64` `associate-*l/_binary64`
2×	`log-pow_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `unsub-neg_binary64` `distribute-lft-out--_binary64` `associate-+l-_binary64`
1×	`log-rec_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-diff_binary64` `1-exp_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_binary64` `*-lft-identity_binary64` `distribute-rgt1-in_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` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_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` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `/-rgt-identity_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-neg-out_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

175 → 159

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	698	25083
1	2404	22541
2	5343	22541

prune483.0ms (1.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	154	5	159
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	154	11	165

Error

0.2b

Counts

165 → 11

Compiler

Compiled 17355 to 11525 computations (33.6% saved)

localize73.0ms (0.3%)

Local error

Found 4 expressions with local error:

9.8b	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))
12.5b	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
12.5b	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
12.5b	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))

rewrite1.4s (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

249×	`add-log-exp_binary64`
147×	`sum-log_binary64`
48×	`diff-log_binary64`
28×	`flip3-+_binary64` `flip-+_binary64` `*-un-lft-identity_binary64`
24×	`frac-sub_binary64`
18×	`associate-+r-_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`frac-add_binary64` `cancel-sign-sub-inv_binary64`
7×	`add-cube-cbrt_binary64`
6×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64` `log-div_binary64` `div-sub_binary64` `associate--l-_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `associate--r+_binary64`
1×	`associate-+r+_binary64` `+-commutative_binary64`

Counts

4 → 148

Calls

4 calls:

60.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
58.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
56.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
15.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))

Compiler

Compiled 42036 to 28222 computations (32.9% saved)

series1.7s (6.1%)

Error

0.1b

Counts

4 → 67

Calls

4 calls:

342.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
341.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
339.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
230.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))

Compiler

Compiled 30931 to 22295 computations (27.9% saved)

simplify490.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

317×	`distribute-rgt-in_binary64`
301×	`distribute-lft-in_binary64`
300×	`associate-/r*_binary64`
268×	`times-frac_binary64`
235×	`associate-l_binary64`
155×	`associate-/l*_binary64`
126×	`*-commutative_binary64`
122×	`associate-*r/_binary64`
111×	`+-commutative_binary64`
105×	`sub-neg_binary64`
101×	`associate-*l/_binary64`
80×	`cancel-sign-sub-inv_binary64`
76×	`associate-+r+_binary64`
70×	`sqr-pow_binary64` `distribute-neg-in_binary64`
45×	`neg-mul-1_binary64` `neg-sub0_binary64`
43×	`distribute-rgt-neg-in_binary64`
25×	`distribute-lft-neg-in_binary64`
19×	`div-sub_binary64`
18×	`unpow3_binary64` `cube-mult_binary64` `distribute-lft-neg-out_binary64`
17×	`associate--r+_binary64`
16×	`unswap-sqr_binary64` `associate-r_binary64`
15×	`associate--l+_binary64`
14×	`distribute-frac-neg_binary64`
13×	`distribute-rgt-out_binary64`
12×	`exp-prod_binary64`
10×	`prod-exp_binary64`
9×	`unpow2_binary64` `unpow1_binary64`
8×	`cube-prod_binary64`
7×	`swap-sqr_binary64` `distribute-rgt-neg-out_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
6×	`exp-sum_binary64` `difference-of-squares_binary64`
5×	`div-exp_binary64`
4×	`distribute-rgt-out--_binary64` `associate-+r-_binary64`
3×	`mul-1-neg_binary64` `distribute-neg-frac_binary64`
2×	`log-div_binary64` `log-prod_binary64` `cube-div_binary64` `unsub-neg_binary64` `*-rgt-identity_binary64` `distribute-rgt1-in_binary64`
1×	`log-rec_binary64` `exp-diff_binary64` `1-exp_binary64` `cube-unmult_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `pow-sqr_binary64` `distribute-lft-out--_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-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_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` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_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-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+l-_binary64`

Counts

215 → 199

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	470	34661
1	1506	33081
2	4878	33081

prune1.7s (6.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	196	3	199
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	198	12	210

Error

0.1b

Counts

210 → 12

Compiler

Compiled 37856 to 25308 computations (33.1% saved)

localize71.0ms (0.3%)

Local error

Found 4 expressions with local error:

9.8b	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))
10.8b	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))))
12.5b	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
12.5b	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))

rewrite2.2s (7.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

205×	`add-log-exp_binary64`
117×	`sum-log_binary64`
41×	`diff-log_binary64`
36×	`flip3-+_binary64` `flip-+_binary64`
35×	`*-un-lft-identity_binary64`
32×	`frac-sub_binary64`
24×	`frac-add_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`cancel-sign-sub-inv_binary64` `associate-+r-_binary64`
9×	`distribute-lft-out_binary64`
8×	`distribute-lft-out--_binary64`
7×	`add-cube-cbrt_binary64`
6×	`log-div_binary64` `div-sub_binary64` `associate--l-_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `associate--r+_binary64`
2×	`associate-+l-_binary64`
1×	`associate-+r+_binary64` `+-commutative_binary64`

Counts

4 → 151

Calls

4 calls:

62.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
56.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
39.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))))
16.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))

Compiler

Compiled 40470 to 27098 computations (33% saved)

series1.6s (5.8%)

Error

0.1b

Counts

4 → 64

Calls

4 calls:

334.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
334.0ms	(-.f64 (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 4)) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (/.f64 (log.f64 (+.f64 x 1)) n)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))))
322.0ms	(-.f64 (+.f64 (/.f64 (log.f64 (+.f64 x 1)) n) (+.f64 (.f64 1/6 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 3)) (.f64 1/2 (pow.f64 (/.f64 (log.f64 (+.f64 x 1)) n) 2)))) (+.f64 (/.f64 (log.f64 x) n) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3)))))
222.0ms	(+.f64 (.f64 1/24 (pow.f64 (/.f64 (log.f64 x) n) 4)) (+.f64 (.f64 1/2 (pow.f64 (/.f64 (log.f64 x) n) 2)) (*.f64 1/6 (pow.f64 (/.f64 (log.f64 x) n) 3))))

Compiler

Compiled 27698 to 19931 computations (28% saved)

simplify491.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

733×	`distribute-rgt-in_binary64`
299×	`times-frac_binary64`
202×	`cancel-sign-sub-inv_binary64` `*-commutative_binary64`
194×	`sub-neg_binary64`
166×	`+-commutative_binary64`
123×	`distribute-neg-in_binary64`
122×	`distribute-rgt-neg-in_binary64`
111×	`associate-+r+_binary64`
90×	`neg-mul-1_binary64`
89×	`neg-sub0_binary64`
85×	`sqr-pow_binary64`
79×	`distribute-lft-neg-in_binary64`
59×	`distribute-lft-in_binary64`
53×	`associate-*r/_binary64`
44×	`distribute-lft-neg-out_binary64`
39×	`associate-r_binary64`
38×	`associate-/r*_binary64`
29×	`associate--r+_binary64`
27×	`unpow3_binary64` `cube-mult_binary64` `associate-l_binary64`
25×	`distribute-rgt-out_binary64`
24×	`associate--l+_binary64`
21×	`cube-prod_binary64` `div-sub_binary64`
20×	`swap-sqr_binary64`
16×	`unswap-sqr_binary64`
14×	`prod-exp_binary64` `distribute-frac-neg_binary64` `associate-/l*_binary64`
13×	`difference-of-squares_binary64`
12×	`exp-prod_binary64`
11×	`distribute-rgt-out--_binary64`
10×	`div-exp_binary64` `exp-sum_binary64` `cube-div_binary64`
9×	`unpow2_binary64` `unpow1_binary64` `distribute-neg-frac_binary64`
8×	`distribute-rgt-neg-out_binary64` `associate-+r-_binary64`
5×	`unsub-neg_binary64` `associate-*l/_binary64`
4×	`mul-1-neg_binary64`
3×	`pow-sqr_binary64` `distribute-lft-out_binary64`
2×	`log-div_binary64` `log-prod_binary64` `exp-diff_binary64` `cube-unmult_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `*-rgt-identity_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64` `associate-+l-_binary64` `associate-+l+_binary64`
1×	`log-rec_binary64` `1-exp_binary64` `cube-neg_binary64` `sqr-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-pow_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_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` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-sqrt-square_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-neg-out_binary64` `distribute-lft1-in_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

215 → 198

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	687	34130
1	2447	32445
2	5308	32445

prune1.0s (3.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	1	9	10
Picked	0	1	1
Done	0	1	1
Total	198	12	210

Error

0.1b

Counts

210 → 12

Compiler

Compiled 35218 to 23426 computations (33.5% saved)

regimes4.6s (16.9%)

Accuracy

Total 11.1b remaining (96.5%)

Threshold costs 0b (0%)

Compiler

Compiled 98976 to 68800 computations (30.5% saved)

bsearch30.0ms (0.1%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

simplify12.0ms (0%)

Algorithm

1×	egg-herbie

Rules

21×	`+-commutative_binary64`
17×	`*-commutative_binary64`
13×	`sub-neg_binary64`
10×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-neg-in_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`
2×	`unsub-neg_binary64` `cancel-sign-sub-inv_binary64` `distribute-neg-frac_binary64`
1×	`1-exp_binary64` `+-lft-identity_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` `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` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	73	224
1	100	224
2	123	224
3	145	224
4	160	224
5	169	224
6	173	224
7	174	224
8	171	224

end4.0ms (0%)

Compiler: Compiled 147 to 108 computations (26.5% saved)

sample7.5s (27.6%)

Algorithm

1×

intervals

Results

1.6s	2681×	body	1024	valid
1.1s	1465×	body	1024	nan
1.1s	1773×	body	2048	valid
513.0ms	2648×	body	128	overflowed
446.0ms	1212×	body	512	valid
337.0ms	733×	body	512	nan
175.0ms	192×	body	1024	invalid
174.0ms	1758×	body	128	valid
128.0ms	576×	body	256	valid
124.0ms	244×	body	512	invalid
99.0ms	388×	body	256	nan
54.0ms	803×	body	128	nan
41.0ms	149×	body	256	invalid
34.0ms	263×	body	128	invalid
3.0ms	3×	body	2048	nan

Compiler

Compiled 1588 to 1129 computations (28.9% saved)

Iter	Nodes	Cost
0	73	224
1	100	224
2	123	224
3	145	224
4	160	224
5	169	224
6	173	224
7	174	224
8	171	224

Iter	Nodes	Cost
0	73	224
1	100	224
2	123	224
3	145	224
4	160	224
5	169	224
6	173	224
7	174	224
8	171	224

Details

analyze1.1s (4.2%)

sample225.0ms (0.8%)

simplify50.0ms (0.2%)

prune1.0ms (0%)

localize7.0ms (0%)

rewrite204.0ms (0.7%)

series176.0ms (0.6%)

simplify126.0ms (0.5%)

prune110.0ms (0.4%)

localize44.0ms (0.2%)

rewrite723.0ms (2.7%)

series805.0ms (3%)

simplify358.0ms (1.3%)

prune483.0ms (1.8%)

localize73.0ms (0.3%)

rewrite1.4s (5.2%)

series1.7s (6.1%)

simplify490.0ms (1.8%)

prune1.7s (6.1%)

localize71.0ms (0.3%)

rewrite2.2s (7.9%)

series1.6s (5.8%)

simplify491.0ms (1.8%)

prune1.0s (3.7%)

regimes4.6s (16.9%)

bsearch30.0ms (0.1%)

simplify12.0ms (0%)

end4.0ms (0%)

sample7.5s (27.6%)

Profiling

Iter	Nodes	Cost
0	73	224
1	100	224
2	123	224
3	145	224
4	160	224
5	169	224
6	173	224
7	174	224
8	171	224