Details

analyze28.0ms (0.5%)

Algorithm

1×	search
2×	egg-herbie

Rules

8×	`sub-neg_binary64`
5×	`+-commutative_binary64`
3×	`sub0-neg_binary64` `associate--r+_binary64` `associate-+l-_binary64` `*-commutative_binary64`
2×	`neg-mul-1_binary64` `--rgt-identity_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
1×	`1-exp_binary64` `neg-sub0_binary64` `associate-l/_binary64` `associate-r/_binary64` `associate--l+_binary64` `associate-+l+_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` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_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` `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-unmult_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` `times-frac_binary64` `div-sub_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_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` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_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` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l_binary64` `associate-r*_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+r-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	32	15
4	38	15
5	46	15
6	53	15
7	61	15
8	64	15
9	45	15
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

Compiler

Compiled 13 to 13 computations (0% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	72×	body	2048	valid
5.0ms	31×	body	1024	valid
5.0ms	130×	body	128	valid
2.0ms	15×	body	512	valid
1.0ms	8×	body	256	valid

Compiler

Compiled 25 to 26 computations (-4% saved)

simplify11.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

8×	`sub-neg_binary64`
5×	`+-commutative_binary64`
3×	`sub0-neg_binary64` `associate--r+_binary64` `associate-+l-_binary64` `*-commutative_binary64`
2×	`neg-mul-1_binary64` `--rgt-identity_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64`
1×	`1-exp_binary64` `neg-sub0_binary64` `associate-l/_binary64` `associate-r/_binary64` `associate--l+_binary64` `associate-+l+_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` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_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` `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-unmult_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` `times-frac_binary64` `div-sub_binary64` `unsub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_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` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_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` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l_binary64` `associate-r*_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+r-_binary64`

Counts

1 → 1

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	18
1	22	15
2	27	15
3	32	15
4	38	15
5	46	15
6	53	15
7	61	15
8	64	15
9	45	15

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

14.7b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
2.0b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite127.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

14.7b

Rules

25×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`
9×	`times-frac_binary64`
7×	`cancel-sign-sub-inv_binary64`
5×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`pow1_binary64` `difference-of-squares_binary64`
3×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`sqrt-div_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

3 → 68

Calls

3 calls:

11.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 1141 to 1035 computations (9.3% saved)

series39.0ms (0.7%)

Error

14.7b

Counts

3 → 9

Calls

3 calls:

14.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
13.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
10.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 226 to 225 computations (0.4% saved)

simplify130.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

950×	`unsub-neg_binary64`
585×	`times-frac_binary64`
366×	`neg-mul-1_binary64`
355×	`neg-sub0_binary64`
253×	`cancel-sign-sub-inv_binary64`
226×	`distribute-neg-out_binary64`
214×	`distribute-rgt-in_binary64`
189×	`*-commutative_binary64`
182×	`distribute-lft-in_binary64`
179×	`distribute-rgt-neg-out_binary64`
176×	`distribute-lft-neg-out_binary64`
151×	`sub-neg_binary64`
134×	`associate-/l*_binary64`
133×	`distribute-rgt-neg-in_binary64`
129×	`associate-l_binary64`
111×	`associate-r_binary64`
110×	`div-sub_binary64`
106×	`distribute-lft-neg-in_binary64`
93×	`associate-/r*_binary64`
80×	`exp-prod_binary64` `sqr-pow_binary64`
68×	`log-prod_binary64`
66×	`associate-+l+_binary64`
58×	`associate-/l/_binary64`
53×	`associate-*l/_binary64`
52×	`distribute-neg-in_binary64`
51×	`+-commutative_binary64`
50×	`distribute-rgt-out--_binary64`
46×	`unswap-sqr_binary64`
43×	`associate-+r+_binary64`
38×	`associate-/r/_binary64` `associate-*r/_binary64`
36×	`cube-prod_binary64`
32×	`*-lft-identity_binary64` `distribute-rgt-out_binary64`
31×	`rem-sqrt-square_binary64`
30×	`*-rgt-identity_binary64` `associate-+l-_binary64`
28×	`distribute-neg-frac_binary64`
27×	`exp-sum_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `distribute-rgt1-in_binary64`
24×	`cancel-sign-sub_binary64`
21×	`unpow3_binary64` `sub0-neg_binary64`
18×	`pow-sqr_binary64`
16×	`cube-unmult_binary64` `swap-sqr_binary64`
14×	`log-div_binary64` `distribute-lft-out_binary64` `associate--r+_binary64`
13×	`pow-plus_binary64` `exp-diff_binary64` `/-rgt-identity_binary64` `difference-of-squares_binary64`
11×	`associate-+r-_binary64`
9×	`cube-div_binary64`
8×	`sqr-neg_binary64` `distribute-lft1-in_binary64`
6×	`+-rgt-identity_binary64` `difference-of-sqr-1_binary64`
5×	`log-pow_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64` `distribute-frac-neg_binary64` `associate--l+_binary64`
4×	`unpow1/2_binary64` `difference-of-sqr--1_binary64`
3×	`exp-neg_binary64` `cube-mult_binary64` `cube-neg_binary64`
2×	`log-rec_binary64` `rem-square-sqrt_binary64` `div0_binary64` `count-2_binary64`
1×	`unpow2_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `remove-double-neg_binary64` `+-lft-identity_binary64` `remove-double-div_binary64` `distribute-lft-out--_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` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `rec-exp_binary64` `prod-exp_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` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

77 → 37

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	118	1302
1	210	1265
2	437	1262
3	1155	1262
4	2272	1244
5	3652	1244
6	4954	1244
7	4828	1244

prune25.0ms (0.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	2	38

Error

14.2b

Counts

38 → 2

Compiler

Compiled 375 to 342 computations (8.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
1.5b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite227.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Error

14.2b

Rules

84×	`*-un-lft-identity_binary64`
83×	`add-sqr-sqrt_binary64`
53×	`times-frac_binary64`
33×	`distribute-lft-out_binary64`
26×	`add-cube-cbrt_binary64`
20×	`sqrt-prod_binary64`
16×	`difference-of-squares_binary64`
13×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `flip--_binary64` `div-inv_binary64` `sqrt-div_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sum-log_binary64` `+-commutative_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64`

Counts

4 → 122

Calls

4 calls:

18.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))

Compiler

Compiled 3096 to 2789 computations (9.9% saved)

series76.0ms (1.3%)

Error

14.2b

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))) (+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))))
15.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
14.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
12.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 574 to 543 computations (5.4% saved)

simplify179.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

478×	`div-sub_binary64`
306×	`associate-l_binary64`
291×	`associate-r_binary64`
259×	`associate-/l*_binary64`
246×	`associate-*l/_binary64`
203×	`exp-prod_binary64`
189×	`associate-*r/_binary64`
173×	`distribute-rgt-in_binary64`
170×	`sub-neg_binary64`
159×	`distribute-lft-in_binary64`
137×	`associate-/l/_binary64`
134×	`*-commutative_binary64`
113×	`associate-/r*_binary64`
100×	`times-frac_binary64`
94×	`distribute-neg-frac_binary64`
87×	`neg-sub0_binary64`
85×	`unsub-neg_binary64`
80×	`neg-mul-1_binary64`
67×	`cancel-sign-sub-inv_binary64` `associate-/r/_binary64`
62×	`distribute-rgt-neg-in_binary64`
60×	`associate-+l+_binary64` `+-commutative_binary64`
54×	`cube-prod_binary64`
52×	`unpow3_binary64`
51×	`associate-+r+_binary64`
41×	`distribute-lft-neg-in_binary64`
31×	`exp-sum_binary64`
30×	`distribute-lft-neg-out_binary64`
24×	`exp-diff_binary64`
23×	`cube-div_binary64` `distribute-rgt-neg-out_binary64`
17×	`associate-+l-_binary64`
16×	`sqr-pow_binary64`
15×	`distribute-rgt-out_binary64`
14×	`*-rgt-identity_binary64`
13×	`distribute-frac-neg_binary64`
12×	`*-lft-identity_binary64`
11×	`cube-unmult_binary64` `associate-+r-_binary64`
10×	`/-rgt-identity_binary64`
9×	`unpow1/2_binary64` `pow-plus_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64`
8×	`associate--r+_binary64`
7×	`log-prod_binary64` `associate--l+_binary64`
6×	`swap-sqr_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out_binary64`
4×	`cube-mult_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `unswap-sqr_binary64`
3×	`associate--r-_binary64`
2×	`log-div_binary64` `exp-sqrt_binary64` `rem-3cbrt-lft_binary64` `div0_binary64`
1×	`div-exp_binary64` `prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `+-rgt-identity_binary64` `*-inverses_binary64` `remove-double-div_binary64` `distribute-lft1-in_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` `log-rec_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` `rec-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `mul-1-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `pow-sqr_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `count-2_binary64`

Counts

134 → 79

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	186	3874
1	448	3705
2	1175	3696
3	3625	3696
4	4902	3694
5	4977	3694

prune42.0ms (0.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	79	2	81

Error

14.2b

Counts

81 → 2

Compiler

Compiled 808 to 726 computations (10.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.8b	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
30.6b	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))

rewrite355.0ms (6.2%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

107×	`add-sqr-sqrt_binary64`
76×	`*-un-lft-identity_binary64`
70×	`times-frac_binary64`
51×	`sqrt-prod_binary64`
50×	`unpow-prod-down_binary64`
44×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64`
20×	`cancel-sign-sub-inv_binary64`
10×	`distribute-lft-out_binary64`
9×	`associate-/l*_binary64`
8×	`sqr-pow_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`div-inv_binary64` `associate-/r*_binary64`
3×	`pow-unpow_binary64` `pow-pow_binary64`
2×	`flip3--_binary64` `flip--_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sqrt-pow2_binary64` `sqrt-div_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `flip3-+_binary64` `flip-+_binary64`

Counts

4 → 161

Calls

4 calls:

23.0ms	(/.f64 (-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
11.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
5.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 5753 to 5204 computations (9.5% saved)

series113.0ms (2%)

Error

14.2b

Counts

4 → 12

Calls

4 calls:

40.0ms	(/.f64 (-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)) (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
25.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
25.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
17.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))

Compiler

Compiled 858 to 802 computations (6.5% saved)

simplify213.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

348×	`associate-/l*_binary64`
280×	`associate-*l/_binary64`
215×	`associate-*r/_binary64`
203×	`exp-prod_binary64`
186×	`times-frac_binary64` `distribute-rgt-in_binary64`
183×	`associate-/r*_binary64`
180×	`distribute-lft-in_binary64`
170×	`associate-/l/_binary64`
140×	`cancel-sign-sub-inv_binary64` `distribute-rgt-neg-in_binary64`
130×	`distribute-lft-neg-in_binary64`
117×	`log-prod_binary64` `sqr-pow_binary64`
108×	`cube-prod_binary64`
92×	`unswap-sqr_binary64`
91×	`log-div_binary64`
89×	`cube-div_binary64`
88×	`associate-/r/_binary64`
79×	`neg-mul-1_binary64`
78×	`associate-r_binary64`
75×	`neg-sub0_binary64`
68×	`distribute-neg-frac_binary64`
67×	`sub-neg_binary64`
61×	`associate-l_binary64`
60×	`*-commutative_binary64`
51×	`div-sub_binary64`
38×	`distribute-lft-neg-out_binary64`
36×	`log-pow_binary64`
34×	`distribute-rgt-neg-out_binary64`
33×	`swap-sqr_binary64`
27×	`unpow1/2_binary64`
24×	`unpow2_binary64` `unpow1_binary64` `exp-sum_binary64` `distribute-rgt-out_binary64`
21×	`+-commutative_binary64`
20×	`pow-plus_binary64`
19×	`unpow3_binary64`
18×	`rem-square-sqrt_binary64`
17×	`cube-unmult_binary64`
15×	`cube-mult_binary64` `*-rgt-identity_binary64`
12×	`/-rgt-identity_binary64` `distribute-lft-out_binary64`
11×	`exp-diff_binary64` `mul-1-neg_binary64` `pow-sqr_binary64`
9×	`distribute-rgt1-in_binary64`
8×	`rem-sqrt-square_binary64`
6×	`distribute-neg-in_binary64`
4×	`distribute-rgt-out--_binary64`
3×	`sqr-abs_binary64` `unsub-neg_binary64` `*-lft-identity_binary64`
2×	`log-rec_binary64` `exp-neg_binary64` `distribute-frac-neg_binary64` `associate--r+_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`div-exp_binary64` `1-exp_binary64` `rem-3cbrt-lft_binary64` `remove-double-neg_binary64` `*-inverses_binary64` `cancel-sign-sub_binary64` `count-2_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` `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` `prod-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `sub0-neg_binary64` `--rgt-identity_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` `difference-of-squares_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

173 → 140

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	256	5265
1	567	4594
2	1500	4244
3	4109	4216
4	4985	4216
5	4895	4216

prune148.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	139	3	142

Error

14.0b

Counts

142 → 3

Compiler

Compiled 3098 to 2786 computations (10.1% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.8b	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
1.5b	(-.f64 1/4 (/.f64 1/4 (pow.f64 (hypot.f64 1 x) 2)))
30.6b	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
30.6b	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))

rewrite669.0ms (11.6%)

Algorithm

1×	rewrite-expression-head

Error

13.9b

Rules

78×	`add-sqr-sqrt_binary64`
68×	`cancel-sign-sub-inv_binary64`
64×	`unpow-prod-down_binary64`
57×	`times-frac_binary64`
52×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
43×	`sqrt-prod_binary64`
15×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
9×	`sqr-pow_binary64`
6×	`pow1_binary64`
5×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64` `div-inv_binary64` `unpow2_binary64`
3×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `pow-unpow_binary64` `pow-pow_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sqrt-pow2_binary64`

Counts

4 → 152

Calls

4 calls:

13.0ms	(-.f64 1/4 (/.f64 1/4 (pow.f64 (hypot.f64 1 x) 2)))
12.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
12.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
5.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)

Compiler

Compiled 9299 to 8459 computations (9% saved)

series120.0ms (2.1%)

Error

14.0b

Counts

4 → 12

Calls

4 calls:

30.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
29.0ms	(pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4)
29.0ms	(-.f64 1/4 (pow.f64 (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))) 4))
23.0ms	(-.f64 1/4 (/.f64 1/4 (pow.f64 (hypot.f64 1 x) 2)))

Compiler

Compiled 1485 to 1375 computations (7.4% saved)

simplify147.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

447×	`associate-*l/_binary64`
365×	`times-frac_binary64`
323×	`associate-/l*_binary64`
319×	`associate-/r*_binary64`
198×	`exp-prod_binary64`
172×	`distribute-rgt-neg-in_binary64`
156×	`cancel-sign-sub-inv_binary64`
147×	`distribute-lft-neg-in_binary64`
132×	`associate-/l/_binary64`
125×	`sqr-pow_binary64`
123×	`neg-sub0_binary64`
119×	`neg-mul-1_binary64`
109×	`*-commutative_binary64`
102×	`distribute-neg-frac_binary64`
94×	`distribute-lft-neg-out_binary64`
90×	`unswap-sqr_binary64`
85×	`distribute-rgt-in_binary64`
81×	`associate-r_binary64`
77×	`sub-neg_binary64`
75×	`distribute-rgt-neg-out_binary64` `distribute-lft-in_binary64`
74×	`cube-div_binary64`
69×	`log-prod_binary64`
68×	`associate-r/_binary64` `associate-l*_binary64`
55×	`log-div_binary64`
53×	`associate-/r/_binary64`
38×	`div-sub_binary64`
34×	`+-commutative_binary64`
32×	`exp-sum_binary64` `distribute-frac-neg_binary64`
30×	`cube-unmult_binary64`
27×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64`
22×	`log-pow_binary64` `pow-plus_binary64`
20×	`rem-square-sqrt_binary64`
18×	`exp-diff_binary64` `cube-prod_binary64`
17×	`swap-sqr_binary64`
16×	`unpow3_binary64`
14×	`pow-sqr_binary64`
13×	`distribute-rgt-out_binary64`
12×	`cube-mult_binary64`
10×	`rem-sqrt-square_binary64` `mul-1-neg_binary64`
8×	`*-rgt-identity_binary64`
7×	`exp-neg_binary64`
6×	`*-lft-identity_binary64`
5×	`/-rgt-identity_binary64` `distribute-rgt1-in_binary64`
4×	`div0_binary64` `distribute-lft-out_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
3×	`rem-3cbrt-lft_binary64` `sqr-abs_binary64` `unsub-neg_binary64`
2×	`div-exp_binary64`
1×	`log-rec_binary64` `1-exp_binary64` `rem-3cbrt-rft_binary64` `distribute-lft1-in_binary64` `count-2_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` `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` `prod-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_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` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64`

Counts

164 → 152

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	3865
1	678	3183
2	1662	2753
3	4365	2673
4	4914	2673

prune181.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	152	3	155

Error

13.9b

Counts

155 → 3

Compiler

Compiled 4472 to 4056 computations (9.3% saved)

regimes1.4s (25%)

Accuracy

Total 0.3b remaining (1.7%)

Threshold costs 0.3b (1.7%)

Compiler

Compiled 25434 to 23916 computations (6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`sub-neg_binary64` `*-commutative_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	20	65
1	28	65
2	32	65
3	34	65
4	35	65
5	33	65

end2.0ms (0%)

Compiler: Compiled 42 to 39 computations (7.1% saved)

sample1.4s (23.9%)

Algorithm

1×

intervals

Results

520.0ms	2089×	body	2048	valid
189.0ms	1006×	body	1024	valid
164.0ms	4166×	body	128	valid
68.0ms	529×	body	512	valid
17.0ms	210×	body	256	valid

Compiler

Compiled 176 to 168 computations (4.5% saved)

Details

analyze28.0ms (0.5%)

sample39.0ms (0.7%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite127.0ms (2.2%)

series39.0ms (0.7%)

simplify130.0ms (2.3%)

prune25.0ms (0.4%)

localize9.0ms (0.2%)

rewrite227.0ms (3.9%)

series76.0ms (1.3%)

simplify179.0ms (3.1%)

prune42.0ms (0.7%)

localize13.0ms (0.2%)

rewrite355.0ms (6.2%)

series113.0ms (2%)

simplify213.0ms (3.7%)

prune148.0ms (2.6%)

localize29.0ms (0.5%)

rewrite669.0ms (11.6%)

series120.0ms (2.1%)

simplify147.0ms (2.6%)

prune181.0ms (3.2%)

regimes1.4s (25%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end2.0ms (0%)

sample1.4s (23.9%)

Profiling