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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	79×	body	2048	valid
5.0ms	128×	body	128	valid
4.0ms	24×	body	1024	valid
3.0ms	19×	body	512	valid
0.0ms	6×	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

14.0b

Counts

2 → 1

Compiler

Compiled 20 to 20 computations (0% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
1.6b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite109.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

14.0b

Rules

28×	`*-un-lft-identity_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`sqrt-prod_binary64`
9×	`times-frac_binary64`
8×	`add-log-exp_binary64`
7×	`cancel-sign-sub-inv_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64` `distribute-lft-out_binary64`
3×	`distribute-lft-out--_binary64` `associate-/l_binary64` `associate-/r_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `sum-log_binary64` `+-commutative_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 80

Calls

4 calls:

10.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
6.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
6.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 1352 to 1225 computations (9.4% saved)

series52.0ms (0.9%)

Error

14.0b

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
14.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
11.0ms	(+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
9.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 298 to 297 computations (0.3% saved)

simplify150.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

475×	`times-frac_binary64`
422×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
330×	`unsub-neg_binary64`
299×	`associate-/l*_binary64`
217×	`associate-l_binary64`
185×	`div-sub_binary64`
184×	`associate-r_binary64`
164×	`associate-/r*_binary64`
162×	`exp-prod_binary64`
159×	`distribute-rgt-out_binary64`
154×	`cancel-sign-sub-inv_binary64`
126×	`log-prod_binary64`
115×	`sqr-pow_binary64`
106×	`neg-mul-1_binary64`
101×	`neg-sub0_binary64` `sub-neg_binary64`
91×	`cube-prod_binary64` `associate-*l/_binary64`
84×	`distribute-lft-out_binary64`
63×	`distribute-rgt-neg-in_binary64`
61×	`*-lft-identity_binary64`
60×	`associate-*r/_binary64`
59×	`*-rgt-identity_binary64` `associate-/l/_binary64`
57×	`unswap-sqr_binary64`
56×	`/-rgt-identity_binary64`
52×	`distribute-lft-neg-in_binary64` `*-commutative_binary64`
50×	`swap-sqr_binary64`
48×	`distribute-lft-neg-out_binary64`
44×	`exp-sum_binary64` `distribute-rgt-neg-out_binary64`
41×	`rem-sqrt-square_binary64`
39×	`associate-/r/_binary64`
36×	`unpow3_binary64` `+-commutative_binary64`
30×	`associate-+l-_binary64`
27×	`mul0-rgt_binary64` `mul0-lft_binary64` `pow-sqr_binary64` `associate-+l+_binary64`
25×	`pow-plus_binary64` `distribute-rgt1-in_binary64`
21×	`sub0-neg_binary64`
20×	`associate-+r+_binary64`
18×	`log-div_binary64`
17×	`exp-diff_binary64`
16×	`log-pow_binary64` `cube-mult_binary64`
14×	`associate--r+_binary64`
13×	`cube-unmult_binary64`
11×	`cube-div_binary64` `distribute-neg-frac_binary64` `distribute-rgt-out--_binary64`
8×	`distribute-neg-in_binary64`
7×	`unpow1/2_binary64`
6×	`sqr-neg_binary64`
5×	`mul-1-neg_binary64` `--rgt-identity_binary64` `associate--l+_binary64`
4×	`cube-neg_binary64` `+-lft-identity_binary64` `difference-of-sqr-1_binary64` `distribute-lft1-in_binary64` `associate-+r-_binary64`
3×	`+-rgt-identity_binary64` `count-2_binary64`
2×	`log-rec_binary64` `unpow2_binary64` `rem-square-sqrt_binary64` `div0_binary64`
1×	`unpow1_binary64` `div-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `remove-double-neg_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` `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-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` `difference-of-sqr--1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

92 → 45

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	124	1520
1	230	1459
2	504	1453
3	1516	1453
4	4215	1453
5	4466	1444
6	4922	1444
7	4823	1444

prune34.0ms (0.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	1	46

Error

13.5b

Counts

46 → 1

Compiler

Compiled 473 to 430 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1/2 (hypot.f64 1 x))
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)))))
1.1b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite227.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

13.5b

Rules

89×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
62×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
32×	`distribute-lft-out_binary64`
16×	`difference-of-squares_binary64` `sqrt-prod_binary64`
13×	`cancel-sign-sub-inv_binary64`
9×	`associate-/l_binary64` `associate-/r_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
4×	`pow1_binary64`
3×	`div-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `flip3-+_binary64` `flip-+_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `sum-log_binary64` `+-commutative_binary64` `div-sub_binary64`

Counts

4 → 133

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)))))
8.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 3371 to 3033 computations (10% saved)

series73.0ms (1.3%)

Error

13.5b

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.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	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
13.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))
10.0ms	(/.f64 1/2 (hypot.f64 1 x))

Compiler

Compiled 560 to 529 computations (5.5% saved)

simplify176.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

466×	`div-sub_binary64`
301×	`associate-l_binary64`
271×	`associate-r_binary64`
262×	`associate-/l*_binary64`
237×	`associate-*l/_binary64`
182×	`associate-*r/_binary64`
171×	`distribute-rgt-in_binary64`
168×	`sub-neg_binary64`
158×	`distribute-lft-in_binary64`
155×	`log-div_binary64`
141×	`associate-/l/_binary64`
135×	`*-commutative_binary64`
121×	`exp-prod_binary64`
115×	`associate-/r*_binary64`
102×	`times-frac_binary64`
96×	`distribute-neg-frac_binary64`
89×	`neg-sub0_binary64`
83×	`unsub-neg_binary64`
82×	`neg-mul-1_binary64`
68×	`associate-/r/_binary64`
66×	`distribute-rgt-neg-in_binary64`
62×	`cancel-sign-sub-inv_binary64`
58×	`+-commutative_binary64`
56×	`associate-+l+_binary64`
54×	`cube-prod_binary64`
53×	`log-prod_binary64`
49×	`associate-+r+_binary64`
45×	`distribute-lft-neg-in_binary64`
31×	`exp-sum_binary64` `distribute-lft-neg-out_binary64`
24×	`exp-diff_binary64` `cube-div_binary64`
23×	`distribute-rgt-neg-out_binary64`
16×	`sqr-pow_binary64`
14×	`*-rgt-identity_binary64` `associate-+l-_binary64`
13×	`distribute-frac-neg_binary64`
12×	`log-rec_binary64` `*-lft-identity_binary64`
11×	`cube-unmult_binary64`
10×	`/-rgt-identity_binary64` `distribute-rgt-out_binary64`
9×	`distribute-neg-in_binary64` `associate--r+_binary64` `associate-+r-_binary64`
8×	`distribute-rgt1-in_binary64`
6×	`unpow3_binary64` `swap-sqr_binary64` `associate--l+_binary64`
4×	`rem-square-sqrt_binary64` `unswap-sqr_binary64` `distribute-lft-out_binary64`
3×	`unpow1/2_binary64` `pow-plus_binary64` `cube-mult_binary64` `rem-sqrt-square_binary64` `associate--r-_binary64`
2×	`log-pow_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-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` `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` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

145 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	3954
1	446	3785
2	1160	3779
3	3547	3779
4	4909	3779
5	5064	3779

prune48.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	75	2	77
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	2	78

Error

13.5b

Counts

78 → 2

Compiler

Compiled 808 to 727 computations (10% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
0.1b	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
1.1b	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))

rewrite283.0ms (5.1%)

Algorithm

1×	rewrite-expression-head

Error

13.3b

Rules

58×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
50×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
32×	`cancel-sign-sub-inv_binary64`
28×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`difference-of-squares_binary64`
5×	`pow1_binary64` `div-inv_binary64`
4×	`associate-/l*_binary64`
3×	`sqr-pow_binary64` `pow-unpow_binary64` `associate-/r*_binary64`
2×	`unpow3_binary64` `cube-mult_binary64` `div-exp_binary64` `pow-exp_binary64` `rem-cube-cbrt_binary64` `cbrt-undiv_binary64` `flip3-+_binary64` `flip-+_binary64` `sqrt-prod_binary64` `associate-/l/_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `distribute-lft-out--_binary64` `pow-pow_binary64` `pow-to-exp_binary64` `cube-div_binary64` `sum-log_binary64` `+-commutative_binary64` `frac-2neg_binary64` `clear-num_binary64`

Counts

4 → 143

Calls

4 calls:

14.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
8.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
5.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)

Compiler

Compiled 4735 to 4205 computations (11.2% saved)

series83.0ms (1.5%)

Error

13.5b

Counts

4 → 12

Calls

4 calls:

20.0ms	(-.f64 1/8 (pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3))
19.0ms	(pow.f64 (/.f64 1/2 (hypot.f64 1 x)) 3)
19.0ms	(/.f64 (+.f64 1/4 (/.f64 1/4 (hypot.f64 1 x))) (hypot.f64 1 x))
17.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

Compiler

Compiled 994 to 907 computations (8.8% saved)

simplify141.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

730×	`times-frac_binary64`
515×	`log-prod_binary64`
403×	`unswap-sqr_binary64`
186×	`associate-r_binary64`
164×	`exp-prod_binary64`
158×	`associate-l_binary64`
110×	`sqr-pow_binary64`
106×	`log-div_binary64`
105×	`cube-prod_binary64`
95×	`associate-*l/_binary64`
94×	`associate-*r/_binary64`
81×	`cube-div_binary64`
76×	`neg-mul-1_binary64`
73×	`neg-sub0_binary64`
67×	`*-commutative_binary64`
63×	`cancel-sign-sub-inv_binary64`
59×	`distribute-rgt-neg-in_binary64`
57×	`sub-neg_binary64`
52×	`associate-/l*_binary64`
47×	`distribute-lft-neg-in_binary64`
44×	`distribute-rgt-in_binary64`
42×	`log-pow_binary64`
37×	`unpow3_binary64`
36×	`distribute-lft-in_binary64`
35×	`cube-mult_binary64`
34×	`+-commutative_binary64`
33×	`associate-/l/_binary64`
23×	`associate-/r*_binary64`
19×	`pow-sqr_binary64` `distribute-lft-neg-out_binary64`
15×	`rem-sqrt-square_binary64` `*-rgt-identity_binary64` `distribute-neg-frac_binary64`
14×	`*-lft-identity_binary64`
12×	`pow-plus_binary64` `swap-sqr_binary64`
10×	`cube-unmult_binary64` `associate-/r/_binary64`
7×	`/-rgt-identity_binary64` `distribute-rgt-neg-out_binary64`
6×	`div-sub_binary64` `associate-+r-_binary64` `associate-+l+_binary64`
5×	`rem-square-sqrt_binary64` `unsub-neg_binary64` `distribute-neg-in_binary64`
4×	`log-rec_binary64` `exp-sum_binary64` `associate--r+_binary64` `associate-+r+_binary64`
3×	`rem-cube-cbrt_binary64` `distribute-rgt1-in_binary64`
2×	`rem-cbrt-cube_binary64` `mul-1-neg_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `associate--l+_binary64` `associate-+l-_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `div-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `1-exp_binary64` `exp-1-e_binary64` `+-rgt-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` `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` `unpow2_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-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-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` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

155 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	233	3265
1	587	2874
2	2183	2784
3	4743	2784
4	5409	2784

prune87.0ms (1.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

13.3b

Counts

109 → 3

Compiler

Compiled 1853 to 1650 computations (11% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (hypot.f64 1 x) 3)
0.2b	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
0.7b	(log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))
31.4b	(-.f64 1/8 (log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))

rewrite396.0ms (7.1%)

Algorithm

1×	rewrite-expression-head

Error

13.3b

Rules

108×	`times-frac_binary64`
83×	`log-pow_binary64`
82×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
80×	`exp-prod_binary64`
79×	`add-cube-cbrt_binary64`
44×	`cancel-sign-sub-inv_binary64`
33×	`unpow-prod-down_binary64` `cube-prod_binary64`
12×	`associate-/r*_binary64`
11×	`unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64`
10×	`add-exp-log_binary64`
8×	`pow1_binary64`
7×	`add-cbrt-cube_binary64`
6×	`log-prod_binary64`
5×	`add-log-exp_binary64`
3×	`div-inv_binary64` `associate--r+_binary64` `div-exp_binary64` `associate-/l*_binary64` `pow-unpow_binary64`
2×	`distribute-lft-out--_binary64` `pow-to-exp_binary64` `pow-exp_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `rem-log-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `clear-num_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64`

Counts

4 → 201

Calls

4 calls:

22.0ms	(-.f64 1/8 (log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))
9.0ms	(log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))
5.0ms	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
2.0ms	(pow.f64 (hypot.f64 1 x) 3)

Compiler

Compiled 7424 to 6628 computations (10.7% saved)

series95.0ms (1.7%)

Error

13.3b

Counts

4 → 12

Calls

4 calls:

31.0ms	(log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))))
31.0ms	(-.f64 1/8 (log.f64 (exp.f64 (/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3)))))
18.0ms	(/.f64 1/8 (pow.f64 (hypot.f64 1 x) 3))
13.0ms	(pow.f64 (hypot.f64 1 x) 3)

Compiler

Compiled 900 to 825 computations (8.3% saved)

simplify107.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

751×	`associate-*l/_binary64`
479×	`associate-/l*_binary64`
362×	`associate-/l/_binary64`
233×	`unswap-sqr_binary64`
195×	`distribute-neg-frac_binary64`
152×	`associate-/r*_binary64`
130×	`associate-/r/_binary64`
105×	`distribute-rgt-neg-in_binary64`
92×	`distribute-lft-neg-in_binary64`
81×	`exp-prod_binary64` `neg-mul-1_binary64` `distribute-rgt-in_binary64`
76×	`neg-sub0_binary64`
72×	`*-commutative_binary64`
71×	`associate-*r/_binary64`
69×	`distribute-lft-in_binary64`
67×	`cancel-sign-sub-inv_binary64`
66×	`distribute-lft-neg-out_binary64`
58×	`log-prod_binary64`
57×	`sub-neg_binary64`
54×	`distribute-rgt-neg-out_binary64`
51×	`associate-r_binary64`
44×	`div-sub_binary64`
39×	`sqr-pow_binary64`
33×	`cube-prod_binary64`
29×	`rem-log-exp_binary64` `associate-l_binary64`
28×	`swap-sqr_binary64`
22×	`times-frac_binary64`
20×	`distribute-frac-neg_binary64`
18×	`*-rgt-identity_binary64`
14×	`+-commutative_binary64`
13×	`log-pow_binary64` `pow-sqr_binary64`
10×	`rem-sqrt-square_binary64`
9×	`cube-unmult_binary64` `cube-div_binary64`
8×	`pow-plus_binary64` `distribute-neg-in_binary64`
6×	`unpow3_binary64` `exp-to-pow_binary64` `*-lft-identity_binary64`
5×	`cube-mult_binary64`
4×	`log-div_binary64` `count-2_binary64`
3×	`exp-sum_binary64` `rem-square-sqrt_binary64` `/-rgt-identity_binary64`
2×	`exp-diff_binary64` `rem-3cbrt-rft_binary64` `mul-1-neg_binary64` `distribute-rgt1-in_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
1×	`unpow1/2_binary64` `unpow1_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-exp-log_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `unsub-neg_binary64` `+-rgt-identity_binary64` `distribute-rgt-out_binary64` `associate--r+_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-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_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` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `remove-double-neg_binary64` `sub0-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` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate-+l-_binary64`

Counts

213 → 177

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3093
1	447	2923
2	1425	2797
3	5104	2797

prune145.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	177	3	180

Error

13.3b

Counts

180 → 3

Compiler

Compiled 3174 to 2822 computations (11.1% saved)

regimes1.8s (32.9%)

Accuracy

Total 0.2b remaining (1.7%)

Threshold costs 0.2b (1.7%)

Compiler

Compiled 34590 to 32022 computations (7.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
2×	`sub-neg_binary64` `*-commutative_binary64`
1×	`1-exp_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `*-lft-identity_binary64` `distribute-neg-frac_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` `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-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	12	27
1	19	27
2	26	27
3	28	27
4	29	27
5	27	27

end1.0ms (0%)

Compiler: Compiled 18 to 17 computations (5.6% saved)

sample1.4s (25%)

Algorithm

1×

intervals

Results

547.0ms	2133×	body	2048	valid
197.0ms	1017×	body	1024	valid
178.0ms	4107×	body	128	valid
66.0ms	501×	body	512	valid
26.0ms	242×	body	256	valid

Compiler

Compiled 128 to 124 computations (3.1% saved)

Details

analyze28.0ms (0.5%)

sample41.0ms (0.7%)

simplify11.0ms (0.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

rewrite109.0ms (2%)

series52.0ms (0.9%)

simplify150.0ms (2.7%)

prune34.0ms (0.6%)

localize9.0ms (0.2%)

rewrite227.0ms (4.1%)

series73.0ms (1.3%)

simplify176.0ms (3.1%)

prune48.0ms (0.9%)

localize20.0ms (0.4%)

rewrite283.0ms (5.1%)

series83.0ms (1.5%)

simplify141.0ms (2.5%)

prune87.0ms (1.6%)

localize20.0ms (0.4%)

rewrite396.0ms (7.1%)

series95.0ms (1.7%)

simplify107.0ms (1.9%)

prune145.0ms (2.6%)

regimes1.8s (32.9%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.4s (25%)

Profiling