Details

analyze410.0ms (11.2%)

Algorithm

1×	search
2×	egg-herbie

Rules

642×	`div-sub_binary64`
482×	`associate-*l/_binary64`
396×	`associate-/r*_binary64`
392×	`cancel-sign-sub-inv_binary64`
336×	`associate-/r/_binary64`
326×	`associate-*r/_binary64`
296×	`associate-/l/_binary64`
234×	`neg-mul-1_binary64`
184×	`distribute-rgt-in_binary64`
178×	`sub-neg_binary64`
160×	`associate-/l*_binary64`
134×	`neg-sub0_binary64` `distribute-neg-frac_binary64`
122×	`distribute-lft-in_binary64`
114×	`times-frac_binary64`
104×	`distribute-rgt-neg-in_binary64`
96×	`associate-r_binary64`
90×	`distribute-lft-neg-in_binary64` `associate-l_binary64`
82×	`*-commutative_binary64`
80×	`unsub-neg_binary64`
58×	`distribute-rgt-neg-out_binary64`
56×	`distribute-frac-neg_binary64`
54×	`distribute-lft-neg-out_binary64`
44×	`div0_binary64`
42×	`*-lft-identity_binary64`
32×	`sqr-pow_binary64`
26×	`mul0-rgt_binary64`
24×	`+-commutative_binary64`
22×	`*-rgt-identity_binary64` `mul0-lft_binary64`
20×	`unswap-sqr_binary64`
16×	`pow-sqr_binary64`
12×	`sub0-neg_binary64` `distribute-neg-in_binary64` `associate-+l-_binary64`
10×	`+-rgt-identity_binary64` `distribute-rgt-out--_binary64`
8×	`/-rgt-identity_binary64`
6×	`exp-diff_binary64` `exp-sum_binary64` `cube-unmult_binary64` `mul-1-neg_binary64` `associate--r+_binary64` `associate-+r-_binary64`
4×	`unpow3_binary64` `exp-prod_binary64` `cube-prod_binary64` `--rgt-identity_binary64` `associate-+l+_binary64`
2×	`sinh-def_binary64` `pow-plus_binary64` `exp-neg_binary64` `remove-double-neg_binary64` `associate-+r+_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` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `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` `div-exp_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-mult_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` `+-lft-identity_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	22
1	28	22
2	61	22
3	136	22
4	300	22
5	665	22
6	1827	22
7	3936	22
8	4736	22
9	4854	22
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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
37.5%	50%	12.6%	7
37.5%	50%	12.6%	8
43.7%	37.5%	18.8%	9
43.7%	37.5%	18.8%	10
46.8%	31.2%	22%	11
46.8%	31.2%	22%	12
48.4%	28.1%	23.5%	13
48.4%	28.1%	23.5%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample61.0ms (1.7%)

Algorithm

1×

intervals

Results

17.0ms	74×	body	1024	valid
13.0ms	70×	body	1024	invalid
7.0ms	150×	body	128	valid
3.0ms	26×	body	512	invalid
2.0ms	18×	body	512	valid
2.0ms	18×	body	256	invalid
1.0ms	14×	body	256	valid
1.0ms	21×	body	128	invalid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

624×	`div-sub_binary64`
491×	`times-frac_binary64`
410×	`associate-/l*_binary64`
354×	`cancel-sign-sub-inv_binary64`
341×	`unsub-neg_binary64`
307×	`associate-l_binary64`
301×	`associate-r_binary64`
249×	`distribute-rgt-in_binary64`
236×	`neg-mul-1_binary64`
212×	`associate-*l/_binary64`
210×	`neg-sub0_binary64`
196×	`distribute-rgt-neg-in_binary64`
184×	`distribute-lft-in_binary64`
181×	`distribute-neg-frac_binary64`
177×	`associate-/r*_binary64`
158×	`distribute-lft-neg-in_binary64`
151×	`associate-/r/_binary64`
145×	`associate-/l/_binary64`
144×	`associate-*r/_binary64`
120×	`distribute-lft-neg-out_binary64`
116×	`distribute-rgt-neg-out_binary64`
100×	`sub-neg_binary64`
99×	`*-commutative_binary64`
68×	`distribute-frac-neg_binary64`
40×	`distribute-neg-in_binary64`
34×	`*-lft-identity_binary64`
27×	`*-rgt-identity_binary64`
22×	`div0_binary64` `+-commutative_binary64`
16×	`associate--r+_binary64`
15×	`/-rgt-identity_binary64`
14×	`sqr-pow_binary64` `unswap-sqr_binary64`
13×	`mul0-rgt_binary64`
12×	`exp-prod_binary64` `associate-+l-_binary64`
11×	`mul0-lft_binary64` `associate--l-_binary64`
9×	`distribute-rgt-out--_binary64`
8×	`sub0-neg_binary64`
7×	`pow-sqr_binary64` `associate-+r-_binary64`
6×	`exp-diff_binary64` `exp-sum_binary64` `associate-+l+_binary64`
5×	`cube-unmult_binary64` `cube-prod_binary64`
4×	`exp-lft-sqr_binary64` `+-rgt-identity_binary64` `associate--l+_binary64` `associate-+r+_binary64`
3×	`exp-sqrt_binary64` `mul-1-neg_binary64` `--rgt-identity_binary64`
2×	`unpow3_binary64` `pow-plus_binary64` `+-lft-identity_binary64` `distribute-lft-out_binary64` `associate--r-_binary64`
1×	`sinh-def_binary64` `prod-exp_binary64` `exp-neg_binary64` `1-exp_binary64` `remove-double-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` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `unpow1/2_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-mult_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` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `count-2_binary64`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	16	11
2	34	11
3	73	11
4	157	11
5	344	11
6	932	11
7	2927	11
8	4087	11
9	5030	11

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

0.0b

Counts

1 → 1

Compiler

Compiled 7 to 6 computations (14.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(sinh.f64 y)
0.0b	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
0.0b	(/.f64 (sinh.f64 y) y)

rewrite64.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

24×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64` `times-frac_binary64` `*-un-lft-identity_binary64`
13×	`associate-r_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
3×	`add-log-exp_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l_binary64`
2×	`div-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `sinh-def_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64`
1×	`frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64`

Counts

3 → 68

Calls

3 calls:

7.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
3.0ms	(/.f64 (sinh.f64 y) y)
1.0ms	(sinh.f64 y)

Compiler

Compiled 915 to 229 computations (75% saved)

series100.0ms (2.7%)

Error

Counts

3 → 23

Calls

3 calls:

48.0ms	(*.f64 (cos.f64 x) (/.f64 (sinh.f64 y) y))
15.0ms	(/.f64 (sinh.f64 y) y)
11.0ms	(sinh.f64 y)

Compiler

Compiled 1007 to 718 computations (28.7% saved)

simplify85.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

498×	`associate-r_binary64`
356×	`associate-/l*_binary64`
319×	`times-frac_binary64`
297×	`associate-*r/_binary64`
288×	`div-sub_binary64`
273×	`associate-*l/_binary64`
184×	`associate-/r*_binary64`
138×	`associate-/l/_binary64`
120×	`associate-/r/_binary64`
109×	`associate-l_binary64`
104×	`associate-+l+_binary64`
91×	`*-commutative_binary64`
79×	`cancel-sign-sub-inv_binary64`
66×	`associate-+r+_binary64`
65×	`sub-neg_binary64`
57×	`exp-prod_binary64`
56×	`log-prod_binary64`
53×	`associate--r+_binary64`
50×	`associate--l+_binary64`
49×	`+-commutative_binary64`
48×	`distribute-rgt-neg-in_binary64`
46×	`log-div_binary64`
45×	`cube-prod_binary64`
43×	`cube-div_binary64`
40×	`distribute-neg-frac_binary64`
36×	`distribute-lft-neg-in_binary64` `distribute-rgt-in_binary64`
31×	`neg-sub0_binary64` `sqr-pow_binary64`
28×	`*-rgt-identity_binary64`
27×	`neg-mul-1_binary64` `distribute-lft-in_binary64`
26×	`associate-+l-_binary64`
23×	`*-lft-identity_binary64`
21×	`associate-+r-_binary64`
18×	`distribute-neg-in_binary64`
17×	`unswap-sqr_binary64`
15×	`exp-sum_binary64`
14×	`distribute-rgt-out_binary64`
12×	`exp-diff_binary64`
10×	`cube-unmult_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-out--_binary64`
8×	`unsub-neg_binary64` `/-rgt-identity_binary64` `associate--l-_binary64`
7×	`unpow3_binary64`
6×	`pow-plus_binary64` `mul-1-neg_binary64` `swap-sqr_binary64`
5×	`exp-sqrt_binary64` `cube-mult_binary64` `distribute-lft-out--_binary64`
4×	`log-rec_binary64`
3×	`unpow1/2_binary64` `distribute-rgt1-in_binary64` `associate--r-_binary64`
2×	`log-pow_binary64` `unpow2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `distribute-lft-out_binary64`
1×	`sinh-def_binary64` `exp-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `sqr-neg_binary64` `distribute-rgt-neg-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` `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` `div-exp_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-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_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` `difference-of-squares_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `count-2_binary64`

Counts

91 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	186	1489
1	454	1379
2	1400	1295
3	4379	1295
4	5349	1295

prune30.0ms (0.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	2	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Error

Counts

44 → 3

Compiler

Compiled 545 to 242 computations (55.6% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/120 (pow.f64 y 4)) (+.f64 (+.f64 1 (.f64 1/6 (.f64 y y))) (.f64 1/5040 (pow.f64 y 6))))
0.1b	(*.f64 1/5040 (pow.f64 y 6))
0.1b	(*.f64 1/120 (pow.f64 y 4))
0.2b	(.f64 1/6 (.f64 y y))

rewrite152.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`add-sqr-sqrt_binary64`
19×	`add-exp-log_binary64`
15×	`associate-r_binary64`
13×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`pow1_binary64` `prod-exp_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`sum-log_binary64`
5×	`cbrt-unprod_binary64`
4×	`sqr-pow_binary64`
3×	`pow-prod-down_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `associate-+r+_binary64` `+-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

9.0ms	(+.f64 (.f64 1/120 (pow.f64 y 4)) (+.f64 (+.f64 1 (.f64 1/6 (.f64 y y))) (.f64 1/5040 (pow.f64 y 6))))
6.0ms	(.f64 1/6 (.f64 y y))
5.0ms	(*.f64 1/120 (pow.f64 y 4))
5.0ms	(*.f64 1/5040 (pow.f64 y 6))

Compiler

Compiled 2298 to 1646 computations (28.4% saved)

series61.0ms (1.7%)

Error

Counts

4 → 21

Calls

4 calls:

22.0ms	(+.f64 (.f64 1/120 (pow.f64 y 4)) (+.f64 (+.f64 1 (.f64 1/6 (.f64 y y))) (.f64 1/5040 (pow.f64 y 6))))
10.0ms	(*.f64 1/5040 (pow.f64 y 6))
9.0ms	(*.f64 1/120 (pow.f64 y 4))
9.0ms	(.f64 1/6 (.f64 y y))

Compiler

Compiled 736 to 637 computations (13.5% saved)

simplify87.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

943×	`distribute-rgt-in_binary64`
893×	`distribute-lft-in_binary64`
160×	`associate-l_binary64`
155×	`associate-r_binary64`
146×	`cancel-sign-sub-inv_binary64`
129×	`exp-prod_binary64`
111×	`log-prod_binary64`
83×	`*-commutative_binary64`
70×	`unswap-sqr_binary64`
68×	`distribute-neg-in_binary64`
66×	`distribute-rgt-neg-in_binary64`
63×	`distribute-lft-neg-in_binary64`
46×	`sqr-pow_binary64`
35×	`sub-neg_binary64`
33×	`cube-prod_binary64` `+-commutative_binary64`
32×	`swap-sqr_binary64`
27×	`distribute-rgt-out_binary64`
25×	`unpow3_binary64`
19×	`exp-sum_binary64`
18×	`log-pow_binary64` `distribute-rgt-out--_binary64` `associate-+l+_binary64`
17×	`associate-+r+_binary64`
16×	`neg-mul-1_binary64` `neg-sub0_binary64`
15×	`distribute-lft-out_binary64`
14×	`distribute-lft-neg-out_binary64`
13×	`pow-plus_binary64` `associate--r+_binary64`
12×	`prod-exp_binary64`
11×	`distribute-rgt-neg-out_binary64`
10×	`-rgt-identity_binary64` `-lft-identity_binary64`
9×	`distribute-lft-out--_binary64`
8×	`pow-sqr_binary64`
7×	`cube-unmult_binary64` `unsub-neg_binary64` `associate--l+_binary64`
6×	`cube-mult_binary64`
3×	`unpow2_binary64` `unpow1/2_binary64` `unpow1_binary64` `rem-sqrt-square_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `rem-square-sqrt_binary64` `difference-of-squares_binary64` `count-2_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-rec_binary64` `log-div_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` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_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` `sqr-abs_binary64` `sqr-neg_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_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`

Counts

104 → 57

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1572
1	354	1476
2	1306	1429
3	4855	1429
4	5014	1429

prune54.0ms (1.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	57	3	60

Error

Counts

60 → 3

Compiler

Compiled 989 to 707 computations (28.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/6 (.f64 y y)) (*.f64 1/120 (pow.f64 y 4)))
0.1b	(*.f64 1/120 (pow.f64 y 4))
0.1b	(.f64 (cos.f64 x) (+.f64 (.f64 1/6 (.f64 y y)) (.f64 1/120 (pow.f64 y 4))))
0.2b	(.f64 1/6 (.f64 y y))

rewrite127.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

18×	`add-sqr-sqrt_binary64`
16×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`pow1_binary64` `associate-r_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`associate-l_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-unprod_binary64` `unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `unpow-prod-down_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `flip-+_binary64` `sqr-pow_binary64`
1×	`distribute-rgt-in_binary64` `distribute-lft-in_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `sum-log_binary64` `+-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

8.0ms	(.f64 (cos.f64 x) (+.f64 (.f64 1/6 (.f64 y y)) (.f64 1/120 (pow.f64 y 4))))
6.0ms	(+.f64 (.f64 1/6 (.f64 y y)) (*.f64 1/120 (pow.f64 y 4)))
5.0ms	(*.f64 1/120 (pow.f64 y 4))
5.0ms	(.f64 1/6 (.f64 y y))

Compiler

Compiled 1844 to 1105 computations (40.1% saved)

series92.0ms (2.5%)

Error

Counts

4 → 21

Calls

4 calls:

42.0ms	(.f64 (cos.f64 x) (+.f64 (.f64 1/6 (.f64 y y)) (.f64 1/120 (pow.f64 y 4))))
19.0ms	(+.f64 (.f64 1/6 (.f64 y y)) (*.f64 1/120 (pow.f64 y 4)))
10.0ms	(.f64 1/6 (.f64 y y))
9.0ms	(*.f64 1/120 (pow.f64 y 4))

Compiler

Compiled 737 to 569 computations (22.8% saved)

simplify111.0ms (3%)

Algorithm

1×	egg-herbie

Rules

431×	`*-commutative_binary64`
278×	`cancel-sign-sub-inv_binary64` `distribute-lft-out_binary64`
249×	`distribute-rgt-out_binary64`
247×	`distribute-rgt-in_binary64`
236×	`distribute-lft-in_binary64`
218×	`distribute-rgt-neg-in_binary64`
199×	`distribute-lft-neg-in_binary64`
196×	`associate-+l+_binary64`
185×	`associate-l_binary64`
184×	`associate-r_binary64`
153×	`sub-neg_binary64`
141×	`exp-prod_binary64`
138×	`unswap-sqr_binary64`
110×	`sqr-pow_binary64`
91×	`neg-mul-1_binary64`
88×	`neg-sub0_binary64`
83×	`distribute-rgt-out--_binary64`
76×	`log-prod_binary64`
75×	`swap-sqr_binary64`
54×	`cube-prod_binary64`
53×	`unsub-neg_binary64`
32×	`*-lft-identity_binary64`
31×	`*-rgt-identity_binary64` `distribute-lft-out--_binary64`
23×	`unpow3_binary64`
22×	`distribute-lft-neg-out_binary64`
21×	`associate-/l*_binary64`
20×	`+-commutative_binary64`
18×	`associate-+l-_binary64`
17×	`cube-mult_binary64`
15×	`pow-plus_binary64` `pow-sqr_binary64` `associate-+r+_binary64`
13×	`log-pow_binary64` `distribute-neg-in_binary64`
12×	`associate-+r-_binary64`
11×	`rem-sqrt-square_binary64` `times-frac_binary64`
7×	`unpow1/2_binary64` `cube-unmult_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
6×	`distribute-rgt-neg-out_binary64` `associate-/r*_binary64`
5×	`unpow2_binary64` `+-rgt-identity_binary64`
4×	`exp-sum_binary64` `associate-/r/_binary64` `associate--r+_binary64`
3×	`unpow1_binary64` `sub0-neg_binary64` `associate--l+_binary64`
2×	`difference-of-squares_binary64` `count-2_binary64`
1×	`prod-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `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` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_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` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-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` `difference-of-sqr--1_binary64` `difference-of-sqr-1_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` `associate-l/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

98 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	138	1608
1	322	1486
2	1066	1453
3	2455	1441
4	4729	1441
5	4955	1441

prune47.0ms (1.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	57	3	60

Error

Counts

60 → 3

Compiler

Compiled 769 to 454 computations (41% saved)

regimes256.0ms (7%)

Accuracy

Total 0.0b remaining (47.9%)

Threshold costs 0.0b (47.9%)

Compiler

Compiled 2790 to 2249 computations (19.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1× *-commutative_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 1-exp_binary64 exp-1-e_binary64 exp-0_binary64 sqr-abs_binary64 sqr-neg_binary64 neg-mul-1_binary64 neg-sub0_binary64 unsub-neg_binary64 sub-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 +-commutative_binary64

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	8	11
2	8	11

end1.0ms (0%)

Compiler: Compiled 7 to 6 computations (14.3% saved)

sample1.8s (49.8%)

Algorithm

1×

intervals

Results

405.0ms	2058×	body	1024	valid
333.0ms	1918×	body	1024	invalid
211.0ms	4442×	body	128	valid
130.0ms	1003×	body	512	valid
110.0ms	894×	body	512	invalid
46.0ms	494×	body	256	valid
42.0ms	446×	body	256	invalid
36.0ms	695×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 64 to 62 computations (3.1% saved)

Details

analyze410.0ms (11.2%)

sample61.0ms (1.7%)

simplify61.0ms (1.7%)

prune1.0ms (0%)

localize6.0ms (0.2%)

rewrite64.0ms (1.7%)

series100.0ms (2.7%)

simplify85.0ms (2.3%)

prune30.0ms (0.8%)

localize20.0ms (0.5%)

rewrite152.0ms (4.1%)

series61.0ms (1.7%)

simplify87.0ms (2.4%)

prune54.0ms (1.5%)

localize11.0ms (0.3%)

rewrite127.0ms (3.5%)

series92.0ms (2.5%)

simplify111.0ms (3%)

prune47.0ms (1.3%)

regimes256.0ms (7%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.8s (49.8%)

Profiling