Details

analyze760.0ms (0.3%)

Algorithm

1×

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
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

Compiler

Compiled 51 to 41 computations (19.6% saved)

sample171.0ms (0.1%)

Algorithm

1×

intervals

Results

101.0ms	106×	body	1024	valid
30.0ms	50×	body	512	valid
15.0ms	81×	body	128	valid
7.0ms	19×	body	256	valid

Compiler

Compiled 101 to 83 computations (17.8% saved)

simplify219.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

523×	`distribute-rgt-neg-out_binary64_6176`
520×	`distribute-lft-neg-out_binary64_6175`
449×	`unsub-neg_binary64_6210`
428×	`distribute-rgt-in_binary64_6166` `distribute-lft-in_binary64_6165`
372×	`associate-*l/_binary64_6159`
334×	`associate-l_binary64_6157`
288×	`associate-r_binary64_6156`
155×	`associate-/l*_binary64_6161`
132×	`neg-sub0_binary64_6211`
124×	`distribute-neg-out_binary64_6178`
117×	`*-commutative_binary64_6147`
89×	`distribute-rgt-out_binary64_6169`
75×	`neg-mul-1_binary64_6212`
70×	`distribute-lft-out_binary64_6167`
65×	`associate-+r+_binary64_6148`
64×	`sub-neg_binary64_6209`
62×	`associate-*r/_binary64_6158`
60×	`associate-+l+_binary64_6149`
50×	`div-sub_binary64_6221`
35×	`distribute-neg-in_binary64_6177`
33×	`distribute-rgt-neg-in_binary64_6174`
29×	`-rgt-identity_binary64_6206` `-lft-identity_binary64_6205` `associate-/r/_binary64_6162`
26×	`distribute-lft-neg-in_binary64_6173` `associate-/r*_binary64_6160`
25×	`cancel-sign-sub-inv_binary64_6182` `+-commutative_binary64_6146`
23×	`mul0-rgt_binary64_6199` `mul0-lft_binary64_6198`
18×	`associate-+r-_binary64_6150`
17×	`distribute-frac-neg_binary64_6179`
13×	`associate-+l-_binary64_6151`
12×	`mul-1-neg_binary64_6208`
8×	`+-rgt-identity_binary64_6201` `associate-/l/_binary64_6163`
7×	`sub0-neg_binary64_6203`
6×	`distribute-neg-frac_binary64_6180`
5×	`/-rgt-identity_binary64_6207`
4×	`div0_binary64_6197`
3×	`distribute-rgt1-in_binary64_6172`
2×	`remove-double-neg_binary64_6204` `swap-sqr_binary64_6183` `distribute-lft1-in_binary64_6171`
1×	`prod-exp_binary64_6265` `1-exp_binary64_6260` `count-2_binary64_6164`
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_6479` `erf-erfc_binary64_6478` `erf-odd_binary64_6477` `if-if-and-not_binary64_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `not-gte_binary64_6468` `not-lte_binary64_6467` `not-gt_binary64_6466` `not-lt_binary64_6465` `gte-same_binary64_6464` `lte-same_binary64_6463` `gt-same_binary64_6462` `lt-same_binary64_6461` `sinh---cosh_binary64_6408` `sinh-+-cosh_binary64_6407` `sinh-cosh_binary64_6406` `tanh-def-c_binary64_6405` `tanh-def-b_binary64_6404` `tanh-def-a_binary64_6403` `cosh-def_binary64_6402` `sinh-def_binary64_6401` `tan-neg_binary64_6348` `cos-neg_binary64_6347` `sin-neg_binary64_6346` `tan-0_binary64_6345` `cos-0_binary64_6344` `sin-0_binary64_6343` `hang-m-tan_binary64_6342` `hang-p-tan_binary64_6341` `hang-m0-tan_binary64_6340` `hang-p0-tan_binary64_6339` `hang-0m-tan_binary64_6338` `hang-0p-tan_binary64_6337` `tan-+PI/2_binary64_6336` `tan-+PI_binary64_6335` `tan-PI_binary64_6334` `tan-PI/3_binary64_6333` `tan-PI/4_binary64_6332` `tan-PI/6_binary64_6331` `cos-+PI/2_binary64_6330` `cos-+PI_binary64_6329` `cos-PI_binary64_6328` `cos-PI/2_binary64_6327` `cos-PI/3_binary64_6326` `cos-PI/4_binary64_6325` `cos-PI/6_binary64_6324` `sin-+PI/2_binary64_6323` `sin-+PI_binary64_6322` `sin-PI_binary64_6321` `sin-PI/2_binary64_6320` `sin-PI/3_binary64_6319` `sin-PI/4_binary64_6318` `sin-PI/6_binary64_6317` `sub-1-sin_binary64_6316` `sub-1-cos_binary64_6315` `-1-add-sin_binary64_6314` `-1-add-cos_binary64_6313` `1-sub-sin_binary64_6312` `1-sub-cos_binary64_6311` `cos-sin-sum_binary64_6310` `log-E_binary64_6306` `log-pow_binary64_6305` `log-rec_binary64_6304` `log-div_binary64_6303` `log-prod_binary64_6302` `pow-base-0_binary64_6300` `unpow1/3_binary64_6283` `unpow3_binary64_6282` `unpow2_binary64_6281` `unpow1/2_binary64_6280` `pow-plus_binary64_6279` `exp-to-pow_binary64_6278` `pow-base-1_binary64_6276` `unpow0_binary64_6275` `unpow1_binary64_6274` `unpow-1_binary64_6273` `exp-lft-cube_binary64_6272` `exp-lft-sqr_binary64_6271` `exp-cbrt_binary64_6270` `exp-sqrt_binary64_6269` `exp-prod_binary64_6268` `div-exp_binary64_6267` `rec-exp_binary64_6266` `exp-diff_binary64_6264` `exp-neg_binary64_6263` `exp-sum_binary64_6262` `e-exp-1_binary64_6261` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `rem-log-exp_binary64_6257` `rem-exp-log_binary64_6256` `cube-unmult_binary64_6253` `cube-mult_binary64_6246` `cube-div_binary64_6245` `cube-prod_binary64_6244` `cube-neg_binary64_6243` `rem-3cbrt-rft_binary64_6242` `rem-3cbrt-lft_binary64_6241` `rem-cbrt-cube_binary64_6240` `rem-cube-cbrt_binary64_6239` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `rem-sqrt-square_binary64_6229` `rem-square-sqrt_binary64_6228` `times-frac_binary64_6222` `--rgt-identity_binary64_6202` `+-lft-identity_binary64_6200` `*-inverses_binary64_6196` `+-inverses_binary64_6195` `lft-mult-inverse_binary64_6194` `rgt-mult-inverse_binary64_6193` `remove-double-div_binary64_6192` `pow-sqr_binary64_6189` `sqr-pow_binary64_6188` `difference-of-sqr--1_binary64_6187` `difference-of-sqr-1_binary64_6186` `difference-of-squares_binary64_6185` `unswap-sqr_binary64_6184` `cancel-sign-sub_binary64_6181` `distribute-rgt-out--_binary64_6170` `distribute-lft-out--_binary64_6168` `associate--r-_binary64_6155` `associate--l-_binary64_6154` `associate--l+_binary64_6153` `associate--r+_binary64_6152`

Counts

1 → 5

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	80
1	77	80
2	191	80
3	623	80
4	2525	80

prune30.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	3	2	5
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	3	3	6

Error

0.3b

Counts

6 → 3

Compiler

Compiled 400 to 292 computations (27% saved)

localize32.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
0.5b	(+.f64 (.f64 (/.f64 (cos.f64 x) 2) (+.f64 (sqrt.f64 5) -1)) (.f64 (/.f64 (cos.f64 y) 2) (-.f64 3 (sqrt.f64 5))))
1.0b	(-.f64 3 (sqrt.f64 5))
1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite936.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

60×	`associate-*r/_binary64_6158`
56×	`distribute-rgt-in_binary64_6166` `distribute-lft-in_binary64_6165`
48×	`frac-times_binary64_6226`
45×	`cancel-sign-sub-inv_binary64_6182`
39×	`flip3--_binary64_6220` `flip--_binary64_6191`
27×	`add-sqr-sqrt_binary64_6238`
25×	`*-un-lft-identity_binary64_6216` `frac-add_binary64_6224`
21×	`add-cube-cbrt_binary64_6251`
18×	`associate-*l/_binary64_6159`
14×	`associate-+r+_binary64_6148`
13×	`pow1_binary64_6277` `add-exp-log_binary64_6254` `add-cbrt-cube_binary64_6252` `sqrt-prod_binary64_6232`
12×	`sub-neg_binary64_6209`
11×	`flip3-+_binary64_6219` `flip-+_binary64_6190`
10×	`add-log-exp_binary64_6255`
6×	`pow-prod-down_binary64_6287` `prod-exp_binary64_6265` `cbrt-unprod_binary64_6249` `associate-l_binary64_6157`
3×	`difference-of-squares_binary64_6185`
2×	`diff-log_binary64_6308` `distribute-lft-out--_binary64_6168` `associate-+l+_binary64_6149`
1×	`diff-cos_binary64_6367` `sum-log_binary64_6307` `+-commutative_binary64_6146` `associate-r_binary64_6156` `*-commutative_binary64_6147`

Counts

4 → 171

Calls

4 calls:

34.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
14.0ms	(+.f64 (.f64 (/.f64 (cos.f64 x) 2) (+.f64 (sqrt.f64 5) -1)) (.f64 (/.f64 (cos.f64 y) 2) (-.f64 3 (sqrt.f64 5))))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 12430 to 8258 computations (33.6% saved)

series1.4s (0.5%)

Error

0.3b

Counts

4 → 36

Calls

4 calls:

578.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
535.0ms	(+.f64 (.f64 (/.f64 (cos.f64 x) 2) (+.f64 (sqrt.f64 5) -1)) (.f64 (/.f64 (cos.f64 y) 2) (-.f64 3 (sqrt.f64 5))))
164.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 5360 to 4115 computations (23.2% saved)

simplify620.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

527×	`distribute-rgt-in_binary64_6166`
521×	`distribute-lft-in_binary64_6165`
281×	`*-commutative_binary64_6147`
204×	`associate-r_binary64_6156`
116×	`sub-neg_binary64_6209`
105×	`+-commutative_binary64_6146`
103×	`cancel-sign-sub-inv_binary64_6182`
99×	`associate-l_binary64_6157`
58×	`neg-sub0_binary64_6211`
56×	`neg-mul-1_binary64_6212`
50×	`sqr-pow_binary64_6188`
49×	`distribute-neg-in_binary64_6177`
44×	`distribute-rgt-neg-in_binary64_6174`
39×	`associate-+r+_binary64_6148`
30×	`distribute-lft-neg-out_binary64_6175`
29×	`distribute-lft-neg-in_binary64_6173`
21×	`pow-sqr_binary64_6189`
20×	`associate--l+_binary64_6153` `associate--r+_binary64_6152`
18×	`unpow3_binary64_6282` `distribute-rgt-neg-out_binary64_6176` `distribute-rgt-out_binary64_6169`
17×	`cube-mult_binary64_6246` `times-frac_binary64_6222`
12×	`difference-of-squares_binary64_6185` `unswap-sqr_binary64_6184` `swap-sqr_binary64_6183`
11×	`distribute-neg-frac_binary64_6180`
10×	`associate-*l/_binary64_6159`
8×	`cube-unmult_binary64_6253` `distribute-lft-out_binary64_6167`
7×	`exp-prod_binary64_6268`
6×	`cube-div_binary64_6245`
5×	`log-prod_binary64_6302`
4×	`unpow2_binary64_6281` `pow-plus_binary64_6279` `exp-sqrt_binary64_6269` `exp-sum_binary64_6262` `cube-prod_binary64_6244` `rem-square-sqrt_binary64_6228` `unsub-neg_binary64_6210` `mul-1-neg_binary64_6208` `associate-*r/_binary64_6158`
3×	`rem-sqrt-square_binary64_6229` `distribute-rgt-out--_binary64_6170`
2×	`div-exp_binary64_6267` `rem-3cbrt-lft_binary64_6241` `*-lft-identity_binary64_6205` `remove-double-neg_binary64_6204` `associate-+r-_binary64_6150`
1×	`prod-exp_binary64_6265` `1-exp_binary64_6260` `div-sub_binary64_6221` `-rgt-identity_binary64_6206` `-inverses_binary64_6196` `distribute-rgt1-in_binary64_6172` `distribute-lft-out--_binary64_6168`
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_6479` `erf-erfc_binary64_6478` `erf-odd_binary64_6477` `if-if-and-not_binary64_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `not-gte_binary64_6468` `not-lte_binary64_6467` `not-gt_binary64_6466` `not-lt_binary64_6465` `gte-same_binary64_6464` `lte-same_binary64_6463` `gt-same_binary64_6462` `lt-same_binary64_6461` `sinh---cosh_binary64_6408` `sinh-+-cosh_binary64_6407` `sinh-cosh_binary64_6406` `tanh-def-c_binary64_6405` `tanh-def-b_binary64_6404` `tanh-def-a_binary64_6403` `cosh-def_binary64_6402` `sinh-def_binary64_6401` `tan-neg_binary64_6348` `cos-neg_binary64_6347` `sin-neg_binary64_6346` `tan-0_binary64_6345` `cos-0_binary64_6344` `sin-0_binary64_6343` `hang-m-tan_binary64_6342` `hang-p-tan_binary64_6341` `hang-m0-tan_binary64_6340` `hang-p0-tan_binary64_6339` `hang-0m-tan_binary64_6338` `hang-0p-tan_binary64_6337` `tan-+PI/2_binary64_6336` `tan-+PI_binary64_6335` `tan-PI_binary64_6334` `tan-PI/3_binary64_6333` `tan-PI/4_binary64_6332` `tan-PI/6_binary64_6331` `cos-+PI/2_binary64_6330` `cos-+PI_binary64_6329` `cos-PI_binary64_6328` `cos-PI/2_binary64_6327` `cos-PI/3_binary64_6326` `cos-PI/4_binary64_6325` `cos-PI/6_binary64_6324` `sin-+PI/2_binary64_6323` `sin-+PI_binary64_6322` `sin-PI_binary64_6321` `sin-PI/2_binary64_6320` `sin-PI/3_binary64_6319` `sin-PI/4_binary64_6318` `sin-PI/6_binary64_6317` `sub-1-sin_binary64_6316` `sub-1-cos_binary64_6315` `-1-add-sin_binary64_6314` `-1-add-cos_binary64_6313` `1-sub-sin_binary64_6312` `1-sub-cos_binary64_6311` `cos-sin-sum_binary64_6310` `log-E_binary64_6306` `log-pow_binary64_6305` `log-rec_binary64_6304` `log-div_binary64_6303` `pow-base-0_binary64_6300` `unpow1/3_binary64_6283` `unpow1/2_binary64_6280` `exp-to-pow_binary64_6278` `pow-base-1_binary64_6276` `unpow0_binary64_6275` `unpow1_binary64_6274` `unpow-1_binary64_6273` `exp-lft-cube_binary64_6272` `exp-lft-sqr_binary64_6271` `exp-cbrt_binary64_6270` `rec-exp_binary64_6266` `exp-diff_binary64_6264` `exp-neg_binary64_6263` `e-exp-1_binary64_6261` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `rem-log-exp_binary64_6257` `rem-exp-log_binary64_6256` `cube-neg_binary64_6243` `rem-3cbrt-rft_binary64_6242` `rem-cbrt-cube_binary64_6240` `rem-cube-cbrt_binary64_6239` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `/-rgt-identity_binary64_6207` `sub0-neg_binary64_6203` `--rgt-identity_binary64_6202` `+-rgt-identity_binary64_6201` `+-lft-identity_binary64_6200` `mul0-rgt_binary64_6199` `mul0-lft_binary64_6198` `div0_binary64_6197` `+-inverses_binary64_6195` `lft-mult-inverse_binary64_6194` `rgt-mult-inverse_binary64_6193` `remove-double-div_binary64_6192` `difference-of-sqr--1_binary64_6187` `difference-of-sqr-1_binary64_6186` `cancel-sign-sub_binary64_6181` `distribute-frac-neg_binary64_6179` `distribute-neg-out_binary64_6178` `distribute-lft1-in_binary64_6171` `count-2_binary64_6164` `associate-/l/_binary64_6163` `associate-/r/_binary64_6162` `associate-/l_binary64_6161` `associate-/r_binary64_6160` `associate--r-_binary64_6155` `associate--l-_binary64_6154` `associate-+l-_binary64_6151` `associate-+l+_binary64_6149`

Counts

207 → 647

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	647	10003
1	1976	9439

prune5.7s (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	637	10	647
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	640	10	650

Error

0.1b

Counts

650 → 10

Compiler

Compiled 49408 to 34093 computations (31% saved)

localize44.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1))) (.f64 (-.f64 (sqrt.f64 5) -1) (+.f64 3 (sqrt.f64 5))))
0.3b	(+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (*.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1)))
0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite19.4s (6.9%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

1120×	`frac-times_binary64_6226`
586×	`associate-*r/_binary64_6158`
578×	`frac-add_binary64_6224`
554×	`associate-*l/_binary64_6159`
439×	`flip3--_binary64_6220` `flip--_binary64_6191`
413×	`flip3-+_binary64_6219` `flip-+_binary64_6190`
291×	`associate-/l/_binary64_6163`
56×	`distribute-rgt-in_binary64_6166` `distribute-lft-in_binary64_6165`
33×	`cancel-sign-sub-inv_binary64_6182`
21×	`add-sqr-sqrt_binary64_6238` `*-un-lft-identity_binary64_6216`
19×	`add-cube-cbrt_binary64_6251`
18×	`add-exp-log_binary64_6254` `add-cbrt-cube_binary64_6252`
13×	`pow1_binary64_6277`
11×	`sub-neg_binary64_6209`
8×	`add-log-exp_binary64_6255` `associate-+r+_binary64_6148` `associate-/r/_binary64_6162`
7×	`prod-exp_binary64_6265` `cbrt-unprod_binary64_6249`
6×	`pow-prod-down_binary64_6287` `associate-l_binary64_6157`
4×	`associate-+l+_binary64_6149`
3×	`sqrt-prod_binary64_6232` `times-frac_binary64_6222` `associate-/l*_binary64_6161`
2×	`div-exp_binary64_6267` `cbrt-undiv_binary64_6250`
1×	`diff-cos_binary64_6367` `diff-log_binary64_6308` `difference-of-squares_binary64_6185` `distribute-lft-out--_binary64_6168` `associate-r_binary64_6156` `-commutative_binary64_6147` `sum-log_binary64_6307` `+-commutative_binary64_6146` `frac-2neg_binary64_6227` `clear-num_binary64_6215` `div-inv_binary64_6213` `associate-/r_binary64_6160`

Counts

4 → 731

Calls

4 calls:

62.0ms	(/.f64 (+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1))) (.f64 (-.f64 (sqrt.f64 5) -1) (+.f64 3 (sqrt.f64 5))))
31.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
29.0ms	(+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (*.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

Compiler

Compiled 96103 to 82339 computations (14.3% saved)

series2.4s (0.9%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

867.0ms	(/.f64 (+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1))) (.f64 (-.f64 (sqrt.f64 5) -1) (+.f64 3 (sqrt.f64 5))))
604.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
546.0ms	(+.f64 (.f64 (+.f64 (sqrt.f64 5) 3) (.f64 (/.f64 (cos.f64 x) 2) (+.f64 5 -1))) (.f64 (.f64 (-.f64 (*.f64 3 3) 5) (/.f64 (cos.f64 y) 2)) (-.f64 (sqrt.f64 5) -1)))
170.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

Compiler

Compiled 9388 to 7695 computations (18% saved)

simplify4.7s (1.7%)

Algorithm

1×	egg-herbie

Rules

400×	`+-commutative_binary64_6146`
165×	`distribute-rgt-in_binary64_6166` `distribute-lft-in_binary64_6165`
126×	`sub-neg_binary64_6209`
85×	`associate-/l*_binary64_6161`
82×	`associate-/r*_binary64_6160`
70×	`cancel-sign-sub-inv_binary64_6182`
59×	`neg-sub0_binary64_6211` `associate-+r+_binary64_6148`
57×	`neg-mul-1_binary64_6212`
54×	`sqr-pow_binary64_6188`
49×	`times-frac_binary64_6222`
48×	`distribute-neg-in_binary64_6177`
43×	`mul-1-neg_binary64_6208`
38×	`distribute-rgt-neg-in_binary64_6174`
29×	`associate-/l/_binary64_6163`
23×	`associate-*r/_binary64_6158` `associate--l+_binary64_6153`
22×	`distribute-lft-neg-out_binary64_6175`
21×	`distribute-lft-neg-in_binary64_6173`
20×	`unpow3_binary64_6282` `cube-mult_binary64_6246` `pow-sqr_binary64_6189` `distribute-lft-out_binary64_6167` `associate--r+_binary64_6152`
17×	`difference-of-squares_binary64_6185`
12×	`associate-/r/_binary64_6162`
11×	`distribute-neg-frac_binary64_6180`
9×	`unswap-sqr_binary64_6184`
8×	`swap-sqr_binary64_6183`
7×	`associate-*l/_binary64_6159`
6×	`cube-prod_binary64_6244` `distribute-rgt-neg-out_binary64_6176` `distribute-rgt-out_binary64_6169`
5×	`div-sub_binary64_6221`
4×	`log-prod_binary64_6302` `unpow2_binary64_6281` `pow-plus_binary64_6279` `exp-prod_binary64_6268` `exp-sum_binary64_6262` `cube-div_binary64_6245` `unsub-neg_binary64_6210` `*-rgt-identity_binary64_6206`
3×	`rem-square-sqrt_binary64_6228` `distribute-rgt-out--_binary64_6170` `associate-+r-_binary64_6150`
2×	`log-div_binary64_6303` `rem-sqrt-square_binary64_6229` `*-lft-identity_binary64_6205`
1×	`exp-sqrt_binary64_6269` `div-exp_binary64_6267` `prod-exp_binary64_6265` `1-exp_binary64_6260` `rem-3cbrt-lft_binary64_6241` `remove-double-neg_binary64_6204` `*-inverses_binary64_6196` `difference-of-sqr--1_binary64_6187` `distribute-neg-out_binary64_6178` `distribute-rgt1-in_binary64_6172` `distribute-lft1-in_binary64_6171`
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_6479` `erf-erfc_binary64_6478` `erf-odd_binary64_6477` `if-if-and-not_binary64_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `not-gte_binary64_6468` `not-lte_binary64_6467` `not-gt_binary64_6466` `not-lt_binary64_6465` `gte-same_binary64_6464` `lte-same_binary64_6463` `gt-same_binary64_6462` `lt-same_binary64_6461` `sinh---cosh_binary64_6408` `sinh-+-cosh_binary64_6407` `sinh-cosh_binary64_6406` `tanh-def-c_binary64_6405` `tanh-def-b_binary64_6404` `tanh-def-a_binary64_6403` `cosh-def_binary64_6402` `sinh-def_binary64_6401` `tan-neg_binary64_6348` `cos-neg_binary64_6347` `sin-neg_binary64_6346` `tan-0_binary64_6345` `cos-0_binary64_6344` `sin-0_binary64_6343` `hang-m-tan_binary64_6342` `hang-p-tan_binary64_6341` `hang-m0-tan_binary64_6340` `hang-p0-tan_binary64_6339` `hang-0m-tan_binary64_6338` `hang-0p-tan_binary64_6337` `tan-+PI/2_binary64_6336` `tan-+PI_binary64_6335` `tan-PI_binary64_6334` `tan-PI/3_binary64_6333` `tan-PI/4_binary64_6332` `tan-PI/6_binary64_6331` `cos-+PI/2_binary64_6330` `cos-+PI_binary64_6329` `cos-PI_binary64_6328` `cos-PI/2_binary64_6327` `cos-PI/3_binary64_6326` `cos-PI/4_binary64_6325` `cos-PI/6_binary64_6324` `sin-+PI/2_binary64_6323` `sin-+PI_binary64_6322` `sin-PI_binary64_6321` `sin-PI/2_binary64_6320` `sin-PI/3_binary64_6319` `sin-PI/4_binary64_6318` `sin-PI/6_binary64_6317` `sub-1-sin_binary64_6316` `sub-1-cos_binary64_6315` `-1-add-sin_binary64_6314` `-1-add-cos_binary64_6313` `1-sub-sin_binary64_6312` `1-sub-cos_binary64_6311` `cos-sin-sum_binary64_6310` `log-E_binary64_6306` `log-pow_binary64_6305` `log-rec_binary64_6304` `pow-base-0_binary64_6300` `unpow1/3_binary64_6283` `unpow1/2_binary64_6280` `exp-to-pow_binary64_6278` `pow-base-1_binary64_6276` `unpow0_binary64_6275` `unpow1_binary64_6274` `unpow-1_binary64_6273` `exp-lft-cube_binary64_6272` `exp-lft-sqr_binary64_6271` `exp-cbrt_binary64_6270` `rec-exp_binary64_6266` `exp-diff_binary64_6264` `exp-neg_binary64_6263` `e-exp-1_binary64_6261` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `rem-log-exp_binary64_6257` `rem-exp-log_binary64_6256` `cube-unmult_binary64_6253` `cube-neg_binary64_6243` `rem-3cbrt-rft_binary64_6242` `rem-cbrt-cube_binary64_6240` `rem-cube-cbrt_binary64_6239` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `/-rgt-identity_binary64_6207` `sub0-neg_binary64_6203` `--rgt-identity_binary64_6202` `+-rgt-identity_binary64_6201` `+-lft-identity_binary64_6200` `mul0-rgt_binary64_6199` `mul0-lft_binary64_6198` `div0_binary64_6197` `+-inverses_binary64_6195` `lft-mult-inverse_binary64_6194` `rgt-mult-inverse_binary64_6193` `remove-double-div_binary64_6192` `difference-of-sqr-1_binary64_6186` `cancel-sign-sub_binary64_6181` `distribute-frac-neg_binary64_6179` `distribute-lft-out--_binary64_6168` `count-2_binary64_6164` `associate-l_binary64_6157` `associate-r_binary64_6156` `associate--r-_binary64_6155` `associate--l-_binary64_6154` `associate-+l-_binary64_6151` `associate-+l+_binary64_6149` `*-commutative_binary64_6147`

Counts

779 → 2562

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	2153	64363
1	4088	62619

prune3.7min (78.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	2562	0	2562
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	2562	10	2572

Error

0.1b

Counts

2572 → 10

Compiler

Compiled 335713 to 290494 computations (13.5% saved)

localize38.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (cos.f64 x) (+.f64 5 -1)) (.f64 (*.f64 (cos.f64 y) (-.f64 3 (sqrt.f64 5))) (-.f64 (sqrt.f64 5) -1)))
0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
1.0b	(-.f64 3 (sqrt.f64 5))
1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite1.0s (0.4%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

72×	`associate-*r/_binary64_6158`
53×	`distribute-rgt-in_binary64_6166` `distribute-lft-in_binary64_6165`
41×	`flip3--_binary64_6220` `flip--_binary64_6191`
39×	`cancel-sign-sub-inv_binary64_6182`
36×	`frac-times_binary64_6226`
25×	`add-sqr-sqrt_binary64_6238`
23×	`*-un-lft-identity_binary64_6216`
19×	`add-cube-cbrt_binary64_6251`
16×	`frac-add_binary64_6224`
13×	`pow1_binary64_6277` `add-exp-log_binary64_6254` `add-cbrt-cube_binary64_6252`
12×	`sub-neg_binary64_6209` `associate-*l/_binary64_6159`
10×	`add-log-exp_binary64_6255`
9×	`flip3-+_binary64_6219` `flip-+_binary64_6190`
8×	`associate-+r+_binary64_6148`
7×	`sqrt-prod_binary64_6232`
6×	`pow-prod-down_binary64_6287` `prod-exp_binary64_6265` `cbrt-unprod_binary64_6249` `associate-l_binary64_6157`
3×	`difference-of-squares_binary64_6185`
2×	`diff-log_binary64_6308` `distribute-lft-out--_binary64_6168` `associate-+l+_binary64_6149`
1×	`diff-cos_binary64_6367` `associate-r_binary64_6156` `*-commutative_binary64_6147` `sum-log_binary64_6307` `+-commutative_binary64_6146`

Counts

4 → 156

Calls

4 calls:

30.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
13.0ms	(+.f64 (.f64 (cos.f64 x) (+.f64 5 -1)) (.f64 (*.f64 (cos.f64 y) (-.f64 3 (sqrt.f64 5))) (-.f64 (sqrt.f64 5) -1)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
5.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 13210 to 9305 computations (29.6% saved)

series1.5s (0.5%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

631.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (*.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (-.f64 (cos.f64 x) (cos.f64 y)))))
562.0ms	(+.f64 (.f64 (cos.f64 x) (+.f64 5 -1)) (.f64 (*.f64 (cos.f64 y) (-.f64 3 (sqrt.f64 5))) (-.f64 (sqrt.f64 5) -1)))
166.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 6296 to 5051 computations (19.8% saved)

simplify609.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

518×	`distribute-rgt-in_binary64_6166`
511×	`distribute-lft-in_binary64_6165`
261×	`*-commutative_binary64_6147`
190×	`associate-r_binary64_6156`
113×	`sub-neg_binary64_6209`
111×	`cancel-sign-sub-inv_binary64_6182`
101×	`+-commutative_binary64_6146`
80×	`associate-l_binary64_6157`
56×	`neg-sub0_binary64_6211`
54×	`neg-mul-1_binary64_6212`
53×	`sqr-pow_binary64_6188`
50×	`distribute-rgt-neg-in_binary64_6174`
46×	`associate-+r+_binary64_6148`
39×	`distribute-neg-in_binary64_6177`
33×	`distribute-lft-neg-in_binary64_6173`
32×	`unswap-sqr_binary64_6184`
31×	`distribute-lft-neg-out_binary64_6175`
24×	`pow-sqr_binary64_6189`
20×	`associate--l+_binary64_6153`
18×	`unpow3_binary64_6282` `cube-mult_binary64_6246` `distribute-rgt-neg-out_binary64_6176` `distribute-rgt-out_binary64_6169`
17×	`associate--r+_binary64_6152`
16×	`difference-of-squares_binary64_6185`
15×	`swap-sqr_binary64_6183`
11×	`associate-/l*_binary64_6161`
10×	`exp-prod_binary64_6268` `mul-1-neg_binary64_6208`
9×	`cube-unmult_binary64_6253` `cube-prod_binary64_6244`
8×	`distribute-neg-frac_binary64_6180` `associate-/r*_binary64_6160`
7×	`unsub-neg_binary64_6210`
5×	`log-prod_binary64_6302` `unpow2_binary64_6281` `pow-plus_binary64_6279`
4×	`exp-sum_binary64_6262` `rem-sqrt-square_binary64_6229` `rem-square-sqrt_binary64_6228`
3×	`distribute-rgt-out--_binary64_6170`
2×	`div-exp_binary64_6267` `cube-div_binary64_6245` `rem-3cbrt-lft_binary64_6241` `-lft-identity_binary64_6205` `difference-of-sqr--1_binary64_6187` `distribute-lft-out_binary64_6167` `associate-l/_binary64_6159` `associate-*r/_binary64_6158` `associate-+r-_binary64_6150`
1×	`prod-exp_binary64_6265` `1-exp_binary64_6260` `times-frac_binary64_6222` `div-sub_binary64_6221` `-rgt-identity_binary64_6206` `remove-double-neg_binary64_6204` `-inverses_binary64_6196`
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_6479` `erf-erfc_binary64_6478` `erf-odd_binary64_6477` `if-if-and-not_binary64_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `not-gte_binary64_6468` `not-lte_binary64_6467` `not-gt_binary64_6466` `not-lt_binary64_6465` `gte-same_binary64_6464` `lte-same_binary64_6463` `gt-same_binary64_6462` `lt-same_binary64_6461` `sinh---cosh_binary64_6408` `sinh-+-cosh_binary64_6407` `sinh-cosh_binary64_6406` `tanh-def-c_binary64_6405` `tanh-def-b_binary64_6404` `tanh-def-a_binary64_6403` `cosh-def_binary64_6402` `sinh-def_binary64_6401` `tan-neg_binary64_6348` `cos-neg_binary64_6347` `sin-neg_binary64_6346` `tan-0_binary64_6345` `cos-0_binary64_6344` `sin-0_binary64_6343` `hang-m-tan_binary64_6342` `hang-p-tan_binary64_6341` `hang-m0-tan_binary64_6340` `hang-p0-tan_binary64_6339` `hang-0m-tan_binary64_6338` `hang-0p-tan_binary64_6337` `tan-+PI/2_binary64_6336` `tan-+PI_binary64_6335` `tan-PI_binary64_6334` `tan-PI/3_binary64_6333` `tan-PI/4_binary64_6332` `tan-PI/6_binary64_6331` `cos-+PI/2_binary64_6330` `cos-+PI_binary64_6329` `cos-PI_binary64_6328` `cos-PI/2_binary64_6327` `cos-PI/3_binary64_6326` `cos-PI/4_binary64_6325` `cos-PI/6_binary64_6324` `sin-+PI/2_binary64_6323` `sin-+PI_binary64_6322` `sin-PI_binary64_6321` `sin-PI/2_binary64_6320` `sin-PI/3_binary64_6319` `sin-PI/4_binary64_6318` `sin-PI/6_binary64_6317` `sub-1-sin_binary64_6316` `sub-1-cos_binary64_6315` `-1-add-sin_binary64_6314` `-1-add-cos_binary64_6313` `1-sub-sin_binary64_6312` `1-sub-cos_binary64_6311` `cos-sin-sum_binary64_6310` `log-E_binary64_6306` `log-pow_binary64_6305` `log-rec_binary64_6304` `log-div_binary64_6303` `pow-base-0_binary64_6300` `unpow1/3_binary64_6283` `unpow1/2_binary64_6280` `exp-to-pow_binary64_6278` `pow-base-1_binary64_6276` `unpow0_binary64_6275` `unpow1_binary64_6274` `unpow-1_binary64_6273` `exp-lft-cube_binary64_6272` `exp-lft-sqr_binary64_6271` `exp-cbrt_binary64_6270` `exp-sqrt_binary64_6269` `rec-exp_binary64_6266` `exp-diff_binary64_6264` `exp-neg_binary64_6263` `e-exp-1_binary64_6261` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `rem-log-exp_binary64_6257` `rem-exp-log_binary64_6256` `cube-neg_binary64_6243` `rem-3cbrt-rft_binary64_6242` `rem-cbrt-cube_binary64_6240` `rem-cube-cbrt_binary64_6239` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `/-rgt-identity_binary64_6207` `sub0-neg_binary64_6203` `--rgt-identity_binary64_6202` `+-rgt-identity_binary64_6201` `+-lft-identity_binary64_6200` `mul0-rgt_binary64_6199` `mul0-lft_binary64_6198` `div0_binary64_6197` `+-inverses_binary64_6195` `lft-mult-inverse_binary64_6194` `rgt-mult-inverse_binary64_6193` `remove-double-div_binary64_6192` `difference-of-sqr-1_binary64_6186` `cancel-sign-sub_binary64_6181` `distribute-frac-neg_binary64_6179` `distribute-neg-out_binary64_6178` `distribute-rgt1-in_binary64_6172` `distribute-lft1-in_binary64_6171` `distribute-lft-out--_binary64_6168` `count-2_binary64_6164` `associate-/l/_binary64_6163` `associate-/r/_binary64_6162` `associate--r-_binary64_6155` `associate--l-_binary64_6154` `associate-+l-_binary64_6151` `associate-+l+_binary64_6149`

Counts

192 → 571

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	625	9429
1	1892	8886

prune6.0s (2.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	570	1	571
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	572	9	581

Error

0.1b

Counts

581 → 9

Compiler

Compiled 50781 to 36938 computations (27.3% saved)

localize42.0ms (0%)

Local error

Found 4 expressions with local error:

0.4b	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (/.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 (cos.f64 y) (cos.f64 y))) (+.f64 (cos.f64 y) (cos.f64 x))))))
0.4b	(+.f64 (cos.f64 y) (cos.f64 x))
1.0b	(-.f64 3 (sqrt.f64 5))
1.8b	(-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 (cos.f64 y) (cos.f64 y)))

rewrite494.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

25×	`associate-*r/_binary64_6158`
18×	`add-exp-log_binary64_6254` `add-cbrt-cube_binary64_6252`
16×	`frac-times_binary64_6226`
14×	`flip3--_binary64_6220` `flip--_binary64_6191`
13×	`pow1_binary64_6277`
12×	`add-sqr-sqrt_binary64_6238` `*-un-lft-identity_binary64_6216`
10×	`add-log-exp_binary64_6255`
9×	`prod-exp_binary64_6265` `cbrt-unprod_binary64_6249`
8×	`add-cube-cbrt_binary64_6251` `associate-*l/_binary64_6159`
7×	`cancel-sign-sub-inv_binary64_6182` `sqrt-prod_binary64_6232`
6×	`pow-prod-down_binary64_6287` `associate-l_binary64_6157`
4×	`cos-mult_binary64_6370`
3×	`difference-of-squares_binary64_6185`
2×	`diff-log_binary64_6308` `sub-neg_binary64_6209` `sqr-cos-a_binary64_6365`
1×	`frac-sub_binary64_6225` `sub-div_binary64_6223` `associate--l+_binary64_6153` `associate--r+_binary64_6152` `distribute-lft-out--_binary64_6168` `sum-cos_binary64_6369` `sum-log_binary64_6307` `flip3-+_binary64_6219` `flip-+_binary64_6190` `distribute-lft-out_binary64_6167` `+-commutative_binary64_6146` `div-exp_binary64_6267` `cbrt-undiv_binary64_6250` `associate-r_binary64_6156` `*-commutative_binary64_6147`

Counts

4 → 93

Calls

4 calls:

30.0ms	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (/.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 (cos.f64 y) (cos.f64 y))) (+.f64 (cos.f64 y) (cos.f64 x))))))
6.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 (cos.f64 y) (cos.f64 y)))
5.0ms	(-.f64 3 (sqrt.f64 5))
4.0ms	(+.f64 (cos.f64 y) (cos.f64 x))

Compiler

Compiled 8270 to 4891 computations (40.9% saved)

series1.8s (0.6%)

Error

0.1b

Counts

4 → 36

Calls

4 calls:

1.2s	(.f64 (sqrt.f64 2) (.f64 (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)) (.f64 (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)) (/.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (*.f64 (cos.f64 y) (cos.f64 y))) (+.f64 (cos.f64 y) (cos.f64 x))))))
247.0ms	(-.f64 (.f64 (cos.f64 x) (cos.f64 x)) (.f64 (cos.f64 y) (cos.f64 y)))
159.0ms	(+.f64 (cos.f64 y) (cos.f64 x))
0.0ms	(-.f64 3 (sqrt.f64 5))

Compiler

Compiled 7708 to 5835 computations (24.3% saved)

simplify799.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-r_binary64_6156`
416×	`associate-l_binary64_6157`
208×	`associate-/l*_binary64_6161`
144×	`*-commutative_binary64_6147`
119×	`times-frac_binary64_6222`
114×	`associate-*r/_binary64_6158`
113×	`associate--l+_binary64_6153`
103×	`distribute-rgt-in_binary64_6166`
100×	`sub-neg_binary64_6209` `associate-/r*_binary64_6160`
99×	`distribute-lft-in_binary64_6165`
93×	`associate-*l/_binary64_6159`
82×	`cancel-sign-sub-inv_binary64_6182`
70×	`+-commutative_binary64_6146`
52×	`sqr-pow_binary64_6188`
48×	`neg-mul-1_binary64_6212` `neg-sub0_binary64_6211`
43×	`unswap-sqr_binary64_6184`
41×	`distribute-rgt-neg-in_binary64_6174`
36×	`associate-+r+_binary64_6148`
31×	`distribute-neg-in_binary64_6177`
30×	`associate-/r/_binary64_6162`
28×	`pow-sqr_binary64_6189`
25×	`distribute-lft-neg-in_binary64_6173`
21×	`difference-of-squares_binary64_6185`
17×	`distribute-lft-neg-out_binary64_6175`
16×	`associate--l-_binary64_6154`
14×	`associate--r+_binary64_6152`
13×	`unpow3_binary64_6282` `cube-mult_binary64_6246`
11×	`distribute-rgt-out_binary64_6169`
10×	`cube-unmult_binary64_6253`
9×	`swap-sqr_binary64_6183`
8×	`unpow2_binary64_6281` `pow-plus_binary64_6279` `exp-prod_binary64_6268` `distribute-neg-frac_binary64_6180`
6×	`log-prod_binary64_6302`
4×	`exp-sum_binary64_6262` `cube-prod_binary64_6244` `div-sub_binary64_6221` `difference-of-sqr-1_binary64_6186` `distribute-rgt-neg-out_binary64_6176`
3×	`rem-sqrt-square_binary64_6229` `rem-square-sqrt_binary64_6228`
2×	`log-div_binary64_6303` `div-exp_binary64_6267` `exp-diff_binary64_6264` `cube-div_binary64_6245` `+-inverses_binary64_6195` `distribute-rgt-out--_binary64_6170` `count-2_binary64_6164` `associate-+r-_binary64_6150`
1×	`cos-0_binary64_6344` `sub-1-cos_binary64_6315` `1-sub-cos_binary64_6311` `prod-exp_binary64_6265` `1-exp_binary64_6260` `rem-3cbrt-lft_binary64_6241` `-rgt-identity_binary64_6206` `-lft-identity_binary64_6205` `*-inverses_binary64_6196` `distribute-lft-out_binary64_6167`
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_6479` `erf-erfc_binary64_6478` `erf-odd_binary64_6477` `if-if-and-not_binary64_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `not-gte_binary64_6468` `not-lte_binary64_6467` `not-gt_binary64_6466` `not-lt_binary64_6465` `gte-same_binary64_6464` `lte-same_binary64_6463` `gt-same_binary64_6462` `lt-same_binary64_6461` `sinh---cosh_binary64_6408` `sinh-+-cosh_binary64_6407` `sinh-cosh_binary64_6406` `tanh-def-c_binary64_6405` `tanh-def-b_binary64_6404` `tanh-def-a_binary64_6403` `cosh-def_binary64_6402` `sinh-def_binary64_6401` `tan-neg_binary64_6348` `cos-neg_binary64_6347` `sin-neg_binary64_6346` `tan-0_binary64_6345` `sin-0_binary64_6343` `hang-m-tan_binary64_6342` `hang-p-tan_binary64_6341` `hang-m0-tan_binary64_6340` `hang-p0-tan_binary64_6339` `hang-0m-tan_binary64_6338` `hang-0p-tan_binary64_6337` `tan-+PI/2_binary64_6336` `tan-+PI_binary64_6335` `tan-PI_binary64_6334` `tan-PI/3_binary64_6333` `tan-PI/4_binary64_6332` `tan-PI/6_binary64_6331` `cos-+PI/2_binary64_6330` `cos-+PI_binary64_6329` `cos-PI_binary64_6328` `cos-PI/2_binary64_6327` `cos-PI/3_binary64_6326` `cos-PI/4_binary64_6325` `cos-PI/6_binary64_6324` `sin-+PI/2_binary64_6323` `sin-+PI_binary64_6322` `sin-PI_binary64_6321` `sin-PI/2_binary64_6320` `sin-PI/3_binary64_6319` `sin-PI/4_binary64_6318` `sin-PI/6_binary64_6317` `sub-1-sin_binary64_6316` `-1-add-sin_binary64_6314` `-1-add-cos_binary64_6313` `1-sub-sin_binary64_6312` `cos-sin-sum_binary64_6310` `log-E_binary64_6306` `log-pow_binary64_6305` `log-rec_binary64_6304` `pow-base-0_binary64_6300` `unpow1/3_binary64_6283` `unpow1/2_binary64_6280` `exp-to-pow_binary64_6278` `pow-base-1_binary64_6276` `unpow0_binary64_6275` `unpow1_binary64_6274` `unpow-1_binary64_6273` `exp-lft-cube_binary64_6272` `exp-lft-sqr_binary64_6271` `exp-cbrt_binary64_6270` `exp-sqrt_binary64_6269` `rec-exp_binary64_6266` `exp-neg_binary64_6263` `e-exp-1_binary64_6261` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `rem-log-exp_binary64_6257` `rem-exp-log_binary64_6256` `cube-neg_binary64_6243` `rem-3cbrt-rft_binary64_6242` `rem-cbrt-cube_binary64_6240` `rem-cube-cbrt_binary64_6239` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `unsub-neg_binary64_6210` `mul-1-neg_binary64_6208` `/-rgt-identity_binary64_6207` `remove-double-neg_binary64_6204` `sub0-neg_binary64_6203` `--rgt-identity_binary64_6202` `+-rgt-identity_binary64_6201` `+-lft-identity_binary64_6200` `mul0-rgt_binary64_6199` `mul0-lft_binary64_6198` `div0_binary64_6197` `lft-mult-inverse_binary64_6194` `rgt-mult-inverse_binary64_6193` `remove-double-div_binary64_6192` `difference-of-sqr--1_binary64_6187` `cancel-sign-sub_binary64_6181` `distribute-frac-neg_binary64_6179` `distribute-neg-out_binary64_6178` `distribute-rgt1-in_binary64_6172` `distribute-lft1-in_binary64_6171` `distribute-lft-out--_binary64_6168` `associate-/l/_binary64_6163` `associate--r-_binary64_6155` `associate-+l-_binary64_6151` `associate-+l+_binary64_6149`

Counts

129 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	460	6043
1	1350	5384

prune1.5s (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	193	9	202

Error

0.1b

Counts

202 → 9

Compiler

Compiled 18413 to 12348 computations (32.9% saved)

regimes1.4s (0.5%)

Accuracy

Total 0.3b remaining (73%)

Threshold costs 0.3b (73%)

Compiler

Compiled 19469 to 16054 computations (17.5% saved)

bsearch0.0ms (0%)

simplify9.0ms (0%)

Algorithm

1×	egg-herbie

Rules

17×	`+-commutative_binary64_6146`
15×	`*-commutative_binary64_6147`
12×	`sub-neg_binary64_6209`
7×	`neg-mul-1_binary64_6212` `neg-sub0_binary64_6211`
2×	`distribute-neg-frac_binary64_6180`
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_6476` `if-if-and_binary64_6475` `if-if-or-not_binary64_6474` `if-if-or_binary64_6473` `if-not_binary64_6472` `if-same_binary64_6471` `if-false_binary64_6470` `if-true_binary64_6469` `tan-0_binary64_6345` `cos-0_binary64_6344` `sin-0_binary64_6343` `unpow1_binary64_6274` `e-exp-1_binary64_6261` `1-exp_binary64_6260` `exp-1-e_binary64_6259` `exp-0_binary64_6258` `sqr-abs_binary64_6231` `sqr-neg_binary64_6230` `unsub-neg_binary64_6210` `mul-1-neg_binary64_6208` `/-rgt-identity_binary64_6207` `-rgt-identity_binary64_6206` `-lft-identity_binary64_6205` `remove-double-neg_binary64_6204` `sub0-neg_binary64_6203` `--rgt-identity_binary64_6202` `+-rgt-identity_binary64_6201` `+-lft-identity_binary64_6200` `cancel-sign-sub-inv_binary64_6182` `cancel-sign-sub_binary64_6181` `distribute-frac-neg_binary64_6179` `distribute-neg-out_binary64_6178` `distribute-neg-in_binary64_6177` `distribute-rgt-neg-out_binary64_6176` `distribute-lft-neg-out_binary64_6175` `distribute-rgt-neg-in_binary64_6174` `distribute-lft-neg-in_binary64_6173`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	111
1	64	111
2	84	111
3	97	111
4	106	111
5	108	111

Proof

(/ f64 (+ f64 2 (* f64 (sqrt f64 2) (* f64 (- f64 (sin f64 h0) (/ f64 (sin f64 h1) 16)) (* f64 (- f64 (sin f64 h1) (/ f64 (sin f64 h0) 16)) (- f64 (cos f64 h1) (cos f64 h0)))))) (+ f64 3 (* f64 3 (/ f64 (+ f64 (* f64 (+ f64 (sqrt f64 5) 3) (* f64 (/ f64 (cos f64 h1) 2) (+ f64 5 -1))) (* f64 (* f64 (- f64 (* f64 3 3) 5) (/ f64 (cos f64 h0) 2)) (- f64 (sqrt f64 5) -1))) (=> (* f64 (- f64 (sqrt f64 5) -1) (+ f64 3 (sqrt f64 5))))))))
*-commutative_binary64_6147 =>
(/ f64 (+ f64 2 (* f64 (sqrt f64 2) (* f64 (- f64 (sin f64 h0) (/ f64 (sin f64 h1) 16)) (* f64 (- f64 (sin f64 h1) (/ f64 (sin f64 h0) 16)) (- f64 (cos f64 h1) (cos f64 h0)))))) (+ f64 3 (* f64 3 (/ f64 (+ f64 (* f64 (=> (+ f64 (sqrt f64 5) 3)) (* f64 (/ f64 (cos f64 h1) 2) (+ f64 5 -1))) (* f64 (* f64 (- f64 (* f64 3 3) 5) (/ f64 (cos f64 h0) 2)) (- f64 (sqrt f64 5) -1))) (* f64 (+ f64 3 (sqrt f64 5)) (- f64 (sqrt f64 5) -1))))))
+-commutative_binary64_6146 =>
(/ f64 (+ f64 2 (* f64 (sqrt f64 2) (* f64 (- f64 (sin f64 h0) (/ f64 (sin f64 h1) 16)) (* f64 (- f64 (sin f64 h1) (/ f64 (sin f64 h0) 16)) (- f64 (cos f64 h1) (cos f64 h0)))))) (+ f64 3 (* f64 3 (/ f64 (+ f64 (* f64 (+ f64 3 (sqrt f64 5)) (* f64 (/ f64 (cos f64 h1) 2) (+ f64 5 -1))) (* f64 (* f64 (- f64 (* f64 3 3) 5) (/ f64 (cos f64 h0) 2)) (- f64 (sqrt f64 5) -1))) (* f64 (+ f64 3 (sqrt f64 5)) (- f64 (sqrt f64 5) -1))))))

end0.0ms (0%)

sample10.1s (3.6%)

Algorithm

1×

intervals

Results

3.2s	3568×	body	1024	valid
845.0ms	1402×	body	512	valid
496.0ms	2455×	body	128	valid
225.0ms	554×	body	256	valid
32.0ms	21×	body	2048	valid

Compiler

Compiled 6576 to 5425 computations (17.5% saved)

Details

analyze760.0ms (0.3%)

sample171.0ms (0.1%)

simplify219.0ms (0.1%)

prune30.0ms (0%)

localize32.0ms (0%)

rewrite936.0ms (0.3%)

series1.4s (0.5%)

simplify620.0ms (0.2%)

prune5.7s (2%)

localize44.0ms (0%)

rewrite19.4s (6.9%)

series2.4s (0.9%)

simplify4.7s (1.7%)

prune3.7min (78.1%)

localize38.0ms (0%)

rewrite1.0s (0.4%)

series1.5s (0.5%)

simplify609.0ms (0.2%)

prune6.0s (2.1%)

localize42.0ms (0%)

rewrite494.0ms (0.2%)

series1.8s (0.6%)

simplify799.0ms (0.3%)

prune1.5s (0.5%)

regimes1.4s (0.5%)

bsearch0.0ms (0%)

simplify9.0ms (0%)

end0.0ms (0%)

sample10.1s (3.6%)

Profiling