Details

analyze602.0ms (12.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

Compiler

Compiled 30 to 30 computations (0% saved)

sample89.0ms (1.9%)

Algorithm

1×

intervals

Results

36.0ms	195×	body	128	valid
20.0ms	25×	body	1024	valid
13.0ms	24×	body	512	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify153.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

566×	`associate-l_binary64_19`
532×	`unswap-sqr_binary64_46`
440×	`associate-r_binary64_18`
375×	`distribute-rgt-out_binary64_31`
367×	`associate-/r/_binary64_24`
356×	`associate-/r*_binary64_22`
337×	`associate-*l/_binary64_21`
336×	`associate-/l/_binary64_25`
302×	`associate-*r/_binary64_20`
197×	`times-frac_binary64_84`
111×	`*-commutative_binary64_9`
99×	`associate-/l*_binary64_23`
92×	`distribute-rgt-in_binary64_28`
78×	`swap-sqr_binary64_45`
67×	`distribute-lft-in_binary64_27`
62×	`sqr-pow_binary64_50`
42×	`distribute-lft-out_binary64_29`
36×	`pow-sqr_binary64_51`
27×	`pow-plus_binary64_141`
16×	`cube-unmult_binary64_115`
15×	`cube-prod_binary64_106`
8×	`+-commutative_binary64_8`
5×	`unpow3_binary64_144`
4×	`*-rgt-identity_binary64_68`
3×	`unpow2_binary64_143` `unpow1_binary64_136` `*-lft-identity_binary64_67` `associate-+l+_binary64_11` `associate-+r+_binary64_10`
2×	`/-rgt-identity_binary64_69`
1×	`1-exp_binary64_122` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-lft1-in_binary64_33` `count-2_binary64_26`
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_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `log-pow_binary64_167` `log-rec_binary64_166` `log-div_binary64_165` `log-prod_binary64_164` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `exp-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `exp-sum_binary64_124` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-mult_binary64_108` `cube-div_binary64_107` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `rem-sqrt-square_binary64_91` `rem-square-sqrt_binary64_90` `div-sub_binary64_83` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `sub-neg_binary64_71` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `cancel-sign-sub-inv_binary64_44` `cancel-sign-sub_binary64_43` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39` `distribute-rgt-neg-out_binary64_38` `distribute-lft-neg-out_binary64_37` `distribute-rgt-neg-in_binary64_36` `distribute-lft-neg-in_binary64_35` `distribute-rgt1-in_binary64_34` `distribute-rgt-out--_binary64_32` `distribute-lft-out--_binary64_30` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--l+_binary64_15` `associate--r+_binary64_14` `associate-+l-_binary64_13` `associate-+r-_binary64_12`

Counts

1 → 3

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	45
1	57	42
2	171	42
3	445	42
4	1982	42
5	4748	42

prune8.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	2	1	3
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	3	1	4

Error

2.3b

Counts

4 → 1

Compiler

Compiled 110 to 98 computations (10.9% saved)

localize20.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 kx) 2)
0.7b	(/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.8b	(*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
6.8b	(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite494.0ms (10.5%)

Algorithm

1×	rewrite-expression-head

Error

1.3b

Rules

87×	`times-frac_binary64_84`
73×	`add-sqr-sqrt_binary64_100`
63×	`*-un-lft-identity_binary64_78`
59×	`add-cube-cbrt_binary64_113`
52×	`unpow-prod-down_binary64_157`
49×	`associate-l_binary64_19`
21×	`add-exp-log_binary64_116`
15×	`sqrt-prod_binary64_94`
8×	`pow1_binary64_139` `add-cbrt-cube_binary64_114`
6×	`unswap-sqr_binary64_46` `associate-/r*_binary64_22`
5×	`prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `sqrt-div_binary64_95` `pow-exp_binary64_146`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `unpow2_binary64_143` `sqr-pow_binary64_50` `associate-/r/_binary64_24` `pow-flip_binary64_152` `associate-/l*_binary64_23` `pow-unpow_binary64_155`
2×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `pow-to-exp_binary64_147` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29`
1×	`rem-sqrt-square_binary64_91` `cbrt-unprod_binary64_111` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `inv-pow_binary64_163` `1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-undiv_binary64_112` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow-pow_binary64_150`

Counts

4 → 158

Calls

4 calls:

28.0ms	(*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
10.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
4.0ms	(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 6638 to 5040 computations (24.1% saved)

series3.0s (64%)

Error

1.0b

Counts

4 → 54

Calls

4 calls:

1.3s	(/.f64 1 (sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
977.0ms	(sqrt.f64 (+.f64 1 (*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
564.0ms	(*.f64 (pow.f64 (/.f64 l (/.f64 Om 2)) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
26.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 5881 to 5196 computations (11.6% saved)

simplify331.0ms (7%)

Algorithm

1×	egg-herbie

Rules

386×	`associate-r_binary64_18`
373×	`associate-l_binary64_19`
357×	`times-frac_binary64_84`
273×	`*-commutative_binary64_9`
222×	`sqr-pow_binary64_50`
189×	`unswap-sqr_binary64_46`
143×	`distribute-rgt-in_binary64_28`
139×	`distribute-lft-in_binary64_27`
105×	`associate-*l/_binary64_21`
83×	`associate-*r/_binary64_20`
62×	`pow-plus_binary64_141`
55×	`exp-prod_binary64_130` `associate-/r/_binary64_24`
54×	`associate-/l*_binary64_23`
53×	`sub-neg_binary64_71`
50×	`unpow2_binary64_143`
49×	`unpow1_binary64_136`
47×	`neg-sub0_binary64_73`
46×	`cube-prod_binary64_106`
45×	`+-commutative_binary64_8`
43×	`neg-mul-1_binary64_74`
41×	`associate-/r*_binary64_22`
39×	`swap-sqr_binary64_45`
38×	`pow-sqr_binary64_51`
32×	`cancel-sign-sub-inv_binary64_44`
31×	`log-prod_binary64_164`
28×	`*-rgt-identity_binary64_68` `distribute-rgt-neg-in_binary64_36`
22×	`*-lft-identity_binary64_67`
20×	`associate-/l/_binary64_25`
19×	`distribute-lft-neg-in_binary64_35`
16×	`unpow3_binary64_144`
13×	`distribute-rgt-out_binary64_31`
12×	`log-pow_binary64_167`
10×	`cube-mult_binary64_108` `rem-sqrt-square_binary64_91` `/-rgt-identity_binary64_69`
9×	`log-div_binary64_165` `associate-+r+_binary64_10`
8×	`cube-unmult_binary64_115`
7×	`associate--r+_binary64_14`
6×	`pow-base-1_binary64_138` `unsub-neg_binary64_72` `distribute-neg-in_binary64_39` `distribute-lft-neg-out_binary64_37` `distribute-lft-out_binary64_29` `associate-+l+_binary64_11`
5×	`cube-div_binary64_107` `rem-square-sqrt_binary64_90` `associate-+r-_binary64_12`
4×	`exp-sum_binary64_124` `mul-1-neg_binary64_70` `distribute-neg-frac_binary64_42`
3×	`difference-of-squares_binary64_47`
2×	`exp-lft-sqr_binary64_133` `div-sub_binary64_83` `+-rgt-identity_binary64_63` `*-inverses_binary64_58` `distribute-rgt-out--_binary64_32`
1×	`log-rec_binary64_166` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `remove-double-neg_binary64_66` `+-lft-identity_binary64_62` `div0_binary64_59` `rgt-mult-inverse_binary64_55` `distribute-rgt1-in_binary64_34` `distribute-lft-out--_binary64_30` `associate--r-_binary64_17` `associate--l+_binary64_15` `associate-+l-_binary64_13`
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_341` `erf-erfc_binary64_340` `erf-odd_binary64_339` `if-if-and-not_binary64_338` `if-if-and_binary64_337` `if-if-or-not_binary64_336` `if-if-or_binary64_335` `if-not_binary64_334` `if-same_binary64_333` `if-false_binary64_332` `if-true_binary64_331` `not-gte_binary64_330` `not-lte_binary64_329` `not-gt_binary64_328` `not-lt_binary64_327` `gte-same_binary64_326` `lte-same_binary64_325` `gt-same_binary64_324` `lt-same_binary64_323` `sinh---cosh_binary64_270` `sinh-+-cosh_binary64_269` `sinh-cosh_binary64_268` `tanh-def-c_binary64_267` `tanh-def-b_binary64_266` `tanh-def-a_binary64_265` `cosh-def_binary64_264` `sinh-def_binary64_263` `tan-neg_binary64_210` `cos-neg_binary64_209` `sin-neg_binary64_208` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `hang-m-tan_binary64_204` `hang-p-tan_binary64_203` `hang-m0-tan_binary64_202` `hang-p0-tan_binary64_201` `hang-0m-tan_binary64_200` `hang-0p-tan_binary64_199` `tan-+PI/2_binary64_198` `tan-+PI_binary64_197` `tan-PI_binary64_196` `tan-PI/3_binary64_195` `tan-PI/4_binary64_194` `tan-PI/6_binary64_193` `cos-+PI/2_binary64_192` `cos-+PI_binary64_191` `cos-PI_binary64_190` `cos-PI/2_binary64_189` `cos-PI/3_binary64_188` `cos-PI/4_binary64_187` `cos-PI/6_binary64_186` `sin-+PI/2_binary64_185` `sin-+PI_binary64_184` `sin-PI_binary64_183` `sin-PI/2_binary64_182` `sin-PI/3_binary64_181` `sin-PI/4_binary64_180` `sin-PI/6_binary64_179` `sub-1-sin_binary64_178` `sub-1-cos_binary64_177` `-1-add-sin_binary64_176` `-1-add-cos_binary64_175` `1-sub-sin_binary64_174` `1-sub-cos_binary64_173` `cos-sin-sum_binary64_172` `log-E_binary64_168` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `unpow1/2_binary64_142` `exp-to-pow_binary64_140` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `exp-sqrt_binary64_131` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt-neg-out_binary64_38` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--l-_binary64_16`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	411	7571
1	1205	7218
2	4011	7215

Details

analyze602.0ms (12.8%)

sample89.0ms (1.9%)

simplify153.0ms (3.2%)

prune8.0ms (0.2%)

localize20.0ms (0.4%)

rewrite494.0ms (10.5%)

series3.0s (64%)

simplify331.0ms (7%)

end0.0ms (0%)

Profiling