Details

analyze599.0ms (3%)

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 (0.4%)

Algorithm

1×

intervals

Results

35.0ms	200×	body	128	valid
27.0ms	29×	body	1024	valid
10.0ms	17×	body	512	valid
4.0ms	10×	body	256	valid

Compiler

Compiled 59 to 63 computations (-6.8% saved)

simplify211.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

681×	`associate-/l/_binary64_25`
579×	`associate-l_binary64_19`
572×	`associate-/r*_binary64_22`
548×	`unswap-sqr_binary64_46`
447×	`associate-r_binary64_18`
366×	`associate-*l/_binary64_21`
328×	`associate-*r/_binary64_20`
122×	`associate-/l*_binary64_23`
99×	`distribute-rgt-out_binary64_31` `distribute-rgt-in_binary64_28`
76×	`distribute-lft-in_binary64_27`
74×	`associate-/r/_binary64_24`
69×	`*-commutative_binary64_9`
47×	`swap-sqr_binary64_45`
44×	`times-frac_binary64_84`
40×	`distribute-lft-out_binary64_29`
25×	`sqr-pow_binary64_50`
16×	`pow-plus_binary64_141` `*-rgt-identity_binary64_68`
15×	`*-lft-identity_binary64_67`
10×	`cube-unmult_binary64_115` `pow-sqr_binary64_51`
8×	`/-rgt-identity_binary64_69`
6×	`+-commutative_binary64_8`
4×	`prod-exp_binary64_127` `cube-div_binary64_107`
3×	`unpow2_binary64_143` `unpow1_binary64_136` `remove-double-div_binary64_54` `distribute-rgt1-in_binary64_34` `associate-+l+_binary64_11` `associate-+r+_binary64_10`
2×	`cube-prod_binary64_106` `count-2_binary64_26`
1×	`exp-prod_binary64_130` `div-exp_binary64_129` `rec-exp_binary64_128` `1-exp_binary64_122` `+-rgt-identity_binary64_63` `*-inverses_binary64_58` `distribute-lft1-in_binary64_33`
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` `unpow3_binary64_144` `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-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-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` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `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-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 → 4

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	45
1	57	42
2	173	42
3	463	42
4	2266	42

prune10.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	3	1	4
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	4	1	5

Error

1.0b

Counts

5 → 1

Compiler

Compiled 137 to 119 computations (13.1% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
1.9b	(.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.9b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite218.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.7b

Rules

18×	`add-exp-log_binary64_116`
16×	`add-sqr-sqrt_binary64_100`
15×	`*-un-lft-identity_binary64_78`
11×	`add-cube-cbrt_binary64_113`
9×	`unpow-prod-down_binary64_157`
7×	`pow1_binary64_139` `prod-exp_binary64_127`
6×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `pow-unpow_binary64_155`
5×	`pow-exp_binary64_146` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `unpow2_binary64_143` `sqr-pow_binary64_50`
3×	`sqrt-prod_binary64_94` `pow-to-exp_binary64_147` `unswap-sqr_binary64_46`
2×	`flip3-+_binary64_81` `sqrt-div_binary64_95` `flip-+_binary64_52` `associate-*r/_binary64_20` `distribute-lft-out_binary64_29` `pow-pow_binary64_150`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `div-exp_binary64_129` `cbrt-unprod_binary64_111` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `*-commutative_binary64_9`

Counts

4 → 83

Calls

4 calls:

14.0ms	(.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3104 to 2379 computations (23.4% saved)

series2.5s (12.6%)

Error

0.4b

Counts

4 → 40

Calls

4 calls:

1.5s	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
887.0ms	(.f64 (pow.f64 (.f64 (/.f64 2 Om) l) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
33.0ms	(pow.f64 (sin.f64 kx) 2)
33.0ms	(pow.f64 (sin.f64 ky) 2)

Compiler

Compiled 4163 to 3710 computations (10.9% saved)

simplify432.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

480×	`times-frac_binary64_84`
349×	`distribute-rgt-in_binary64_28`
337×	`distribute-lft-in_binary64_27`
295×	`unswap-sqr_binary64_46`
157×	`associate-l_binary64_19` `associate-r_binary64_18`
152×	`associate-/r/_binary64_24`
130×	`cancel-sign-sub-inv_binary64_44`
102×	`sqr-pow_binary64_50`
95×	`*-commutative_binary64_9`
89×	`distribute-rgt-neg-in_binary64_36`
75×	`distribute-lft-neg-in_binary64_35`
72×	`associate-/l/_binary64_25`
65×	`exp-prod_binary64_130`
56×	`distribute-rgt-out_binary64_31`
52×	`log-prod_binary64_164`
49×	`associate-/l*_binary64_23`
41×	`cube-prod_binary64_106` `pow-sqr_binary64_51` `associate-*r/_binary64_20`
38×	`pow-plus_binary64_141`
37×	`associate-*l/_binary64_21`
33×	`+-commutative_binary64_8`
31×	`sub-neg_binary64_71`
30×	`associate-/r*_binary64_22`
28×	`neg-sub0_binary64_73`
26×	`log-pow_binary64_167` `neg-mul-1_binary64_74` `*-lft-identity_binary64_67`
22×	`*-rgt-identity_binary64_68`
19×	`distribute-neg-in_binary64_39`
18×	`swap-sqr_binary64_45` `distribute-lft-out_binary64_29`
17×	`log-div_binary64_165`
16×	`distribute-neg-frac_binary64_42`
14×	`unpow2_binary64_143`
13×	`unpow1_binary64_136` `cube-div_binary64_107` `distribute-lft-neg-out_binary64_37` `distribute-rgt-out--_binary64_32`
12×	`rem-sqrt-square_binary64_91`
11×	`difference-of-squares_binary64_47`
10×	`unpow3_binary64_144`
9×	`cube-unmult_binary64_115` `/-rgt-identity_binary64_69` `distribute-rgt1-in_binary64_34`
8×	`distribute-rgt-neg-out_binary64_38` `associate-+l+_binary64_11`
6×	`exp-sqrt_binary64_131` `associate-+r+_binary64_10`
5×	`pow-base-1_binary64_138`
4×	`div-exp_binary64_129` `prod-exp_binary64_127` `exp-sum_binary64_124` `cube-mult_binary64_108` `distribute-lft-out--_binary64_30` `associate--r+_binary64_14`
3×	`rem-square-sqrt_binary64_90` `unsub-neg_binary64_72` `count-2_binary64_26`
2×	`log-rec_binary64_166` `rec-exp_binary64_128` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `mul-1-neg_binary64_70` `difference-of-sqr-1_binary64_48` `distribute-lft1-in_binary64_33` `associate-+l-_binary64_13` `associate-+r-_binary64_12`
1×	`1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `*-inverses_binary64_58` `associate--l+_binary64_15`
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-lft-sqr_binary64_133` `exp-cbrt_binary64_132` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `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` `div-sub_binary64_83` `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` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `difference-of-sqr--1_binary64_49` `cancel-sign-sub_binary64_43` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

123 → 242

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	3264
1	511	3114
2	1758	3013

prune698.0ms (3.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	240	2	242
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	240	3	243

Error

0.0b

Counts

243 → 3

Compiler

Compiled 9332 to 6527 computations (30.1% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.2b	(pow.f64 (sin.f64 kx) 2)
1.0b	(pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
1.1b	(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))

rewrite229.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`*-un-lft-identity_binary64_78`
15×	`unpow-prod-down_binary64_157`
13×	`add-cube-cbrt_binary64_113` `add-sqr-sqrt_binary64_100`
11×	`pow-unpow_binary64_155`
9×	`pow-pow_binary64_150`
8×	`log-prod_binary64_164`
7×	`pow1_binary64_139` `add-exp-log_binary64_116`
6×	`exp-prod_binary64_130`
5×	`sqr-pow_binary64_50`
4×	`pow-to-exp_binary64_147` `pow-exp_binary64_146` `add-log-exp_binary64_117` `add-cbrt-cube_binary64_114`
3×	`rem-log-exp_binary64_119` `unpow2_binary64_143`
2×	`unpow-prod-up_binary64_156` `distribute-lft-out_binary64_29`
1×	`log-pow_binary64_167`

Counts

4 → 81

Calls

4 calls:

13.0ms	(pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
5.0ms	(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
3.0ms	(pow.f64 (sin.f64 ky) 2)
3.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 3110 to 2430 computations (21.9% saved)

series3.7s (18.7%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

2.0s	(log.f64 (pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))
1.5s	(pow.f64 (exp.f64 (pow.f64 (*.f64 l (/.f64 2 Om)) 2)) (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
38.0ms	(pow.f64 (sin.f64 ky) 2)
35.0ms	(pow.f64 (sin.f64 kx) 2)

Compiler

Compiled 4969 to 4320 computations (13.1% saved)

simplify676.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-/l*_binary64_23`
356×	`unswap-sqr_binary64_46`
247×	`associate-/r/_binary64_24`
176×	`associate-r_binary64_18`
171×	`sqr-pow_binary64_50`
154×	`distribute-rgt-in_binary64_28`
149×	`distribute-lft-in_binary64_27`
136×	`associate-l_binary64_19`
128×	`associate-+r+_binary64_10`
116×	`exp-prod_binary64_130` `associate-/l/_binary64_25`
95×	`*-commutative_binary64_9`
87×	`log-prod_binary64_164`
79×	`pow-sqr_binary64_51`
72×	`times-frac_binary64_84`
70×	`associate-+l+_binary64_11`
68×	`distribute-rgt-out_binary64_31`
62×	`associate-/r*_binary64_22`
61×	`+-commutative_binary64_8`
58×	`log-pow_binary64_167`
47×	`associate-l/_binary64_21` `associate-r/_binary64_20`
38×	`pow-plus_binary64_141`
37×	`swap-sqr_binary64_45`
29×	`cube-prod_binary64_106`
25×	`distribute-lft-out_binary64_29`
16×	`unpow2_binary64_143` `unpow1_binary64_136`
15×	`exp-sum_binary64_124` `/-rgt-identity_binary64_69` `*-lft-identity_binary64_67` `count-2_binary64_26`
14×	`cube-unmult_binary64_115` `*-rgt-identity_binary64_68`
13×	`rem-sqrt-square_binary64_91`
12×	`log-div_binary64_165`
8×	`exp-to-pow_binary64_140` `rem-log-exp_binary64_119`
7×	`cube-div_binary64_107`
6×	`pow-base-1_binary64_138` `distribute-rgt1-in_binary64_34`
5×	`exp-sqrt_binary64_131`
4×	`prod-exp_binary64_127`
3×	`exp-lft-sqr_binary64_133`
2×	`rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-square-sqrt_binary64_90` `distribute-lft1-in_binary64_33`
1×	`log-rec_binary64_166` `exp-diff_binary64_126` `1-exp_binary64_122` `rem-exp-log_binary64_118` `sub-neg_binary64_71` `*-inverses_binary64_58`
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` `unpow3_binary64_144` `unpow1/2_binary64_142` `unpow0_binary64_137` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `cube-mult_binary64_108` `cube-neg_binary64_105` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `div-sub_binary64_83` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `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` `rgt-mult-inverse_binary64_55` `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-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

122 → 241

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	252	3992
1	617	3717
2	2246	3677

prune966.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	241	0	241
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	241	3	244

Error

0.0b

Counts

244 → 3

Compiler

Compiled 11277 to 8086 computations (28.3% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.4b	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
1.4b	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
23.9b	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
24.2b	(sqrt.f64 (/.f64 1 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))))

rewrite381.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

29×	`pow1_binary64_139`
18×	`*-un-lft-identity_binary64_78`
16×	`associate-*r/_binary64_20`
15×	`add-sqr-sqrt_binary64_100`
14×	`pow-prod-down_binary64_149`
10×	`add-cube-cbrt_binary64_113` `sqrt-pow1_binary64_96` `sqrt-prod_binary64_94` `associate-r_binary64_18`
8×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`associate-l_binary64_19`
4×	`add-log-exp_binary64_117` `pow-flip_binary64_152` `flip3-+_binary64_81` `flip-+_binary64_52` `unpow-prod-down_binary64_157` `distribute-lft-out_binary64_29`
3×	`sqrt-div_binary64_95` `times-frac_binary64_84`
2×	`pow1/2_binary64_158` `associate-/r/_binary64_24` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `*-commutative_binary64_9`
1×	`inv-pow_binary64_163` `div-inv_binary64_75` `rem-sqrt-square_binary64_91`

Counts

4 → 88

Calls

4 calls:

19.0ms	(sqrt.f64 (/.f64 1 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))))
14.0ms	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
12.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
12.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))

Compiler

Compiled 5124 to 3610 computations (29.5% saved)

series2.5s (12.3%)

Error

0.0b

Counts

4 → 44

Calls

4 calls:

939.0ms	(sqrt.f64 (/.f64 1 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))))))
577.0ms	(sqrt.f64 (.f64 4 (.f64 l (*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2))))))
422.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))
409.0ms	(*.f64 l (+.f64 (pow.f64 (sin.f64 ky) 2) (pow.f64 (sin.f64 kx) 2)))

Compiler

Compiled 6025 to 4771 computations (20.8% saved)

simplify378.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

411×	`associate-/r*_binary64_22`
322×	`associate-/l*_binary64_23`
308×	`distribute-rgt-in_binary64_28`
299×	`distribute-lft-in_binary64_27`
271×	`*-commutative_binary64_9`
264×	`unswap-sqr_binary64_46`
171×	`associate-*r/_binary64_20`
163×	`associate-r_binary64_18`
157×	`associate-l/_binary64_21` `associate-l*_binary64_19`
132×	`sqr-pow_binary64_50`
82×	`*-lft-identity_binary64_67` `pow-sqr_binary64_51`
76×	`*-rgt-identity_binary64_68`
70×	`associate-/r/_binary64_24`
66×	`associate-/l/_binary64_25`
63×	`exp-prod_binary64_130` `cancel-sign-sub-inv_binary64_44`
61×	`times-frac_binary64_84`
60×	`sub-neg_binary64_71`
59×	`/-rgt-identity_binary64_69`
57×	`neg-mul-1_binary64_74`
56×	`neg-sub0_binary64_73`
47×	`pow-plus_binary64_141` `difference-of-squares_binary64_47`
37×	`distribute-rgt-neg-in_binary64_36`
33×	`+-commutative_binary64_8`
29×	`div-sub_binary64_83`
28×	`unsub-neg_binary64_72` `distribute-lft-neg-in_binary64_35`
26×	`associate-+l+_binary64_11`
23×	`distribute-neg-frac_binary64_42`
22×	`exp-sqrt_binary64_131` `cube-div_binary64_107`
21×	`log-prod_binary64_164` `cube-prod_binary64_106` `associate-+r+_binary64_10`
19×	`distribute-lft-neg-out_binary64_37`
18×	`distribute-rgt-out_binary64_31`
15×	`log-pow_binary64_167` `log-div_binary64_165`
11×	`associate-+r-_binary64_12`
10×	`+-rgt-identity_binary64_63`
9×	`unpow3_binary64_144` `cube-unmult_binary64_115` `associate--l+_binary64_15` `associate-+l-_binary64_13`
8×	`exp-lft-sqr_binary64_133`
6×	`pow-base-1_binary64_138` `sub0-neg_binary64_65`
5×	`unpow2_binary64_143` `rem-sqrt-square_binary64_91`
4×	`unpow1_binary64_136` `div-exp_binary64_129` `prod-exp_binary64_127` `exp-sum_binary64_124` `cube-mult_binary64_108` `swap-sqr_binary64_45` `distribute-rgt-out--_binary64_32` `distribute-lft-out_binary64_29`
3×	`distribute-rgt-neg-out_binary64_38`
2×	`log-rec_binary64_166` `rec-exp_binary64_128` `rem-square-sqrt_binary64_90` `remove-double-div_binary64_54` `distribute-lft-out--_binary64_30`
1×	`exp-diff_binary64_126` `1-exp_binary64_122` `exp-1-e_binary64_121` `rem-log-exp_binary64_119` `rem-cbrt-cube_binary64_102` `div0_binary64_59` `*-inverses_binary64_58` `rgt-mult-inverse_binary64_55` `distribute-frac-neg_binary64_41`
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-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `rem-exp-log_binary64_118` `cube-neg_binary64_105` `rem-3cbrt-rft_binary64_104` `rem-3cbrt-lft_binary64_103` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `mul-1-neg_binary64_70` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `cancel-sign-sub_binary64_43` `distribute-neg-out_binary64_40` `distribute-neg-in_binary64_39` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate--r-_binary64_17` `associate--l-_binary64_16` `associate--r+_binary64_14`

Counts

132 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	175	3061
1	413	2844
2	1619	2802
3	4297	2796

prune1.3s (6.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	276	0	276
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	276	3	279

Error

0.0b

Counts

279 → 3

Compiler

Compiled 16244 to 11396 computations (29.8% saved)

regimes1.6s (8%)

Accuracy

Total 1.1b remaining (96.2%)

Threshold costs 0b (0%)

Compiler

Compiled 16643 to 15550 computations (6.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64_9` `+-commutative_binary64_8`
1×	`1-exp_binary64_122`
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_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` `tan-0_binary64_207` `cos-0_binary64_206` `sin-0_binary64_205` `unpow1_binary64_136` `e-exp-1_binary64_123` `exp-1-e_binary64_121` `exp-0_binary64_120` `sqr-abs_binary64_93` `sqr-neg_binary64_92` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `unsub-neg_binary64_72` `sub-neg_binary64_71` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `-rgt-identity_binary64_68` `-lft-identity_binary64_67` `remove-double-neg_binary64_66` `sub0-neg_binary64_65` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `+-lft-identity_binary64_62` `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`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	45
1	31	45

Proof

(sqrt f64 (* f64 (/ f64 1 2) (+ f64 1 (/ f64 1 (sqrt f64 (+ f64 1 (* f64 (pow f64 (/ f64 (* f64 2 h0) h1) 2) (+ f64 (pow f64 (sin f64 h2) 2) (pow f64 (sin f64 h3) 2)))))))))

end0.0ms (0%)

sample3.4s (17.1%)

Algorithm

1×

intervals

Results

1.1s	6354×	body	128	valid
633.0ms	781×	body	1024	valid
307.0ms	535×	body	512	valid
127.0ms	329×	body	256	valid
1.0ms	1×	body	2048	valid

Compiler

Compiled 914 to 857 computations (6.2% saved)

Details

analyze599.0ms (3%)

sample89.0ms (0.4%)

simplify211.0ms (1.1%)

prune10.0ms (0.1%)

localize19.0ms (0.1%)

rewrite218.0ms (1.1%)

series2.5s (12.6%)

simplify432.0ms (2.2%)

prune698.0ms (3.5%)

localize22.0ms (0.1%)

rewrite229.0ms (1.1%)

series3.7s (18.7%)

simplify676.0ms (3.4%)

prune966.0ms (4.8%)

localize27.0ms (0.1%)

rewrite381.0ms (1.9%)

series2.5s (12.3%)

simplify378.0ms (1.9%)

prune1.3s (6.5%)

regimes1.6s (8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample3.4s (17.1%)

Profiling