Details

analyze3.6s (11.8%)

Algorithm

1×	search
2×	egg-herbie

Rules

501×	`unsub-neg_binary64_72`
469×	`distribute-rgt-in_binary64_28`
417×	`distribute-rgt-neg-in_binary64_36`
332×	`distribute-lft-in_binary64_27`
290×	`cancel-sign-sub-inv_binary64_44`
267×	`distribute-lft-neg-in_binary64_35`
266×	`neg-mul-1_binary64_74`
265×	`neg-sub0_binary64_73`
247×	`distribute-lft-neg-out_binary64_37`
229×	`associate--r+_binary64_14`
192×	`sub-neg_binary64_71`
189×	`distribute-neg-in_binary64_39`
168×	`*-commutative_binary64_9`
153×	`distribute-rgt-neg-out_binary64_38`
142×	`associate-r_binary64_18`
140×	`associate-l_binary64_19`
113×	`mul0-rgt_binary64_61` `mul0-lft_binary64_60`
102×	`+-commutative_binary64_8`
93×	`remove-double-neg_binary64_66`
47×	`*-lft-identity_binary64_67`
46×	`*-rgt-identity_binary64_68`
38×	`associate-+l-_binary64_13`
35×	`associate--r-_binary64_17`
31×	`sub0-neg_binary64_65`
24×	`associate--l+_binary64_15`
23×	`associate-+r+_binary64_10`
17×	`associate-+r-_binary64_12`
15×	`associate-+l+_binary64_11`
14×	`cos-neg_binary64_209` `mul-1-neg_binary64_70` `+-rgt-identity_binary64_63`
12×	`sin-neg_binary64_208` `distribute-rgt-out--_binary64_32` `associate--l-_binary64_16`
8×	`cancel-sign-sub_binary64_43`
5×	`+-lft-identity_binary64_62` `distribute-lft-out--_binary64_30`
3×	`distribute-neg-out_binary64_40`
1×	`1-exp_binary64_122` `swap-lambda1-lambda2` `swap-phi1-phi2`
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` `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` `unpow2_binary64_143` `unpow1/2_binary64_142` `pow-plus_binary64_141` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `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-unmult_binary64_115` `cube-mult_binary64_108` `cube-div_binary64_107` `cube-prod_binary64_106` `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` `times-frac_binary64_84` `div-sub_binary64_83` `/-rgt-identity_binary64_69` `--rgt-identity_binary64_64` `div0_binary64_59` `-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `pow-sqr_binary64_51` `sqr-pow_binary64_50` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `unswap-sqr_binary64_46` `swap-sqr_binary64_45` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-rgt-out_binary64_31` `distribute-lft-out_binary64_29` `count-2_binary64_26` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `associate-/l_binary64_23` `associate-/r_binary64_22` `associate-l/_binary64_21` `associate-*r/_binary64_20`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	341
1	164	341
2	237	341
3	274	341
4	306	341
5	447	341
6	475	341
7	707	341
8	1046	341
9	1135	341
10	1279	341
11	1600	341
12	1905	341
13	2500	341
14	2503	341
15	2479	341
16	2493	341
17	2493	341
18	2893	341
19	2619	341
20	2619	341
21	2619	341
22	2619	341
23	2392	341
0	5	5
1	5	5

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 20 to 18 computations (10% saved)

sample233.0ms (0.8%)

Algorithm

1×

intervals

Results

160.0ms	187×	body	1024	valid
19.0ms	38×	body	512	valid
16.0ms	9×	body	2048	valid
4.0ms	13×	body	256	valid
1.0ms	9×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify15.0ms (0%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64_71`
14×	`cancel-sign-sub-inv_binary64_44`
10×	`distribute-rgt-in_binary64_28` `*-commutative_binary64_9`
9×	`neg-mul-1_binary64_74`
8×	`associate--r+_binary64_14`
7×	`unsub-neg_binary64_72`
6×	`neg-sub0_binary64_73` `associate--r-_binary64_17`
5×	`distribute-neg-in_binary64_39` `distribute-lft-neg-out_binary64_37` `distribute-rgt-neg-in_binary64_36` `distribute-lft-in_binary64_27` `+-commutative_binary64_8`
4×	`*-lft-identity_binary64_67` `sub0-neg_binary64_65` `associate-+l-_binary64_13`
3×	`+-lft-identity_binary64_62` `distribute-rgt-neg-out_binary64_38` `associate-l_binary64_19` `associate-r_binary64_18` `associate-+l+_binary64_11`
2×	`cos-neg_binary64_209` `*-rgt-identity_binary64_68`
1×	`1-exp_binary64_122` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `+-rgt-identity_binary64_63` `distribute-lft-neg-in_binary64_35` `associate--l+_binary64_15` `associate-+r-_binary64_12` `associate-+r+_binary64_10`
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` `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` `unpow2_binary64_143` `unpow1/2_binary64_142` `pow-plus_binary64_141` `exp-to-pow_binary64_140` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `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-unmult_binary64_115` `cube-mult_binary64_108` `cube-div_binary64_107` `cube-prod_binary64_106` `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` `times-frac_binary64_84` `div-sub_binary64_83` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `-inverses_binary64_58` `+-inverses_binary64_57` `lft-mult-inverse_binary64_56` `rgt-mult-inverse_binary64_55` `remove-double-div_binary64_54` `pow-sqr_binary64_51` `sqr-pow_binary64_50` `difference-of-sqr--1_binary64_49` `difference-of-sqr-1_binary64_48` `difference-of-squares_binary64_47` `unswap-sqr_binary64_46` `swap-sqr_binary64_45` `cancel-sign-sub_binary64_43` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `distribute-rgt-out--_binary64_32` `distribute-rgt-out_binary64_31` `distribute-lft-out--_binary64_30` `distribute-lft-out_binary64_29` `count-2_binary64_26` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `associate-/l_binary64_23` `associate-/r_binary64_22` `associate-l/_binary64_21` `associate-*r/_binary64_20` `associate--l-_binary64_16`

Counts

1 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

prune3.0ms (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

17.9b

Counts

1 → 1

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite108.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.9b

Rules

11×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-r_binary64_18`
4×	`cos-sum_binary64_212` `add-log-exp_binary64_117` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `associate-l_binary64_19`
3×	`cos-diff_binary64_215` `cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9`
1×	`sub-neg_binary64_71` `acos-asin_binary64_259` `unswap-sqr_binary64_46` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `cos-mult_binary64_232` `associate-*l/_binary64_21`

Counts

4 → 59

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
3.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1775 to 321 computations (81.9% saved)

series1.3s (4%)

Error

17.4b

Counts

4 → 58

Calls

4 calls:

603.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
342.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
162.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
84.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3617 to 2098 computations (42% saved)

simplify198.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

527×	`sub-neg_binary64_71`
400×	`distribute-rgt-neg-in_binary64_36`
339×	`distribute-lft-neg-in_binary64_35`
289×	`neg-mul-1_binary64_74`
279×	`cancel-sign-sub-inv_binary64_44`
256×	`associate-l_binary64_19`
249×	`neg-sub0_binary64_73`
247×	`associate-r_binary64_18`
170×	`unsub-neg_binary64_72`
151×	`*-commutative_binary64_9`
144×	`sqr-pow_binary64_50`
121×	`distribute-rgt-out--_binary64_32`
120×	`distribute-lft-in_binary64_27`
112×	`distribute-rgt-out_binary64_31`
109×	`+-commutative_binary64_8`
87×	`pow-sqr_binary64_51` `distribute-rgt-in_binary64_28`
85×	`distribute-lft-out--_binary64_30`
82×	`associate-+l+_binary64_11`
80×	`associate-+l-_binary64_13`
76×	`distribute-lft-out_binary64_29`
60×	`associate-+r+_binary64_10`
57×	`distribute-lft-neg-out_binary64_37`
56×	`exp-prod_binary64_130`
52×	`log-prod_binary64_164`
51×	`sub0-neg_binary64_65`
48×	`cube-prod_binary64_106`
47×	`unswap-sqr_binary64_46`
46×	`+-rgt-identity_binary64_63`
44×	`remove-double-neg_binary64_66` `associate-+r-_binary64_12`
39×	`distribute-rgt-neg-out_binary64_38`
38×	`associate--l+_binary64_15`
36×	`rem-sqrt-square_binary64_91`
33×	`mul0-rgt_binary64_61` `mul0-lft_binary64_60`
30×	`swap-sqr_binary64_45`
28×	`associate--r+_binary64_14`
26×	`cancel-sign-sub_binary64_43`
24×	`*-rgt-identity_binary64_68`
21×	`*-lft-identity_binary64_67`
16×	`cube-unmult_binary64_115`
15×	`associate--l-_binary64_16`
13×	`unpow3_binary64_144`
12×	`unpow1/2_binary64_142`
11×	`--rgt-identity_binary64_64` `associate--r-_binary64_17`
10×	`exp-sum_binary64_124` `associate-/l*_binary64_23`
9×	`cube-mult_binary64_108` `+-lft-identity_binary64_62` `distribute-neg-in_binary64_39` `distribute-rgt1-in_binary64_34`
6×	`cos-neg_binary64_209` `exp-diff_binary64_126` `div-sub_binary64_83` `difference-of-squares_binary64_47`
5×	`sin-neg_binary64_208` `pow-plus_binary64_141`
4×	`unpow2_binary64_143` `unpow1_binary64_136` `sqr-neg_binary64_92` `distribute-lft1-in_binary64_33`
3×	`cube-neg_binary64_105`
2×	`mul-1-neg_binary64_70` `distribute-neg-out_binary64_40` `associate-/l/_binary64_25` `associate-*r/_binary64_20`
1×	`1-exp_binary64_122` `exp-1-e_binary64_121` `rem-3cbrt-lft_binary64_103` `rem-square-sqrt_binary64_90` `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` `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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `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` `div-exp_binary64_129` `rec-exp_binary64_128` `prod-exp_binary64_127` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `cube-div_binary64_107` `rem-3cbrt-rft_binary64_104` `rem-cbrt-cube_binary64_102` `rem-cube-cbrt_binary64_101` `sqr-abs_binary64_93` `times-frac_binary64_84` `/-rgt-identity_binary64_69` `div0_binary64_59` `-inverses_binary64_58` `+-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` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `associate-/r/_binary64_24` `associate-/r_binary64_22` `associate-*l/_binary64_21`

Counts

117 → 57

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	196	3281
1	463	2925
2	1398	2852
3	2381	2827
4	4336	2827
5	4730	2827
6	4933	2827
7	4887	2827

prune116.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	45	12	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	12	58

Error

4.9b

Counts

58 → 12

Compiler

Compiled 1945 to 554 computations (71.5% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite152.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

13×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `-un-lft-identity_binary64_78` `associate-r*_binary64_18`
7×	`associate-l_binary64_19`
6×	`cos-mult_binary64_232`
5×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
4×	`add-log-exp_binary64_117`
3×	`-commutative_binary64_9` `sin-mult_binary64_233` `frac-times_binary64_88` `associate-r/_binary64_20`
2×	`unswap-sqr_binary64_46` `frac-add_binary64_86` `flip3-+_binary64_81` `flip-+_binary64_52`
1×	`acos-asin_binary64_259` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `associate-*l/_binary64_21`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2888 to 452 computations (84.3% saved)

series2.1s (6.6%)

Error

4.9b

Counts

4 → 57

Calls

4 calls:

1.1s	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
532.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
225.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
158.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5396 to 2755 computations (48.9% saved)

simplify160.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

784×	`cancel-sign-sub-inv_binary64_44`
470×	`associate-r_binary64_18`
457×	`associate-l_binary64_19`
282×	`distribute-rgt-neg-in_binary64_36`
257×	`distribute-lft-neg-in_binary64_35`
248×	`neg-mul-1_binary64_74` `neg-sub0_binary64_73`
233×	`*-commutative_binary64_9`
196×	`sub-neg_binary64_71`
185×	`distribute-rgt-out_binary64_31`
152×	`exp-prod_binary64_130` `sqr-pow_binary64_50`
94×	`distribute-rgt-in_binary64_28`
91×	`distribute-lft-in_binary64_27`
75×	`+-commutative_binary64_8`
53×	`unsub-neg_binary64_72`
48×	`distribute-rgt-out--_binary64_32`
45×	`associate--l+_binary64_15`
44×	`cube-prod_binary64_106`
42×	`log-prod_binary64_164`
34×	`*-lft-identity_binary64_67`
32×	`*-rgt-identity_binary64_68` `associate-+l+_binary64_11`
29×	`associate--r+_binary64_14`
28×	`distribute-neg-in_binary64_39`
26×	`distribute-lft-neg-out_binary64_37`
25×	`swap-sqr_binary64_45` `associate-+r+_binary64_10`
18×	`pow-sqr_binary64_51`
17×	`unswap-sqr_binary64_46`
13×	`cube-unmult_binary64_115`
12×	`unpow3_binary64_144`
9×	`distribute-lft-out_binary64_29`
8×	`exp-sum_binary64_124` `cube-mult_binary64_108`
7×	`unpow1/2_binary64_142` `distribute-rgt-neg-out_binary64_38`
4×	`unpow2_binary64_143` `pow-plus_binary64_141` `unpow1_binary64_136` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47`
3×	`distribute-rgt1-in_binary64_34`
1×	`1-exp_binary64_122` `exp-1-e_binary64_121` `distribute-lft1-in_binary64_33` `associate-+l-_binary64_13` `associate-+r-_binary64_12`
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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `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` `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-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-square-sqrt_binary64_90` `times-frac_binary64_84` `div-sub_binary64_83` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `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_58` `+-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` `cancel-sign-sub_binary64_43` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-lft-out--_binary64_30` `count-2_binary64_26` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `associate-/l_binary64_23` `associate-/r_binary64_22` `associate-l/_binary64_21` `associate-*r/_binary64_20` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

129 → 99

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	5142
1	763	4542
2	2857	4461
3	4301	4461
4	5111	4461

prune201.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	85	14	99
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	96	15	111

Error

4.8b

Counts

111 → 15

Compiler

Compiled 4100 to 865 computations (78.9% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite143.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.8b

Rules

20×	`pow1_binary64_139` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
12×	`add-sqr-sqrt_binary64_100`
10×	`pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `sin-mult_binary64_233`
2×	`unswap-sqr_binary64_46` `cos-mult_binary64_232`
1×	`acos-asin_binary64_259` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20`

Counts

4 → 70

Calls

4 calls:

9.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 3146 to 420 computations (86.6% saved)

series1.7s (5.6%)

Error

4.8b

Counts

4 → 55

Calls

4 calls:

719.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
554.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
235.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (.f64 (cos.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
146.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5355 to 2620 computations (51.1% saved)

simplify167.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

404×	`distribute-rgt-neg-in_binary64_36`
386×	`distribute-lft-neg-in_binary64_35`
364×	`associate-r_binary64_18`
348×	`distribute-lft-out--_binary64_30`
335×	`cancel-sign-sub-inv_binary64_44`
329×	`associate-l_binary64_19`
243×	`neg-mul-1_binary64_74`
205×	`sub-neg_binary64_71`
173×	`*-commutative_binary64_9`
149×	`neg-sub0_binary64_73`
114×	`sqr-pow_binary64_50`
98×	`distribute-rgt-out--_binary64_32`
96×	`distribute-rgt-out_binary64_31`
80×	`exp-prod_binary64_130`
77×	`+-commutative_binary64_8`
70×	`swap-sqr_binary64_45`
68×	`log-prod_binary64_164`
65×	`cube-prod_binary64_106`
56×	`unswap-sqr_binary64_46`
50×	`associate-+r+_binary64_10`
42×	`associate-+l+_binary64_11`
32×	`distribute-rgt-in_binary64_28`
31×	`associate-+l-_binary64_13`
30×	`associate--l+_binary64_15`
28×	`associate-+r-_binary64_12`
26×	`distribute-lft-in_binary64_27`
19×	`*-rgt-identity_binary64_68` `+-rgt-identity_binary64_63`
18×	`associate--r+_binary64_14`
17×	`*-lft-identity_binary64_67` `pow-sqr_binary64_51`
16×	`sub0-neg_binary64_65`
15×	`unsub-neg_binary64_72`
14×	`unpow3_binary64_144` `distribute-lft-neg-out_binary64_37`
13×	`cube-unmult_binary64_115`
12×	`cube-mult_binary64_108` `distribute-lft-out_binary64_29`
8×	`distribute-rgt-neg-out_binary64_38`
7×	`unpow1/2_binary64_142`
6×	`rem-sqrt-square_binary64_91` `cancel-sign-sub_binary64_43` `distribute-neg-in_binary64_39`
3×	`difference-of-squares_binary64_47` `associate-/l*_binary64_23`
2×	`cos-neg_binary64_209` `unpow2_binary64_143` `pow-plus_binary64_141` `unpow1_binary64_136` `exp-sum_binary64_124`
1×	`1-exp_binary64_122` `exp-1-e_binary64_121`
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` `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` `pow-base-0_binary64_162` `unpow1/3_binary64_145` `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` `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-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-square-sqrt_binary64_90` `times-frac_binary64_84` `div-sub_binary64_83` `mul-1-neg_binary64_70` `/-rgt-identity_binary64_69` `remove-double-neg_binary64_66` `--rgt-identity_binary64_64` `+-lft-identity_binary64_62` `mul0-rgt_binary64_61` `mul0-lft_binary64_60` `div0_binary64_59` `-inverses_binary64_58` `+-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` `distribute-neg-frac_binary64_42` `distribute-frac-neg_binary64_41` `distribute-neg-out_binary64_40` `distribute-rgt1-in_binary64_34` `distribute-lft1-in_binary64_33` `count-2_binary64_26` `associate-/l/_binary64_25` `associate-/r/_binary64_24` `associate-/r_binary64_22` `associate-l/_binary64_21` `associate-r/_binary64_20` `associate--r-_binary64_17` `associate--l-_binary64_16`

Counts

125 → 93

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	212	4924
1	509	3840
2	1685	3710
3	2914	3675
4	4965	3675
5	5027	3675

prune159.0ms (0.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Error

4.8b

Counts

108 → 14

Compiler

Compiled 3939 to 820 computations (79.2% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
0.7b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

rewrite128.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.7b

Rules

12×	`add-sqr-sqrt_binary64_100`
10×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
9×	`exp-prod_binary64_130`
8×	`pow1_binary64_139` `log-pow_binary64_167`
7×	`associate-l_binary64_19`
6×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
5×	`add-log-exp_binary64_117`
3×	`acos-asin_binary64_259` `log-prod_binary64_164` `associate-r_binary64_18`
2×	`exp-diff_binary64_126`
1×	`log-div_binary64_165` `rem-log-exp_binary64_119` `rem-exp-log_binary64_118` `pow-prod-down_binary64_149` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `*-commutative_binary64_9`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 2764 to 221 computations (92% saved)

series4.7s (15.3%)

Error

4.8b

Counts

4 → 51

Calls

4 calls:

2.4s	(.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))) R)
1.7s	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))))
407.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1))))))))
239.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))))

Compiler

Compiled 5202 to 2575 computations (50.5% saved)

simplify342.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64_84`
426×	`unswap-sqr_binary64_46`
398×	`distribute-rgt-in_binary64_28`
359×	`distribute-lft-in_binary64_27`
340×	`log-prod_binary64_164`
324×	`distribute-rgt-out_binary64_31`
302×	`associate-l_binary64_19`
273×	`*-commutative_binary64_9`
223×	`associate-r_binary64_18`
202×	`associate-+l+_binary64_11`
181×	`associate-*l/_binary64_21`
168×	`sqr-pow_binary64_50`
133×	`log-pow_binary64_167`
120×	`exp-prod_binary64_130`
118×	`associate-*r/_binary64_20`
104×	`log-div_binary64_165`
97×	`associate-+r+_binary64_10`
93×	`exp-sum_binary64_124`
75×	`cube-prod_binary64_106`
70×	`count-2_binary64_26`
67×	`distribute-lft-out_binary64_29`
64×	`associate-/l/_binary64_25`
62×	`exp-to-pow_binary64_140` `associate-/l*_binary64_23`
58×	`pow-sqr_binary64_51`
57×	`cube-div_binary64_107`
49×	`unpow3_binary64_144`
43×	`unsub-neg_binary64_72`
40×	`swap-sqr_binary64_45`
37×	`distribute-rgt1-in_binary64_34`
35×	`pow-plus_binary64_141`
31×	`*-rgt-identity_binary64_68`
29×	`exp-sqrt_binary64_131` `rem-sqrt-square_binary64_91`
27×	`*-lft-identity_binary64_67` `associate-/r/_binary64_24`
26×	`cube-unmult_binary64_115`
19×	`associate-/r*_binary64_22`
18×	`log-rec_binary64_166`
11×	`distribute-lft1-in_binary64_33`
10×	`unpow1/2_binary64_142` `rem-log-exp_binary64_119` `+-commutative_binary64_8`
9×	`cube-mult_binary64_108`
8×	`exp-lft-sqr_binary64_133`
7×	`rem-exp-log_binary64_118`
5×	`prod-exp_binary64_127`
3×	`sub-neg_binary64_71`
1×	`unpow2_binary64_143` `1-exp_binary64_122` `exp-1-e_binary64_121` `neg-mul-1_binary64_74` `neg-sub0_binary64_73` `/-rgt-identity_binary64_69`
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` `pow-base-1_binary64_138` `unpow0_binary64_137` `unpow1_binary64_136` `unpow-1_binary64_135` `exp-lft-cube_binary64_134` `exp-cbrt_binary64_132` `div-exp_binary64_129` `rec-exp_binary64_128` `exp-diff_binary64_126` `exp-neg_binary64_125` `e-exp-1_binary64_123` `exp-0_binary64_120` `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-square-sqrt_binary64_90` `div-sub_binary64_83` `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_58` `+-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

109 → 89

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	98	5911
1	159	4846
2	324	4846
3	450	4846
4	623	4840
5	1298	4840
6	2920	4840
7	4531	4840
8	4947	4840
9	4996	4840
10	4866	4840

prune116.0ms (0.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	89	14	103

Error

4.8b

Counts

103 → 14

Compiler

Compiled 2945 to 143 computations (95.1% saved)

regimes4.6s (14.9%)

Accuracy

Total 0.4b remaining (9.7%)

Threshold costs 0.4b (9.7%)

Compiler

Compiled 58187 to 32703 computations (43.8% saved)

bsearch0.0ms (0%)

simplify48.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64_9`
2×	`+-commutative_binary64_8`
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` `1-exp_binary64_122` `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	24	53
1	33	53
2	33	53

Remove

(sort phi1 phi2)

Compiler

Compiled 192 to 138 computations (28.1% saved)

end0.0ms (0%)

sample10.6s (34.1%)

Algorithm

1×

intervals

Results

4.6s	5502×	body	1024	valid
747.0ms	1376×	body	512	valid
570.0ms	304×	body	2048	valid
173.0ms	523×	body	256	valid
57.0ms	295×	body	128	valid

Compiler

Compiled 5401 to 3045 computations (43.6% saved)

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31

Details

analyze3.6s (11.8%)

sample233.0ms (0.8%)

simplify15.0ms (0%)

prune3.0ms (0%)

localize26.0ms (0.1%)

rewrite108.0ms (0.3%)

series1.3s (4%)

simplify198.0ms (0.6%)

prune116.0ms (0.4%)

localize26.0ms (0.1%)

rewrite152.0ms (0.5%)

series2.1s (6.6%)

simplify160.0ms (0.5%)

prune201.0ms (0.6%)

localize29.0ms (0.1%)

rewrite143.0ms (0.5%)

series1.7s (5.6%)

simplify167.0ms (0.5%)

prune159.0ms (0.5%)

localize32.0ms (0.1%)

rewrite128.0ms (0.4%)

series4.7s (15.3%)

simplify342.0ms (1.1%)

prune116.0ms (0.4%)

regimes4.6s (14.9%)

bsearch0.0ms (0%)

simplify48.0ms (0.2%)

end0.0ms (0%)

sample10.6s (34.1%)

Profiling

Iter	Nodes	Cost
0	18	31
1	27	31
2	38	31
3	44	31
4	50	31
5	66	31
6	89	31
7	102	31
8	114	31
9	116	31
10	110	31
11	96	31