Details

analyze3.6s (18.3%)

Algorithm

1×	search
2×	egg-herbie

Rules

501×	`unsub-neg_binary64`
469×	`distribute-rgt-in_binary64`
417×	`distribute-rgt-neg-in_binary64`
332×	`distribute-lft-in_binary64`
290×	`cancel-sign-sub-inv_binary64`
267×	`distribute-lft-neg-in_binary64`
266×	`neg-mul-1_binary64`
265×	`neg-sub0_binary64`
247×	`distribute-lft-neg-out_binary64`
229×	`associate--r+_binary64`
192×	`sub-neg_binary64`
189×	`distribute-neg-in_binary64`
168×	`*-commutative_binary64`
153×	`distribute-rgt-neg-out_binary64`
142×	`associate-r_binary64`
140×	`associate-l_binary64`
113×	`mul0-rgt_binary64` `mul0-lft_binary64`
102×	`+-commutative_binary64`
93×	`remove-double-neg_binary64`
47×	`*-lft-identity_binary64`
46×	`*-rgt-identity_binary64`
38×	`associate-+l-_binary64`
35×	`associate--r-_binary64`
31×	`sub0-neg_binary64`
24×	`associate--l+_binary64`
23×	`associate-+r+_binary64`
17×	`associate-+r-_binary64`
15×	`associate-+l+_binary64`
14×	`cos-neg_binary64` `mul-1-neg_binary64` `+-rgt-identity_binary64`
12×	`sin-neg_binary64` `distribute-rgt-out--_binary64` `associate--l-_binary64`
8×	`cancel-sign-sub_binary64`
5×	`+-lft-identity_binary64` `distribute-lft-out--_binary64`
3×	`distribute-neg-out_binary64`
1×	`1-exp_binary64` `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` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `--rgt-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64`

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)

sample234.0ms (1.2%)

Algorithm

1×

intervals

Results

155.0ms	182×	body	1024	valid
23.0ms	42×	body	512	valid
13.0ms	7×	body	2048	valid
6.0ms	18×	body	256	valid
1.0ms	7×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64` `*-commutative_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`
7×	`unsub-neg_binary64`
6×	`neg-sub0_binary64` `associate--r-_binary64`
5×	`distribute-neg-in_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-in_binary64` `+-commutative_binary64`
4×	`*-lft-identity_binary64` `sub0-neg_binary64` `associate-+l-_binary64`
3×	`+-lft-identity_binary64` `distribute-rgt-neg-out_binary64` `associate-l_binary64` `associate-r_binary64` `associate-+l+_binary64`
2×	`cos-neg_binary64` `*-rgt-identity_binary64`
1×	`1-exp_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `distribute-lft-neg-in_binary64` `associate--l+_binary64` `associate-+r-_binary64` `associate-+r+_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `log-prod_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow3_binary64` `unpow2_binary64` `unpow1/2_binary64` `pow-plus_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `exp-prod_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-unmult_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-prod_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `pow-sqr_binary64` `sqr-pow_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `unswap-sqr_binary64` `swap-sqr_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `distribute-rgt-out--_binary64` `distribute-rgt-out_binary64` `distribute-lft-out--_binary64` `distribute-lft-out_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--l-_binary64`

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

prune2.0ms (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

13.5b

Counts

1 → 1

Compiler

Compiled 19 to 17 computations (10.5% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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)
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite94.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

13×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-l_binary64` `associate-r_binary64`
4×	`cos-sum_binary64` `add-log-exp_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`cos-diff_binary64` `sub-neg_binary64` `acos-asin_binary64` `sin-mult_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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 1583 to 295 computations (81.4% saved)

series154.0ms (0.8%)

Error

13.1b

Counts

4 → 46

Calls

4 calls:

57.0ms	(.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)
34.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
27.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2032 to 1611 computations (20.7% saved)

simplify142.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

465×	`neg-mul-1_binary64`
430×	`neg-sub0_binary64`
424×	`sub-neg_binary64`
371×	`associate-l_binary64`
341×	`cancel-sign-sub_binary64`
292×	`associate-r_binary64`
276×	`unsub-neg_binary64`
218×	`distribute-rgt-neg-in_binary64`
200×	`distribute-lft-neg-in_binary64`
187×	`distribute-lft-neg-out_binary64`
146×	`*-commutative_binary64`
129×	`distribute-rgt-neg-out_binary64`
116×	`cancel-sign-sub-inv_binary64`
103×	`sqr-pow_binary64`
88×	`associate-+l-_binary64`
81×	`distribute-neg-in_binary64`
78×	`distribute-rgt-out--_binary64`
77×	`distribute-rgt-in_binary64`
74×	`unswap-sqr_binary64`
70×	`associate-+l+_binary64`
68×	`distribute-lft-in_binary64`
67×	`+-commutative_binary64`
55×	`distribute-lft-out--_binary64`
52×	`associate--l+_binary64`
50×	`associate-+r+_binary64`
47×	`sub0-neg_binary64`
46×	`distribute-lft-out_binary64`
45×	`distribute-neg-out_binary64` `distribute-rgt-out_binary64`
41×	`associate-+r-_binary64`
35×	`mul0-rgt_binary64` `mul0-lft_binary64`
31×	`cube-prod_binary64`
30×	`associate--r+_binary64`
26×	`remove-double-neg_binary64`
25×	`-rgt-identity_binary64` `-lft-identity_binary64`
24×	`cube-unmult_binary64` `+-rgt-identity_binary64`
22×	`rem-sqrt-square_binary64` `pow-sqr_binary64`
21×	`associate--l-_binary64`
20×	`exp-prod_binary64`
18×	`log-prod_binary64`
15×	`unpow3_binary64` `associate--r-_binary64`
13×	`--rgt-identity_binary64`
12×	`swap-sqr_binary64`
11×	`fabs-mul_binary64`
9×	`cos-neg_binary64` `pow-plus_binary64`
8×	`sqr-neg_binary64` `difference-of-squares_binary64`
7×	`sin-neg_binary64` `unpow1/2_binary64`
4×	`cube-neg_binary64` `fabs-sqr_binary64` `associate-/l*_binary64`
3×	`fabs-sub_binary64` `distribute-rgt1-in_binary64`
2×	`cube-mult_binary64` `mul-1-neg_binary64` `distribute-lft1-in_binary64` `associate-/l/_binary64` `associate-*r/_binary64`
1×	`unpow2_binary64` `unpow1_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `+-lft-identity_binary64` `count-2_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `exp-sum_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-neg_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `times-frac_binary64` `div-sub_binary64` `/-rgt-identity_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `associate-/r/_binary64` `associate-/r_binary64` `associate-*l/_binary64`

Counts

103 → 42

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	164	2571
1	326	2315
2	781	2300
3	1659	2293
4	3184	2293
5	4389	2293
6	4838	2293

prune60.0ms (0.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	30	12	42
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	12	43

Error

3.2b

Counts

43 → 12

Compiler

Compiled 1446 to 459 computations (68.3% saved)

localize26.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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)
0.9b	(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))))))

rewrite150.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `-un-lft-identity_binary64` `associate-r*_binary64`
7×	`associate-l_binary64`
6×	`cos-mult_binary64`
5×	`pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64`
4×	`add-log-exp_binary64`
3×	`-commutative_binary64` `sin-mult_binary64` `frac-times_binary64` `associate-r/_binary64`
2×	`unswap-sqr_binary64` `frac-add_binary64` `flip3-+_binary64` `flip-+_binary64`
1×	`acos-asin_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-*l/_binary64`

Counts

4 → 72

Calls

4 calls:

10.0ms	(.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 phi1) (sin.f64 phi2))
3.0ms	(.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)
2.0ms	(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 2720 to 392 computations (85.6% saved)

series335.0ms (1.7%)

Error

3.2b

Counts

4 → 58

Calls

4 calls:

135.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
90.0ms	(.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)
45.0ms	(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))))))
27.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4377 to 2775 computations (36.6% saved)

simplify200.0ms (1%)

Algorithm

1×	egg-herbie

Rules

931×	`cancel-sign-sub-inv_binary64`
530×	`associate-r_binary64`
496×	`associate-l_binary64`
302×	`distribute-rgt-neg-in_binary64`
257×	`*-commutative_binary64`
167×	`exp-prod_binary64`
151×	`sub-neg_binary64`
94×	`distribute-rgt-in_binary64`
91×	`distribute-lft-in_binary64`
89×	`+-commutative_binary64`
71×	`sqr-pow_binary64`
62×	`neg-mul-1_binary64` `neg-sub0_binary64`
58×	`associate--l+_binary64`
50×	`distribute-neg-in_binary64`
44×	`*-rgt-identity_binary64`
42×	`log-prod_binary64` `associate--r+_binary64`
41×	`associate-+l+_binary64`
38×	`*-lft-identity_binary64`
34×	`associate-+r+_binary64`
30×	`distribute-lft-neg-out_binary64`
29×	`swap-sqr_binary64`
27×	`cube-prod_binary64`
26×	`unsub-neg_binary64`
20×	`distribute-rgt-out_binary64`
19×	`unswap-sqr_binary64` `distribute-lft-neg-in_binary64`
15×	`unpow3_binary64`
13×	`cube-unmult_binary64`
10×	`distribute-lft-out_binary64`
9×	`cube-mult_binary64`
7×	`distribute-rgt-neg-out_binary64`
6×	`unpow1/2_binary64` `exp-sum_binary64`
5×	`pow-plus_binary64`
3×	`unpow2_binary64` `unpow1_binary64` `pow-sqr_binary64` `distribute-rgt-out--_binary64`
2×	`difference-of-squares_binary64` `distribute-rgt1-in_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `associate-+l-_binary64` `associate-+r-_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-pow_binary64` `log-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `exp-to-pow_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-lft-sqr_binary64` `exp-cbrt_binary64` `exp-sqrt_binary64` `div-exp_binary64` `rec-exp_binary64` `prod-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-sqrt-square_binary64` `rem-square-sqrt_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64` `distribute-lft-out--_binary64` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

130 → 95

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	293	5364
1	832	4685
2	3191	4685
3	4896	4685
4	4997	4685
5	4968	4685

prune108.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	94	13	107

Error

3.2b

Counts

107 → 13

Compiler

Compiled 2955 to 778 computations (73.7% saved)

localize29.0ms (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)
0.3b	(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))))))))
0.6b	(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)))))))))
0.9b	(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)))))))

rewrite115.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

12×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
9×	`exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`acos-asin_binary64` `log-prod_binary64` `associate-r_binary64`
2×	`exp-diff_binary64`
1×	`log-div_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.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))))))))
1.0ms	(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 2584 to 212 computations (91.8% saved)

series574.0ms (2.9%)

Error

3.2b

Counts

4 → 51

Calls

4 calls:

266.0ms	(.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)
187.0ms	(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)))))))))
68.0ms	(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))))))))
49.0ms	(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 3502 to 2575 computations (26.5% saved)

simplify263.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
339×	`log-prod_binary64`
336×	`unswap-sqr_binary64`
323×	`distribute-rgt-out_binary64`
285×	`associate-l_binary64`
270×	`exp-prod_binary64`
250×	`distribute-lft-in_binary64`
248×	`distribute-rgt-in_binary64`
228×	`*-commutative_binary64`
204×	`associate-r_binary64`
199×	`associate-+l+_binary64`
178×	`associate-*l/_binary64`
168×	`sqr-pow_binary64`
118×	`associate-*r/_binary64`
104×	`log-div_binary64`
94×	`associate-+r+_binary64`
83×	`exp-sum_binary64` `cube-prod_binary64`
74×	`log-pow_binary64`
64×	`associate-/l/_binary64`
62×	`associate-/l*_binary64`
57×	`cube-div_binary64`
56×	`pow-sqr_binary64`
53×	`exp-to-pow_binary64`
51×	`unpow3_binary64`
45×	`count-2_binary64`
43×	`unsub-neg_binary64`
42×	`swap-sqr_binary64`
36×	`distribute-rgt1-in_binary64`
34×	`pow-plus_binary64`
33×	`exp-sqrt_binary64`
32×	`rem-sqrt-square_binary64`
29×	`*-rgt-identity_binary64`
27×	`cube-unmult_binary64` `associate-/r/_binary64`
26×	`*-lft-identity_binary64`
21×	`fabs-mul_binary64`
19×	`associate-/r*_binary64`
17×	`exp-lft-sqr_binary64`
13×	`log-rec_binary64` `distribute-lft-out_binary64`
10×	`unpow1/2_binary64` `rem-log-exp_binary64` `distribute-lft1-in_binary64` `+-commutative_binary64`
9×	`cube-mult_binary64`
7×	`fabs-sqr_binary64`
6×	`rem-exp-log_binary64`
5×	`prod-exp_binary64`
3×	`sub-neg_binary64`
1×	`unpow2_binary64` `exp-lft-cube_binary64` `1-exp_binary64` `exp-1-e_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `/-rgt-identity_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow1_binary64` `unpow-1_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `rem-square-sqrt_binary64` `div-sub_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

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	1142	4840
6	2974	4840
7	4482	4840
8	4969	4840

prune60.0ms (0.3%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	87	15	102

Error

3.1b

Counts

102 → 15

Compiler

Compiled 2127 to 529 computations (75.1% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)))))))
0.6b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))
0.6b	(log.f64 (exp.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))

rewrite170.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

16×	`log-pow_binary64` `exp-prod_binary64`
12×	`log-prod_binary64`
11×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
7×	`pow1_binary64`
5×	`add-log-exp_binary64`
4×	`acos-asin_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `exp-diff_binary64`
3×	`log-div_binary64` `exp-sum_binary64`
2×	`rem-log-exp_binary64`
1×	`rem-exp-log_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(log.f64 (exp.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))))
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)))))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))

Compiler

Compiled 3334 to 310 computations (90.7% saved)

series646.0ms (3.3%)

Error

3.1b

Counts

4 → 48

Calls

4 calls:

328.0ms	(log.f64 (exp.f64 (log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))))
188.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))))
72.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1)))))))
52.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (sin.f64 lambda2) (.f64 (sin.f64 lambda1) (.f64 (cos.f64 phi1) (cos.f64 phi2)))) (.f64 (cos.f64 lambda2) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 lambda1))))))

Compiler

Compiled 3492 to 2619 computations (25% saved)

simplify275.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

915×	`log-prod_binary64`
850×	`unswap-sqr_binary64`
395×	`associate-/l/_binary64`
328×	`associate-l_binary64`
232×	`associate-r_binary64`
216×	`associate-/r/_binary64`
200×	`times-frac_binary64`
136×	`distribute-rgt-in_binary64`
113×	`distribute-lft-in_binary64`
102×	`sqr-pow_binary64`
96×	`log-pow_binary64` `*-commutative_binary64`
93×	`distribute-rgt-out_binary64`
81×	`exp-prod_binary64` `associate-/l*_binary64`
69×	`distribute-lft-out_binary64`
53×	`exp-sum_binary64`
39×	`pow-sqr_binary64`
38×	`associate-*r/_binary64`
35×	`associate-*l/_binary64`
29×	`exp-to-pow_binary64`
22×	`count-2_binary64`
21×	`exp-sqrt_binary64` `cube-unmult_binary64`
20×	`rem-log-exp_binary64`
18×	`cube-prod_binary64`
16×	`associate-/r*_binary64` `associate-+r+_binary64`
15×	`pow-plus_binary64` `rem-sqrt-square_binary64` `associate-+l+_binary64`
13×	`prod-exp_binary64` `rem-exp-log_binary64`
11×	`fabs-mul_binary64` `swap-sqr_binary64`
9×	`distribute-rgt1-in_binary64`
8×	`exp-lft-sqr_binary64` `+-commutative_binary64`
6×	`/-rgt-identity_binary64` `distribute-lft1-in_binary64`
3×	`log-div_binary64`
2×	`unpow3_binary64` `unpow1/2_binary64` `unpow1_binary64` `-rgt-identity_binary64` `-lft-identity_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `rem-square-sqrt_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `erfc-erf_binary64` `erf-erfc_binary64` `erf-odd_binary64` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `not-gte_binary64` `not-lte_binary64` `not-gt_binary64` `not-lt_binary64` `gte-same_binary64` `lte-same_binary64` `gt-same_binary64` `lt-same_binary64` `sinh---cosh_binary64` `sinh-+-cosh_binary64` `sinh-cosh_binary64` `tanh-def-c_binary64` `tanh-def-b_binary64` `tanh-def-a_binary64` `cosh-def_binary64` `sinh-def_binary64` `tan-neg_binary64` `cos-neg_binary64` `sin-neg_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `hang-m-tan_binary64` `hang-p-tan_binary64` `hang-m0-tan_binary64` `hang-p0-tan_binary64` `hang-0m-tan_binary64` `hang-0p-tan_binary64` `tan-+PI/2_binary64` `tan-+PI_binary64` `tan-PI_binary64` `tan-PI/3_binary64` `tan-PI/4_binary64` `tan-PI/6_binary64` `cos-+PI/2_binary64` `cos-+PI_binary64` `cos-PI_binary64` `cos-PI/2_binary64` `cos-PI/3_binary64` `cos-PI/4_binary64` `cos-PI/6_binary64` `sin-+PI/2_binary64` `sin-+PI_binary64` `sin-PI_binary64` `sin-PI/2_binary64` `sin-PI/3_binary64` `sin-PI/4_binary64` `sin-PI/6_binary64` `sub-1-sin_binary64` `sub-1-cos_binary64` `-1-add-sin_binary64` `-1-add-cos_binary64` `1-sub-sin_binary64` `1-sub-cos_binary64` `cos-sin-sum_binary64` `log-E_binary64` `log-rec_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_binary64` `pow-base-1_binary64` `unpow0_binary64` `unpow-1_binary64` `exp-lft-cube_binary64` `exp-cbrt_binary64` `div-exp_binary64` `rec-exp_binary64` `exp-diff_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `cube-mult_binary64` `cube-div_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `fabs-div_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `div-sub_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `div0_binary64` `*-inverses_binary64` `+-inverses_binary64` `lft-mult-inverse_binary64` `rgt-mult-inverse_binary64` `remove-double-div_binary64` `difference-of-sqr--1_binary64` `difference-of-sqr-1_binary64` `difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out--_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate--l+_binary64` `associate--r+_binary64` `associate-+l-_binary64` `associate-+r-_binary64`

Counts

107 → 96

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	103	6477
1	95	4743
2	160	4743
3	223	4739
4	269	4739
5	372	4739
6	621	4739
7	1444	4721
8	4293	4721
9	5366	4721

prune100.0ms (0.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	93	18	111

Error

3.1b

Counts

111 → 18

Compiler

Compiled 2111 to 244 computations (88.4% saved)

regimes4.7s (23.8%)

Accuracy

Total 0.4b remaining (11.8%)

Threshold costs 0.4b (11.8%)

Compiler

Compiled 87819 to 55392 computations (36.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
0×	`not-true` `not-false` `not-not` `not-and` `not-or` `and-true-l` `and-true-r` `and-false-l` `and-false-r` `and-same` `or-true-l` `or-true-r` `or-false-l` `or-false-r` `or-same` `if-if-and-not_binary64` `if-if-and_binary64` `if-if-or-not_binary64` `if-if-or_binary64` `if-not_binary64` `if-same_binary64` `if-false_binary64` `if-true_binary64` `tan-0_binary64` `cos-0_binary64` `sin-0_binary64` `unpow1_binary64` `e-exp-1_binary64` `1-exp_binary64` `exp-1-e_binary64` `exp-0_binary64` `fabs-div_binary64` `fabs-mul_binary64` `fabs-sqr_binary64` `fabs-neg_binary64` `fabs-sub_binary64` `fabs-fabs_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `neg-mul-1_binary64` `neg-sub0_binary64` `unsub-neg_binary64` `sub-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `remove-double-neg_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub-inv_binary64` `cancel-sign-sub_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	47
1	33	47
2	33	47

end25.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 140 to 120 computations (14.3% saved)

sample7.5s (38.4%)

Algorithm

1×

intervals

Results

4.8s	5547×	body	1024	valid
760.0ms	1362×	body	512	valid
512.0ms	261×	body	2048	valid
178.0ms	518×	body	256	valid
53.0ms	312×	body	128	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	512	invalid

Compiler

Compiled 1013 to 557 computations (45% 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 (18.3%)

sample234.0ms (1.2%)

simplify13.0ms (0.1%)

prune2.0ms (0%)

localize19.0ms (0.1%)

rewrite94.0ms (0.5%)

series154.0ms (0.8%)

simplify142.0ms (0.7%)

prune60.0ms (0.3%)

localize26.0ms (0.1%)

rewrite150.0ms (0.8%)

series335.0ms (1.7%)

simplify200.0ms (1%)

prune108.0ms (0.6%)

localize29.0ms (0.1%)

rewrite115.0ms (0.6%)

series574.0ms (2.9%)

simplify263.0ms (1.3%)

prune60.0ms (0.3%)

localize34.0ms (0.2%)

rewrite170.0ms (0.9%)

series646.0ms (3.3%)

simplify275.0ms (1.4%)

prune100.0ms (0.5%)

regimes4.7s (23.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end25.0ms (0.1%)

sample7.5s (38.4%)

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