Details

analyze3.6s (17.7%)

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` `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)

sample454.0ms (2.2%)

Algorithm

1×

intervals

Results

379.0ms	181×	body	1024	valid
26.0ms	49×	body	512	valid
12.0ms	5×	body	2048	valid
4.0ms	13×	body	256	valid
1.0ms	8×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify14.0ms (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` `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

16.0b

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 (.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)
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)))))
3.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite105.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.5b

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`associate-r_binary64`
4×	`cos-sum_binary64` `add-log-exp_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64`
3×	`cos-diff_binary64` `cancel-sign-sub-inv_binary64`
2×	`*-commutative_binary64`
1×	`sub-neg_binary64` `acos-asin_binary64` `unswap-sqr_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `cos-mult_binary64` `associate-*l/_binary64`

Counts

4 → 59

Calls

4 calls:

7.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(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 1691 to 307 computations (81.8% saved)

series228.0ms (1.1%)

Error

15.1b

Counts

4 → 61

Calls

4 calls:

80.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
58.0ms	(.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)
35.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
23.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3016 to 2109 computations (30.1% saved)

simplify151.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

534×	`distribute-rgt-neg-in_binary64`
464×	`distribute-lft-neg-in_binary64`
449×	`sub-neg_binary64`
436×	`cancel-sign-sub-inv_binary64`
434×	`neg-mul-1_binary64`
416×	`neg-sub0_binary64`
283×	`associate-r_binary64`
278×	`associate-l_binary64`
257×	`unsub-neg_binary64`
160×	`*-commutative_binary64`
150×	`distribute-lft-neg-out_binary64`
130×	`cancel-sign-sub_binary64`
97×	`distribute-rgt-neg-out_binary64`
90×	`sqr-pow_binary64`
79×	`+-commutative_binary64`
56×	`distribute-rgt-out--_binary64`
52×	`distribute-rgt-out_binary64`
50×	`distribute-neg-out_binary64` `associate--l+_binary64`
47×	`unswap-sqr_binary64` `associate-+l+_binary64`
46×	`associate-+l-_binary64`
40×	`cube-prod_binary64`
38×	`associate-+r-_binary64`
37×	`exp-prod_binary64`
35×	`associate-+r+_binary64`
33×	`log-prod_binary64`
32×	`associate--r+_binary64`
30×	`swap-sqr_binary64`
27×	`*-rgt-identity_binary64`
24×	`+-rgt-identity_binary64`
21×	`remove-double-neg_binary64` `sub0-neg_binary64`
20×	`*-lft-identity_binary64`
16×	`cube-unmult_binary64` `pow-sqr_binary64`
14×	`distribute-rgt-in_binary64`
13×	`distribute-neg-in_binary64`
12×	`unpow3_binary64` `rem-sqrt-square_binary64`
9×	`unpow1/2_binary64`
6×	`cos-neg_binary64` `difference-of-squares_binary64`
5×	`cube-mult_binary64` `distribute-lft-out--_binary64`
4×	`sin-neg_binary64` `unpow2_binary64` `pow-plus_binary64` `unpow1_binary64` `distribute-rgt1-in_binary64` `distribute-lft-in_binary64`
2×	`exp-sum_binary64` `mul0-rgt_binary64` `mul0-lft_binary64` `associate--l-_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `sqr-neg_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` `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` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `--rgt-identity_binary64` `+-lft-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` `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`

Counts

120 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	210	3470
1	513	3100
2	1646	2998
3	3018	2996
4	4448	2994
5	5063	2994

prune77.0ms (0.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	47	13	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	13	61

Error

3.5b

Counts

61 → 13

Compiler

Compiled 1880 to 599 computations (68.1% 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 (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)
0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
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))))))

rewrite166.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

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×	`sin-mult_binary64` `frac-times_binary64` `associate-r/_binary64` `-commutative_binary64`
2×	`frac-add_binary64` `flip3-+_binary64` `flip-+_binary64` `unswap-sqr_binary64`
1×	`acos-asin_binary64` `distribute-rgt-in_binary64` `distribute-lft-in_binary64` `associate-*l/_binary64`

Counts

4 → 72

Calls

4 calls:

12.0ms	(.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)
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 2720 to 392 computations (85.6% saved)

series343.0ms (1.7%)

Error

3.5b

Counts

4 → 58

Calls

4 calls:

137.0ms	(.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)
46.0ms	(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))))))
29.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4368 to 2759 computations (36.8% saved)

simplify169.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

895×	`cancel-sign-sub-inv_binary64`
522×	`associate-r_binary64`
484×	`associate-l_binary64`
325×	`distribute-rgt-neg-in_binary64`
302×	`distribute-lft-neg-in_binary64`
292×	`neg-mul-1_binary64` `neg-sub0_binary64`
254×	`*-commutative_binary64`
173×	`sub-neg_binary64`
164×	`sqr-pow_binary64`
157×	`exp-prod_binary64`
94×	`distribute-rgt-in_binary64`
91×	`distribute-lft-in_binary64`
79×	`+-commutative_binary64`
53×	`unsub-neg_binary64`
49×	`cube-prod_binary64` `associate--l+_binary64`
42×	`log-prod_binary64`
40×	`*-rgt-identity_binary64`
35×	`*-lft-identity_binary64`
33×	`associate--r+_binary64` `associate-+l+_binary64`
30×	`distribute-neg-in_binary64`
28×	`distribute-lft-neg-out_binary64`
27×	`swap-sqr_binary64`
25×	`associate-+r+_binary64`
20×	`pow-sqr_binary64`
18×	`distribute-rgt-out_binary64`
17×	`unswap-sqr_binary64`
16×	`unpow3_binary64` `cube-unmult_binary64`
12×	`cube-mult_binary64`
9×	`distribute-lft-out_binary64`
8×	`exp-sum_binary64`
7×	`unpow1/2_binary64` `distribute-rgt-neg-out_binary64`
4×	`unpow2_binary64` `pow-plus_binary64` `unpow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-rgt-out--_binary64`
2×	`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` `sqr-abs_binary64` `sqr-neg_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	281	5286
1	807	4622
2	3074	4622
3	4265	4622
4	5142	4622

prune119.0ms (0.6%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	84	11	95
Fresh	8	4	12
Picked	0	1	1
Done	0	0	0
Total	92	16	108

Error

3.4b

Counts

108 → 16

Compiler

Compiled 3008 to 787 computations (73.8% saved)

localize32.0ms (0.2%)

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)))))))

rewrite115.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

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:

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))))))))
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)

series576.0ms (2.8%)

Error

3.4b

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)
189.0ms	(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)

simplify348.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

666×	`times-frac_binary64`
426×	`unswap-sqr_binary64`
398×	`distribute-rgt-in_binary64`
359×	`distribute-lft-in_binary64`
340×	`log-prod_binary64`
324×	`distribute-rgt-out_binary64`
302×	`associate-l_binary64`
273×	`*-commutative_binary64`
223×	`associate-r_binary64`
202×	`associate-+l+_binary64`
181×	`associate-*l/_binary64`
168×	`sqr-pow_binary64`
133×	`log-pow_binary64`
120×	`exp-prod_binary64`
118×	`associate-*r/_binary64`
104×	`log-div_binary64`
97×	`associate-+r+_binary64`
93×	`exp-sum_binary64`
75×	`cube-prod_binary64`
70×	`count-2_binary64`
67×	`distribute-lft-out_binary64`
64×	`associate-/l/_binary64`
62×	`exp-to-pow_binary64` `associate-/l*_binary64`
58×	`pow-sqr_binary64`
57×	`cube-div_binary64`
49×	`unpow3_binary64`
43×	`unsub-neg_binary64`
40×	`swap-sqr_binary64`
37×	`distribute-rgt1-in_binary64`
35×	`pow-plus_binary64`
31×	`*-rgt-identity_binary64`
29×	`exp-sqrt_binary64` `rem-sqrt-square_binary64`
27×	`*-lft-identity_binary64` `associate-/r/_binary64`
26×	`cube-unmult_binary64`
19×	`associate-/r*_binary64`
18×	`log-rec_binary64`
11×	`distribute-lft1-in_binary64`
10×	`unpow1/2_binary64` `rem-log-exp_binary64` `+-commutative_binary64`
9×	`cube-mult_binary64`
8×	`exp-lft-sqr_binary64`
7×	`rem-exp-log_binary64`
5×	`prod-exp_binary64`
3×	`sub-neg_binary64`
1×	`unpow2_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-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-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_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	1298	4840
6	2920	4840
7	4531	4840
8	4947	4840
9	4996	4840
10	4866	4840

prune68.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	83	6	89
Fresh	4	10	14
Picked	1	0	1
Done	1	0	1
Total	89	16	105

Error

3.4b

Counts

105 → 16

Compiler

Compiled 2170 to 541 computations (75.1% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
0.5b	(asin.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)))))))
0.8b	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))

rewrite144.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

3.2b

Rules

23×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64` `associate-l_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64`
4×	`difference-of-squares_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`flip3--_binary64` `flip--_binary64` `times-frac_binary64` `distribute-lft-out--_binary64` `asin-acos_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`diff-log_binary64` `sub-neg_binary64` `associate--r-_binary64` `sin-mult_binary64`

Counts

4 → 68

Calls

4 calls:

11.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))
11.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
1.0ms	(asin.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 3170 to 577 computations (81.8% saved)

series272.0ms (1.3%)

Error

3.3b

Counts

4 → 47

Calls

4 calls:

112.0ms	(.f64 (-.f64 (/.f64 PI.f64 2) (asin.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)
65.0ms	(-.f64 (/.f64 PI.f64 2) (asin.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))))))))
50.0ms	(asin.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)))))))
31.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3530 to 2593 computations (26.5% saved)

simplify193.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

597×	`unsub-neg_binary64`
470×	`associate-l_binary64`
389×	`associate-r_binary64`
363×	`neg-sub0_binary64`
357×	`neg-mul-1_binary64`
181×	`cancel-sign-sub-inv_binary64`
166×	`distribute-rgt-neg-out_binary64`
156×	`*-commutative_binary64`
151×	`distribute-lft-neg-out_binary64`
140×	`associate-*l/_binary64`
134×	`distribute-lft-in_binary64` `associate-*r/_binary64`
130×	`distribute-rgt-in_binary64`
120×	`exp-prod_binary64`
106×	`+-commutative_binary64`
98×	`distribute-lft-neg-in_binary64`
88×	`distribute-rgt-neg-in_binary64`
79×	`associate-+r+_binary64`
72×	`associate-/l*_binary64` `associate-+l+_binary64`
69×	`sqr-pow_binary64`
63×	`sub-neg_binary64`
39×	`times-frac_binary64`
38×	`unswap-sqr_binary64`
33×	`exp-sum_binary64`
32×	`distribute-rgt-out_binary64`
31×	`log-prod_binary64` `-rgt-identity_binary64` `-lft-identity_binary64`
20×	`cube-prod_binary64` `div-sub_binary64` `swap-sqr_binary64`
19×	`associate-/l/_binary64` `associate-+l-_binary64`
18×	`exp-neg_binary64` `associate-/r/_binary64`
17×	`cube-unmult_binary64`
16×	`exp-diff_binary64`
15×	`distribute-lft-out_binary64` `associate-/r*_binary64` `associate-+r-_binary64`
12×	`mul0-rgt_binary64` `mul0-lft_binary64`
11×	`+-rgt-identity_binary64`
10×	`unpow3_binary64` `sub0-neg_binary64` `pow-sqr_binary64` `distribute-rgt-out--_binary64`
9×	`exp-sqrt_binary64` `associate--r+_binary64`
8×	`mul-1-neg_binary64` `difference-of-squares_binary64`
7×	`sqr-neg_binary64`
6×	`rem-sqrt-square_binary64` `distribute-lft-out--_binary64`
4×	`unpow1/2_binary64` `pow-plus_binary64` `cube-mult_binary64` `cube-div_binary64` `associate--l+_binary64`
3×	`distribute-neg-in_binary64`
2×	`distribute-rgt1-in_binary64` `count-2_binary64`
1×	`cos-neg_binary64` `log-pow_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_binary64` `+-inverses_binary64` `distribute-neg-frac_binary64` `distribute-lft1-in_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-rec_binary64` `log-div_binary64` `pow-base-0_binary64` `unpow1/3_binary64` `unpow2_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` `rec-exp_binary64` `prod-exp_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `rem-3cbrt-rft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `/-rgt-identity_binary64` `remove-double-neg_binary64` `--rgt-identity_binary64` `+-lft-identity_binary64` `div0_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-frac-neg_binary64` `distribute-neg-out_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

115 → 76

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	155	5679
1	337	4948
2	825	4934
3	2173	4860
4	3985	4860
5	5243	4860

prune54.0ms (0.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	71	5	76
Fresh	3	12	15
Picked	1	0	1
Done	0	0	0
Total	75	17	92

Error

3.2b

Counts

92 → 17

Compiler

Compiled 1497 to 313 computations (79.1% saved)

regimes5.4s (26.2%)

Accuracy

Total 0.5b remaining (14.4%)

Threshold costs 0.5b (14.4%)

Compiler

Compiled 108874 to 67779 computations (37.7% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
8×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`neg-mul-1_binary64` `neg-sub0_binary64`
4×	`distribute-neg-in_binary64`
3×	`distribute-rgt-neg-in_binary64`
2×	`unsub-neg_binary64` `distribute-lft-neg-out_binary64` `distribute-lft-neg-in_binary64`
1×	`1-exp_binary64` `remove-double-neg_binary64` `distribute-neg-frac_binary64` `distribute-rgt-neg-out_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` `exp-1-e_binary64` `exp-0_binary64` `sqr-abs_binary64` `sqr-neg_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `-rgt-identity_binary64` `-lft-identity_binary64` `sub0-neg_binary64` `--rgt-identity_binary64` `+-rgt-identity_binary64` `+-lft-identity_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	57
1	40	57
2	51	57
3	66	57
4	80	57
5	85	57
6	86	57
7	82	57

end30.0ms (0.1%)

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 170 to 145 computations (14.7% saved)

sample7.8s (37.9%)

Algorithm

1×

intervals

Results

5.0s	5442×	body	1024	valid
806.0ms	1459×	body	512	valid
550.0ms	271×	body	2048	valid
180.0ms	498×	body	256	valid
61.0ms	330×	body	128	valid
1.0ms	1×	body	1024	invalid
1.0ms	1×	body	512	invalid

Compiler

Compiled 1045 to 541 computations (48.2% 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 (17.7%)

sample454.0ms (2.2%)

simplify14.0ms (0.1%)

prune2.0ms (0%)

localize19.0ms (0.1%)

rewrite105.0ms (0.5%)

series228.0ms (1.1%)

simplify151.0ms (0.7%)

prune77.0ms (0.4%)

localize26.0ms (0.1%)

rewrite166.0ms (0.8%)

series343.0ms (1.7%)

simplify169.0ms (0.8%)

prune119.0ms (0.6%)

localize32.0ms (0.2%)

rewrite115.0ms (0.6%)

series576.0ms (2.8%)

simplify348.0ms (1.7%)

prune68.0ms (0.3%)

localize29.0ms (0.1%)

rewrite144.0ms (0.7%)

series272.0ms (1.3%)

simplify193.0ms (0.9%)

prune54.0ms (0.3%)

regimes5.4s (26.2%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end30.0ms (0.1%)

sample7.8s (37.9%)

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