Details

analyze3.5s (17.4%)

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)

sample234.0ms (1.2%)

Algorithm

1×

intervals

Results

157.0ms	177×	body	1024	valid
25.0ms	50×	body	512	valid
15.0ms	9×	body	2048	valid
5.0ms	15×	body	256	valid
1.0ms	5×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify15.0ms (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

19.1b

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))
0.3b	(.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)))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite95.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.4b

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	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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 1583 to 295 computations (81.4% saved)

series148.0ms (0.7%)

Error

18.0b

Counts

4 → 44

Calls

4 calls:

60.0ms	(.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)
30.0ms	(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))
20.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 1914 to 1545 computations (19.3% saved)

simplify177.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

441×	`sub-neg_binary64`
437×	`unsub-neg_binary64`
397×	`distribute-rgt-neg-in_binary64`
340×	`distribute-lft-neg-in_binary64`
317×	`cancel-sign-sub-inv_binary64`
288×	`neg-mul-1_binary64`
287×	`*-commutative_binary64`
283×	`associate-l_binary64`
275×	`neg-sub0_binary64`
258×	`unswap-sqr_binary64`
237×	`cancel-sign-sub_binary64`
236×	`sqr-pow_binary64`
215×	`associate-r_binary64`
184×	`distribute-lft-neg-out_binary64`
147×	`distribute-rgt-neg-out_binary64`
134×	`distribute-lft-out--_binary64`
130×	`distribute-neg-in_binary64`
116×	`distribute-lft-out_binary64`
94×	`remove-double-neg_binary64`
90×	`pow-sqr_binary64`
79×	`distribute-rgt-in_binary64`
78×	`distribute-rgt-out--_binary64`
70×	`distribute-lft-in_binary64`
61×	`associate--r-_binary64`
57×	`associate-+l-_binary64`
56×	`distribute-rgt-out_binary64`
51×	`associate-+l+_binary64` `+-commutative_binary64`
40×	`mul0-rgt_binary64` `mul0-lft_binary64` `associate-+r+_binary64`
38×	`cube-prod_binary64`
32×	`sub0-neg_binary64` `distribute-neg-out_binary64`
27×	`associate-+r-_binary64`
26×	`rem-sqrt-square_binary64`
25×	`associate--l+_binary64`
22×	`cube-unmult_binary64`
21×	`difference-of-squares_binary64`
20×	`exp-prod_binary64` `--rgt-identity_binary64`
18×	`log-prod_binary64` `-lft-identity_binary64` `associate-/l_binary64`
17×	`pow-plus_binary64`
16×	`associate--r+_binary64`
14×	`+-rgt-identity_binary64` `swap-sqr_binary64` `associate-/l/_binary64` `associate--l-_binary64`
13×	`*-rgt-identity_binary64`
12×	`unpow3_binary64`
8×	`cos-neg_binary64` `unpow1/2_binary64` `associate-*r/_binary64`
6×	`sin-neg_binary64` `unpow2_binary64`
5×	`distribute-rgt1-in_binary64`
4×	`sqr-neg_binary64` `associate-/r/_binary64` `associate-/r*_binary64`
3×	`unpow1_binary64` `cube-neg_binary64` `mul-1-neg_binary64` `distribute-lft1-in_binary64`
2×	`/-rgt-identity_binary64` `associate-*l/_binary64`
1×	`1-exp_binary64` `exp-1-e_binary64` `cube-mult_binary64` `rem-3cbrt-lft_binary64` `rem-square-sqrt_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` `sqr-abs_binary64` `times-frac_binary64` `div-sub_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`

Counts

101 → 40

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	150	2494
1	285	2258
2	626	2251
3	1199	2243
4	2452	2243
5	3915	2243
6	4677	2243
7	4900	2243

prune282.0ms (1.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	27	13	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	28	13	41

Error

3.4b

Counts

41 → 13

Compiler

Compiled 1382 to 442 computations (68% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

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 (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)
0.8b	(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))))))

rewrite173.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

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:

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))))
6.0ms	(*.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)

series354.0ms (1.7%)

Error

3.4b

Counts

4 → 63

Calls

4 calls:

140.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
89.0ms	(.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))))))
33.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 4760 to 2949 computations (38% saved)

simplify186.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

587×	`associate-r_binary64`
529×	`associate-l_binary64`
405×	`distribute-rgt-neg-in_binary64`
373×	`distribute-lft-neg-in_binary64`
281×	`*-commutative_binary64`
180×	`sub-neg_binary64`
157×	`exp-prod_binary64`
113×	`cancel-sign-sub-inv_binary64`
101×	`+-commutative_binary64`
94×	`distribute-rgt-in_binary64`
91×	`distribute-lft-in_binary64`
84×	`sqr-pow_binary64`
78×	`neg-mul-1_binary64` `neg-sub0_binary64`
70×	`associate--l+_binary64`
54×	`distribute-neg-in_binary64`
50×	`associate--r+_binary64`
46×	`*-rgt-identity_binary64`
44×	`associate-+l+_binary64`
42×	`log-prod_binary64`
38×	`*-lft-identity_binary64`
34×	`distribute-lft-neg-out_binary64` `associate-+r+_binary64`
33×	`unsub-neg_binary64`
29×	`swap-sqr_binary64`
28×	`cube-prod_binary64`
25×	`unswap-sqr_binary64`
24×	`distribute-rgt-out_binary64`
18×	`unpow3_binary64`
15×	`cube-unmult_binary64`
10×	`cube-mult_binary64` `distribute-lft-out_binary64`
7×	`unpow1/2_binary64` `distribute-rgt-neg-out_binary64`
6×	`pow-plus_binary64` `exp-sum_binary64`
5×	`distribute-rgt-out--_binary64`
4×	`unpow2_binary64` `unpow1_binary64` `difference-of-squares_binary64`
3×	`pow-sqr_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-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

135 → 100

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	317	5600
1	922	4881
2	3545	4881
3	4957	4881
4	5014	4881

prune120.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	86	14	100
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	98	15	113

Error

3.3b

Counts

113 → 15

Compiler

Compiled 3216 to 892 computations (72.3% saved)

localize31.0ms (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))))))))
0.5b	(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)))))))))
0.8b	(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)))))))

rewrite124.0ms (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)
2.0ms	(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)

series583.0ms (2.9%)

Error

3.3b

Counts

4 → 51

Calls

4 calls:

269.0ms	(.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)
192.0ms	(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))))))))
50.0ms	(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)

simplify355.0ms (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

prune62.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	88	16	104

Error

3.3b

Counts

104 → 16

Compiler

Compiled 2125 to 548 computations (74.2% saved)

localize34.0ms (0.2%)

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)
0.6b	(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)))))))
0.6b	(-.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))))))))

rewrite136.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

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:

10.0ms	(.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)
8.0ms	(-.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))))))))
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)

series280.0ms (1.4%)

Error

3.3b

Counts

4 → 51

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)
63.0ms	(-.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))))))))
48.0ms	(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)))))))
36.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

Compiler

Compiled 3830 to 2751 computations (28.2% saved)

simplify206.0ms (1%)

Algorithm

1×	egg-herbie

Rules

397×	`unsub-neg_binary64`
336×	`cancel-sign-sub-inv_binary64`
312×	`*-commutative_binary64`
302×	`neg-mul-1_binary64`
286×	`neg-sub0_binary64`
179×	`distribute-rgt-neg-in_binary64`
161×	`+-commutative_binary64`
159×	`distribute-lft-neg-in_binary64`
152×	`sub-neg_binary64`
134×	`distribute-lft-in_binary64`
132×	`distribute-rgt-in_binary64`
128×	`associate-l_binary64`
127×	`associate-r_binary64`
123×	`associate-*l/_binary64`
121×	`associate-+l+_binary64`
115×	`associate-*r/_binary64`
110×	`associate-+r+_binary64`
90×	`distribute-lft-neg-out_binary64`
85×	`sqr-pow_binary64` `distribute-rgt-neg-out_binary64` `associate-+l-_binary64`
66×	`exp-prod_binary64` `associate-/l*_binary64`
59×	`distribute-lft-out_binary64`
58×	`associate--l+_binary64`
48×	`distribute-lft-out--_binary64`
45×	`associate-+r-_binary64`
41×	`times-frac_binary64`
40×	`distribute-rgt-out--_binary64`
39×	`associate--r+_binary64`
37×	`distribute-rgt-out_binary64`
32×	`*-rgt-identity_binary64`
31×	`exp-sum_binary64`
30×	`*-lft-identity_binary64`
26×	`swap-sqr_binary64`
25×	`log-prod_binary64`
20×	`div-sub_binary64` `unswap-sqr_binary64`
19×	`associate-/l/_binary64` `associate-/r/_binary64`
18×	`cube-prod_binary64` `+-rgt-identity_binary64`
16×	`sub0-neg_binary64`
15×	`associate-/r*_binary64`
14×	`exp-diff_binary64`
13×	`associate--l-_binary64`
12×	`mul0-rgt_binary64` `mul0-lft_binary64`
11×	`distribute-neg-in_binary64`
10×	`pow-sqr_binary64`
9×	`exp-sqrt_binary64` `cube-unmult_binary64`
8×	`exp-neg_binary64` `difference-of-squares_binary64`
7×	`unpow3_binary64` `sqr-neg_binary64`
6×	`rem-sqrt-square_binary64`
5×	`cube-mult_binary64`
4×	`unpow1/2_binary64` `cube-div_binary64` `associate--r-_binary64`
2×	`distribute-rgt1-in_binary64` `distribute-lft1-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`
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` `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` `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` `mul-1-neg_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`

Counts

119 → 80

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	5829
1	409	5068
2	1086	5039
3	2119	4965
4	4277	4965
5	5003	4965

prune59.0ms (0.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	72	8	80
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	80	16	96

Error

3.1b

Counts

96 → 16

Compiler

Compiled 1667 to 387 computations (76.8% saved)

regimes5.2s (25.7%)

Accuracy

Total 0.6b remaining (14.2%)

Threshold costs 0.6b (14.2%)

Compiler

Compiled 105680 to 66605 computations (37% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
2×	`+-commutative_binary64`
1×	`unpow1_binary64` `1-exp_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` `e-exp-1_binary64` `exp-1-e_binary64` `exp-0_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	43
1	35	43
2	34	43

end29.0ms (0.1%)

Remove: (sort lambda1 lambda2)
Compiler: Compiled 182 to 154 computations (15.4% saved)

sample7.8s (38.5%)

Algorithm

1×

intervals

Results

5.0s	5471×	body	1024	valid
749.0ms	1429×	body	512	valid
507.0ms	257×	body	2048	valid
181.0ms	528×	body	256	valid
52.0ms	315×	body	128	valid
2.0ms	2×	body	1024	invalid
1.0ms	2×	body	512	invalid

Compiler

Compiled 1001 to 544 computations (45.7% 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

analyze3.5s (17.4%)

sample234.0ms (1.2%)

simplify15.0ms (0.1%)

prune2.0ms (0%)

localize19.0ms (0.1%)

rewrite95.0ms (0.5%)

series148.0ms (0.7%)

simplify177.0ms (0.9%)

prune282.0ms (1.4%)

localize28.0ms (0.1%)

rewrite173.0ms (0.8%)

series354.0ms (1.7%)

simplify186.0ms (0.9%)

prune120.0ms (0.6%)

localize31.0ms (0.2%)

rewrite124.0ms (0.6%)

series583.0ms (2.9%)

simplify355.0ms (1.7%)

prune62.0ms (0.3%)

localize34.0ms (0.2%)

rewrite136.0ms (0.7%)

series280.0ms (1.4%)

simplify206.0ms (1%)

prune59.0ms (0.3%)

regimes5.2s (25.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end29.0ms (0.1%)

sample7.8s (38.5%)

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