Details

analyze4.0s (21.6%)

Algorithm

1×	search
2×	egg-herbie

Rules

966×	`distribute-rgt-in_binary64`
910×	`unsub-neg_binary64`
843×	`distribute-lft-in_binary64`
580×	`distribute-rgt-neg-out_binary64`
450×	`distribute-lft-neg-out_binary64`
437×	`neg-sub0_binary64`
376×	`neg-mul-1_binary64`
344×	`distribute-rgt-neg-in_binary64`
295×	`sub-neg_binary64`
276×	`*-commutative_binary64`
230×	`cancel-sign-sub-inv_binary64`
180×	`distribute-neg-out_binary64`
165×	`distribute-lft-neg-in_binary64`
160×	`associate-l_binary64` `associate-r_binary64` `associate--r+_binary64`
137×	`remove-double-neg_binary64`
130×	`distribute-neg-in_binary64`
113×	`+-commutative_binary64`
100×	`associate-+l-_binary64`
73×	`*-lft-identity_binary64`
67×	`mul0-rgt_binary64` `mul0-lft_binary64`
60×	`+-lft-identity_binary64`
55×	`sub0-neg_binary64`
51×	`*-rgt-identity_binary64`
50×	`associate--r-_binary64`
30×	`distribute-lft-out_binary64`
25×	`--rgt-identity_binary64`
20×	`cancel-sign-sub_binary64` `associate--l+_binary64`
10×	`associate-+r-_binary64` `associate-+l+_binary64` `associate-+r+_binary64`
6×	`distribute-rgt-out--_binary64`
5×	`+-rgt-identity_binary64`
4×	`distribute-lft-out--_binary64`
1×	`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` `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` `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` `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` `count-2_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `associate-/l_binary64` `associate-/r_binary64` `associate-l/_binary64` `associate-*r/_binary64` `associate--l-_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	131	605
1	263	605
2	417	605
3	512	605
4	598	605
5	1028	605
6	994	605
7	1659	605
8	2449	605
9	2458	605
10	2534	605
11	2537	605
12	2537	605
13	2903	605
14	2948	605
15	2948	605
16	4374	605
17	4909	605
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
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample239.0ms (1.3%)

Algorithm

1×

intervals

Results

156.0ms	131×	body	1024	valid
36.0ms	40×	body	512	valid
13.0ms	63×	body	128	valid
10.0ms	21×	body	256	valid
2.0ms	1×	body	2048	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify53.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

103×	`unsub-neg_binary64`
90×	`associate-l_binary64`
88×	`distribute-rgt-in_binary64`
82×	`cancel-sign-sub-inv_binary64`
80×	`associate-r_binary64`
70×	`distribute-rgt-neg-in_binary64`
58×	`distribute-lft-neg-out_binary64`
57×	`distribute-lft-in_binary64`
56×	`distribute-rgt-neg-out_binary64`
49×	`sub-neg_binary64`
41×	`neg-sub0_binary64`
40×	`distribute-lft-neg-in_binary64`
34×	`neg-mul-1_binary64`
33×	`associate--r+_binary64`
28×	`*-commutative_binary64`
25×	`distribute-neg-in_binary64`
21×	`mul0-rgt_binary64` `mul0-lft_binary64`
17×	`+-commutative_binary64`
14×	`associate-+l-_binary64`
13×	`*-lft-identity_binary64`
12×	`remove-double-neg_binary64`
8×	`sub0-neg_binary64` `+-lft-identity_binary64`
7×	`*-rgt-identity_binary64`
5×	`associate--l+_binary64` `associate-+l+_binary64`
4×	`mul-1-neg_binary64`
3×	`--rgt-identity_binary64` `associate--r-_binary64` `associate--l-_binary64` `associate-+r+_binary64`
2×	`+-rgt-identity_binary64`
1×	`1-exp_binary64` `cancel-sign-sub_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` `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` `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-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`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

0.1b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite130.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64` `associate-r_binary64`
2×	`sin-mult_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `asin-acos_binary64`

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
4.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2513 to 351 computations (86% saved)

series231.0ms (1.2%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

85.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
70.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
29.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
28.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))

Compiler

Compiled 3021 to 1832 computations (39.4% saved)

simplify160.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

560×	`unsub-neg_binary64`
445×	`distribute-rgt-in_binary64`
337×	`distribute-rgt-neg-in_binary64`
331×	`distribute-lft-in_binary64`
292×	`distribute-lft-neg-in_binary64`
267×	`cancel-sign-sub-inv_binary64`
247×	`*-commutative_binary64`
239×	`neg-mul-1_binary64`
218×	`neg-sub0_binary64`
186×	`sub-neg_binary64`
147×	`+-commutative_binary64`
130×	`sqr-pow_binary64`
128×	`times-frac_binary64`
109×	`associate-l_binary64`
98×	`associate-r_binary64`
81×	`associate-+l-_binary64`
78×	`associate--r+_binary64`
71×	`distribute-neg-in_binary64`
59×	`associate-+l+_binary64`
57×	`distribute-lft-neg-out_binary64` `associate-+r+_binary64`
49×	`exp-prod_binary64`
47×	`distribute-rgt-neg-out_binary64`
42×	`distribute-rgt-out_binary64`
38×	`associate-/l*_binary64`
34×	`exp-sum_binary64`
33×	`distribute-neg-out_binary64`
32×	`unswap-sqr_binary64`
30×	`associate-+r-_binary64`
29×	`mul0-rgt_binary64` `mul0-lft_binary64`
28×	`sub0-neg_binary64` `pow-sqr_binary64` `associate-/r*_binary64`
27×	`cube-prod_binary64`
26×	`rem-sqrt-square_binary64`
21×	`swap-sqr_binary64` `associate--l+_binary64`
20×	`log-prod_binary64` `distribute-rgt-out--_binary64`
19×	`div-sub_binary64` `+-rgt-identity_binary64`
18×	`difference-of-squares_binary64`
17×	`*-lft-identity_binary64` `associate-/l/_binary64`
16×	`exp-diff_binary64`
15×	`cube-unmult_binary64` `-rgt-identity_binary64` `associate-r/_binary64`
11×	`unpow3_binary64` `unpow1/2_binary64`
10×	`associate--r-_binary64`
9×	`distribute-lft-out_binary64`
6×	`associate-*l/_binary64`
5×	`cube-mult_binary64` `remove-double-neg_binary64`
4×	`sqr-neg_binary64` `+-lft-identity_binary64` `associate-/r/_binary64`
3×	`cos-neg_binary64` `cube-neg_binary64` `--rgt-identity_binary64` `cancel-sign-sub_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64` `associate--l-_binary64`
2×	`distribute-lft1-in_binary64`
1×	`sin-neg_binary64` `unpow2_binary64` `pow-plus_binary64` `unpow1_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_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` `rec-exp_binary64` `prod-exp_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-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `mul-1-neg_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`

Counts

97 → 73

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	3100
1	318	2935
2	806	2872
3	1428	2872
4	2518	2872
5	4253	2872
6	4919	2872

prune98.0ms (0.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	66	7	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	7	74

Error

0.0b

Counts

74 → 7

Compiler

Compiled 2520 to 512 computations (79.7% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.4b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)

rewrite409.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64` `associate-l_binary64` `associate-r_binary64`
4×	`unpow-prod-down_binary64` `add-log-exp_binary64` `cube-prod_binary64`
3×	`pow-prod-down_binary64` `pow-pow_binary64` `prod-exp_binary64` `pow-exp_binary64` `sin-mult_binary64` `rem-cube-cbrt_binary64` `cbrt-unprod_binary64`
2×	`pow-to-exp_binary64` `unpow3_binary64` `cube-mult_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`cube-div_binary64`

Counts

4 → 84

Calls

4 calls:

7.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
5.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
5.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
2.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 6969 to 832 computations (88.1% saved)

series356.0ms (1.9%)

Error

0.0b

Counts

4 → 35

Calls

4 calls:

129.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
81.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
80.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
17.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 7054 to 2510 computations (64.4% saved)

simplify191.0ms (1%)

Algorithm

1×	egg-herbie

Rules

413×	`log-prod_binary64`
401×	`exp-prod_binary64`
339×	`unswap-sqr_binary64`
291×	`*-commutative_binary64`
267×	`sqr-pow_binary64`
235×	`cube-prod_binary64`
175×	`associate-+l+_binary64`
166×	`swap-sqr_binary64`
131×	`associate-+r+_binary64`
124×	`unpow3_binary64`
118×	`distribute-rgt-neg-in_binary64`
116×	`distribute-rgt-in_binary64`
113×	`distribute-lft-neg-in_binary64`
112×	`distribute-lft-in_binary64`
109×	`associate-r_binary64`
108×	`associate-l_binary64`
89×	`log-pow_binary64`
77×	`associate-/l*_binary64`
76×	`cancel-sign-sub-inv_binary64`
69×	`pow-sqr_binary64`
50×	`pow-plus_binary64`
43×	`neg-mul-1_binary64` `neg-sub0_binary64`
42×	`sub-neg_binary64`
35×	`cube-mult_binary64`
29×	`+-commutative_binary64`
25×	`distribute-rgt-out_binary64`
23×	`cube-unmult_binary64`
21×	`count-2_binary64`
18×	`rem-sqrt-square_binary64`
14×	`*-lft-identity_binary64`
13×	`*-rgt-identity_binary64`
12×	`distribute-rgt-neg-out_binary64` `distribute-lft-neg-out_binary64` `associate-/l/_binary64`
9×	`associate-+l-_binary64`
8×	`unpow1/2_binary64` `distribute-rgt-out--_binary64` `distribute-lft-out_binary64`
7×	`associate-*r/_binary64`
6×	`sub0-neg_binary64` `+-rgt-identity_binary64` `associate-+r-_binary64`
5×	`unsub-neg_binary64`
4×	`unpow2_binary64`
3×	`unpow1_binary64` `distribute-lft-out--_binary64` `associate-*l/_binary64`
2×	`rem-cbrt-cube_binary64` `associate-/r/_binary64` `associate--l+_binary64` `associate--r+_binary64`
1×	`cos-neg_binary64` `1-exp_binary64` `exp-1-e_binary64` `rem-cube-cbrt_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` `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` `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` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-3cbrt-lft_binary64` `sqr-abs_binary64` `times-frac_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_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_binary64` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-neg-in_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_binary64` `associate-/r_binary64` `associate--r-_binary64` `associate--l-_binary64`

Counts

119 → 72

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	121	3647
1	261	3505
2	862	3403
3	2209	3403
4	4712	3397
5	4993	3397
6	4933	3397

prune139.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	70	9	79

Error

0.0b

Counts

79 → 9

Compiler

Compiled 3091 to 569 computations (81.6% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
0.3b	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))

rewrite481.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

47×	`pow1_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64`
12×	`add-sqr-sqrt_binary64` `sin-mult_binary64`
10×	`prod-exp_binary64` `cbrt-unprod_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`associate-l_binary64` `associate-r_binary64`
6×	`add-log-exp_binary64`
5×	`cos-mult_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64`
3×	`associate-l/_binary64` `associate-r/_binary64` `*-commutative_binary64` `frac-sub_binary64`
2×	`pow-plus_binary64` `frac-times_binary64` `sub-div_binary64` `unswap-sqr_binary64`
1×	`pow2_binary64` `swap-sqr_binary64` `diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `difference-of-squares_binary64` `cancel-sign-sub-inv_binary64` `sqr-cos-a_binary64` `associate--l+_binary64`

Counts

4 → 94

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
10.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
5.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))

Compiler

Compiled 7940 to 541 computations (93.2% saved)

series437.0ms (2.3%)

Error

0.0b

Counts

4 → 41

Calls

4 calls:

124.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))))
104.0ms	(.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1))))))))
75.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
73.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))

Compiler

Compiled 6658 to 2513 computations (62.3% saved)

simplify224.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

490×	`cancel-sign-sub-inv_binary64`
459×	`unswap-sqr_binary64`
358×	`*-commutative_binary64`
201×	`distribute-rgt-neg-in_binary64`
186×	`exp-prod_binary64`
176×	`distribute-lft-neg-in_binary64`
167×	`associate-r_binary64`
165×	`distribute-rgt-in_binary64`
158×	`distribute-lft-in_binary64`
156×	`associate-l_binary64`
143×	`neg-sub0_binary64`
142×	`neg-mul-1_binary64`
133×	`sub-neg_binary64`
124×	`sqr-pow_binary64`
102×	`swap-sqr_binary64`
96×	`distribute-rgt-neg-out_binary64`
93×	`unsub-neg_binary64`
72×	`cube-prod_binary64`
69×	`log-prod_binary64`
55×	`exp-sum_binary64`
52×	`distribute-neg-in_binary64`
44×	`+-commutative_binary64`
42×	`distribute-rgt-out_binary64`
34×	`distribute-lft-neg-out_binary64`
32×	`associate-+r+_binary64`
30×	`difference-of-squares_binary64`
29×	`associate-+l+_binary64`
24×	`pow-sqr_binary64`
22×	`unpow3_binary64`
20×	`pow-plus_binary64` `exp-diff_binary64`
19×	`associate--r+_binary64`
18×	`associate-+l-_binary64`
16×	`sub0-neg_binary64` `associate-+r-_binary64`
15×	`+-rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
14×	`cube-unmult_binary64`
13×	`*-lft-identity_binary64` `remove-double-neg_binary64` `associate--l+_binary64`
12×	`times-frac_binary64` `*-rgt-identity_binary64`
10×	`distribute-lft-out_binary64`
9×	`unpow1/2_binary64`
8×	`log-pow_binary64`
7×	`cube-mult_binary64` `rem-sqrt-square_binary64`
6×	`unpow2_binary64` `associate-/l*_binary64`
5×	`unpow1_binary64` `distribute-rgt-out--_binary64`
4×	`distribute-neg-out_binary64`
3×	`exp-neg_binary64` `count-2_binary64`
2×	`sqr-neg_binary64` `div-sub_binary64` `distribute-lft-out--_binary64`
1×	`cos-neg_binary64` `cos-0_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `+-inverses_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_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` `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` `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` `rec-exp_binary64` `prod-exp_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` `rem-square-sqrt_binary64` `mul-1-neg_binary64` `/-rgt-identity_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` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-rgt1-in_binary64` `distribute-lft1-in_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: 4 (0.0ms)

Iter	Nodes	Cost
0	145	6013
1	355	5664
2	1129	5537
3	2767	5537
4	4797	5420
5	4922	5420

prune213.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	100	9	109

Error

0.0b

Counts

109 → 9

Compiler

Compiled 3962 to 667 computations (83.2% saved)

localize43.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 phi1) (pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2))))
0.4b	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)

rewrite372.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`unpow-prod-down_binary64` `pow-unpow_binary64` `associate-l_binary64` `associate-r_binary64`
1×	`pow-pow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `diff-log_binary64` `flip3--_binary64` `sub-neg_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `sqr-cos-a_binary64` `associate--l+_binary64` `sin-mult_binary64` `pow-prod-down_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `*-commutative_binary64` `asin-acos_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 phi1) (pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2))))
5.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
3.0ms	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 4456 to 726 computations (83.7% saved)

series345.0ms (1.8%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

121.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 phi1) (.f64 (sin.f64 phi1) (pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2))))
75.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
72.0ms	(pow.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))) 2)
36.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 5390 to 2433 computations (54.9% saved)

simplify161.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

420×	`distribute-rgt-neg-in_binary64`
389×	`distribute-lft-neg-in_binary64`
387×	`cancel-sign-sub-inv_binary64`
298×	`exp-prod_binary64`
235×	`*-commutative_binary64`
208×	`distribute-rgt-in_binary64`
166×	`sqr-pow_binary64` `distribute-lft-in_binary64`
165×	`times-frac_binary64`
119×	`unswap-sqr_binary64`
118×	`associate-r_binary64`
117×	`cube-prod_binary64`
115×	`associate-l_binary64`
100×	`swap-sqr_binary64`
89×	`associate-/l*_binary64`
85×	`log-prod_binary64`
82×	`sub-neg_binary64`
79×	`neg-sub0_binary64`
78×	`neg-mul-1_binary64`
64×	`associate-+r+_binary64`
60×	`associate-+l+_binary64`
52×	`associate-/r*_binary64`
51×	`exp-sum_binary64`
49×	`+-commutative_binary64`
47×	`distribute-rgt-out_binary64`
40×	`unpow3_binary64`
39×	`pow-sqr_binary64` `difference-of-squares_binary64`
30×	`unsub-neg_binary64`
28×	`cube-mult_binary64` `distribute-lft-neg-out_binary64`
25×	`log-pow_binary64`
24×	`associate-+l-_binary64`
23×	`exp-diff_binary64`
22×	`associate-/l/_binary64`
21×	`rem-sqrt-square_binary64`
18×	`pow-plus_binary64` `associate-*r/_binary64`
15×	`associate-+r-_binary64`
14×	`unpow1/2_binary64` `cube-unmult_binary64`
13×	`distribute-rgt-neg-out_binary64` `distribute-lft-out_binary64`
12×	`sqr-neg_binary64`
11×	`sub0-neg_binary64` `associate-/r/_binary64`
10×	`associate--r+_binary64`
9×	`unpow2_binary64` `*-lft-identity_binary64` `+-rgt-identity_binary64`
8×	`unpow1_binary64` `*-rgt-identity_binary64` `mul0-rgt_binary64` `mul0-lft_binary64`
7×	`distribute-rgt-out--_binary64`
5×	`associate--l+_binary64`
4×	`distribute-neg-in_binary64` `count-2_binary64` `associate-*l/_binary64`
2×	`associate--r-_binary64`
1×	`cos-neg_binary64` `div-exp_binary64` `1-exp_binary64` `exp-1-e_binary64` `cube-neg_binary64` `rem-3cbrt-rft_binary64` `rem-square-sqrt_binary64` `difference-of-sqr-1_binary64` `cancel-sign-sub_binary64` `distribute-rgt1-in_binary64` `distribute-lft-out--_binary64` `associate--l-_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` `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` `rec-exp_binary64` `prod-exp_binary64` `exp-neg_binary64` `e-exp-1_binary64` `exp-0_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `cube-div_binary64` `rem-3cbrt-lft_binary64` `rem-cbrt-cube_binary64` `rem-cube-cbrt_binary64` `sqr-abs_binary64` `div-sub_binary64` `mul-1-neg_binary64` `/-rgt-identity_binary64` `remove-double-neg_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` `distribute-neg-frac_binary64` `distribute-frac-neg_binary64` `distribute-neg-out_binary64` `distribute-lft1-in_binary64`

Counts

97 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	131	3998
1	295	3666
2	871	3614
3	1972	3614
4	4500	3545
5	4982	3545

prune131.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	51	9	60

Error

0.0b

Counts

60 → 9

Compiler

Compiled 2112 to 356 computations (83.1% saved)

regimes2.8s (15%)

Accuracy

Total 0.1b remaining (50.5%)

Threshold costs 0.1b (50.5%)

Compiler

Compiled 81041 to 36817 computations (54.6% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
6×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-mul-1_binary64` `neg-sub0_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` `sqr-abs_binary64` `sqr-neg_binary64` `unsub-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	35	214
1	50	214
2	55	214
3	57	214
4	58	214
5	58	214

end2.0ms (0%)

Compiler: Compiled 127 to 36 computations (71.7% saved)

sample7.3s (39%)

Algorithm

1×

intervals

Results

4.6s	3961×	body	1024	valid
948.0ms	1286×	body	512	valid
475.0ms	2207×	body	128	valid
269.0ms	538×	body	256	valid
19.0ms	8×	body	2048	valid

Compiler

Compiled 782 to 363 computations (53.6% saved)

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55

Details

analyze4.0s (21.6%)

sample239.0ms (1.3%)

simplify53.0ms (0.3%)

prune4.0ms (0%)

localize28.0ms (0.2%)

rewrite130.0ms (0.7%)

series231.0ms (1.2%)

simplify160.0ms (0.9%)

prune98.0ms (0.5%)

localize45.0ms (0.2%)

rewrite409.0ms (2.2%)

series356.0ms (1.9%)

simplify191.0ms (1%)

prune139.0ms (0.7%)

localize41.0ms (0.2%)

rewrite481.0ms (2.6%)

series437.0ms (2.3%)

simplify224.0ms (1.2%)

prune213.0ms (1.1%)

localize43.0ms (0.2%)

rewrite372.0ms (2%)

series345.0ms (1.8%)

simplify161.0ms (0.9%)

prune131.0ms (0.7%)

regimes2.8s (15%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end2.0ms (0%)

sample7.3s (39%)

Profiling

Iter	Nodes	Cost
0	23	55
1	39	55
2	61	55
3	72	55
4	83	55
5	107	55
6	134	55
7	164	55
8	217	55
9	216	55
10	240	55
11	275	55
12	317	55
13	431	55
14	486	55
15	534	55
16	567	55
17	521	55
18	523	55
19	525	55
20	526	55
21	463	55