Details

analyze2.1s (12.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1273	224
1	1273	224
0	4	4
1	4	4

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Symmetry

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample140.0ms (0.8%)

Algorithm

1×

intervals

Results

85.0ms	130×	body	1024	valid
21.0ms	55×	body	512	valid
6.0ms	5×	body	2048	valid
6.0ms	23×	body	256	valid
5.0ms	43×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify27.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune9.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.6b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.6b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.1b	(cos.f64 (-.f64 lambda1 lambda2))
3.1b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite86.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.4b

Rules

6×	`add-cube-cbrt_binary64_795` `cancel-sign-sub-inv_binary64_726` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760` `add-log-exp_binary64_799`
4×	`sin-sum_binary64_893` `pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `cos-sum_binary64_894`
3×	`cos-diff_binary64_897`
2×	`sub-neg_binary64_753` `associate-+r+_binary64_692`
1×	`sin-diff_binary64_896` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `+-commutative_binary64_690`

Counts

4 → 44

Calls

4 calls:

5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

Compiler

Compiled 1356 to 285 computations (79% saved)

series613.0ms (3.6%)

Error

0.6b

Counts

4 → 54

Calls

4 calls:

341.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
113.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
54.0ms	(sin.f64 (-.f64 lambda1 lambda2))
53.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3343 to 1667 computations (50.1% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5182	1885

prune134.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	85	13	98
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	86	13	99

Error

0.4b

Counts

99 → 13

Compiler

Compiled 2823 to 640 computations (77.3% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.1b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite86.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

9×	`add-sqr-sqrt_binary64_782`
7×	`add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`pow1_binary64_821` `add-log-exp_binary64_799` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
4×	`sin-sum_binary64_893`
3×	`cancel-sign-sub-inv_binary64_726` `associate-l_binary64_701` `associate-r_binary64_700`
2×	`associate-+r+_binary64_692`
1×	`sin-diff_binary64_896` `sub-neg_binary64_753` `sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `+-commutative_binary64_690` `sin-mult_binary64_915` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `*-commutative_binary64_691`

Counts

4 → 51

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 1946 to 351 computations (82% saved)

series1.1s (6.2%)

Error

0.3b

Counts

4 → 52

Calls

4 calls:

705.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
147.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
93.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
58.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4316 to 2155 computations (50.1% saved)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5390	2546

prune133.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	105	11	116

Error

0.1b

Counts

116 → 11

Compiler

Compiled 3644 to 675 computations (81.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite107.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`add-sqr-sqrt_binary64_782`
8×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `add-cube-cbrt_binary64_795` `*-un-lft-identity_binary64_760`
6×	`add-log-exp_binary64_799` `associate-l_binary64_701` `associate-r_binary64_700`
3×	`distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709`
2×	`associate-+r+_binary64_692` `pow-prod-down_binary64_831` `prod-exp_binary64_809` `cbrt-unprod_binary64_793` `unswap-sqr_binary64_728` `-commutative_binary64_691` `sub-neg_binary64_753` `cancel-sign-sub-inv_binary64_726` `associate-r/_binary64_702`
1×	`sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `+-commutative_binary64_690` `sin-mult_binary64_915` `flip3--_binary64_764` `flip--_binary64_735`

Counts

4 → 63

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2921 to 391 computations (86.6% saved)

series1.4s (8.2%)

Error

0.1b

Counts

4 → 57

Calls

4 calls:

681.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
373.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
178.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
98.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5731 to 2479 computations (56.7% saved)

simplify95.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5008	3588

prune154.0ms (0.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	122	9	131

Error

0.1b

Counts

131 → 9

Compiler

Compiled 5070 to 746 computations (85.3% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.6b	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
0.6b	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
0.6b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite133.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

10×	`cbrt-div_binary64_792`
9×	`cbrt-prod_binary64_791`
8×	`sin-cos-mult_binary64_916`
7×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782` `*-un-lft-identity_binary64_760`
6×	`add-log-exp_binary64_799`
4×	`pow1_binary64_821` `add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
3×	`pow1/3_binary64_842` `flip3--_binary64_764` `flip--_binary64_735`
2×	`associate-+r+_binary64_692` `frac-sub_binary64_769` `sub-div_binary64_767`
1×	`sum-log_binary64_851` `flip3-+_binary64_763` `flip-+_binary64_734` `distribute-rgt-in_binary64_710` `distribute-lft-in_binary64_709` `+-commutative_binary64_690`

Counts

4 → 56

Calls

4 calls:

6.0ms	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
6.0ms	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
4.0ms	(cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))

Compiler

Compiled 4255 to 427 computations (90% saved)

series2.0s (11.7%)

Error

0.1b

Counts

4 → 45

Calls

4 calls:

700.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
415.0ms	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
412.0ms	(cbrt.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda2) (cos.f64 lambda1))))
408.0ms	(cbrt.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2))))

Compiler

Compiled 8007 to 3040 computations (62% saved)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5018	3067

prune170.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	97	4	101
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	98	12	110

Error

0.1b

Counts

110 → 12

Compiler

Compiled 6880 to 692 computations (89.9% saved)

regimes1.7s (9.9%)

Accuracy

Total 0.1b remaining (63.5%)

Threshold costs 0.1b (63.5%)

Compiler

Compiled 23079 to 12750 computations (44.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

Removed

()

end0.0ms (0%)

sample6.6s (38.7%)

Algorithm

1×

intervals

Results

2.8s	4453×	body	1024	valid
694.0ms	1763×	body	512	valid
188.0ms	722×	body	256	valid
167.0ms	120×	body	2048	valid
123.0ms	942×	body	128	valid

Compiler

Compiled 3344 to 1850 computations (44.7% saved)

Details

analyze2.1s (12.3%)

sample140.0ms (0.8%)

simplify27.0ms (0.2%)

prune9.0ms (0.1%)

localize18.0ms (0.1%)

rewrite86.0ms (0.5%)

series613.0ms (3.6%)

simplify82.0ms (0.5%)

prune134.0ms (0.8%)

localize24.0ms (0.1%)

rewrite86.0ms (0.5%)

series1.1s (6.2%)

simplify81.0ms (0.5%)

prune133.0ms (0.8%)

localize24.0ms (0.1%)

rewrite107.0ms (0.6%)

series1.4s (8.2%)

simplify95.0ms (0.6%)

prune154.0ms (0.9%)

localize41.0ms (0.2%)

rewrite133.0ms (0.8%)

series2.0s (11.7%)

simplify67.0ms (0.4%)

prune170.0ms (1%)

regimes1.7s (9.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.6s (38.7%)

Profiling