Details

analyze2.0s (18.6%)

Algorithm

1×

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

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample200.0ms (1.9%)

Algorithm

1×

intervals

Results

125.0ms	119×	body	1280	valid
44.0ms	78×	body	640	valid
11.0ms	29×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	15×	body	80	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify36.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	272	32
1	272	32

prune6.0ms (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

Merged error: 1.3b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`sub-neg_binary64`
3×	`associate-r_binary64` `sin-sum_binary64` `associate-l_binary64` `cos-diff_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sin-diff_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 51

Calls

4 calls:

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

series54.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
14.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
6.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify104.0ms (1%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4935	945
1	4935	945

prune99.0ms (0.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	50	13	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	13	64

Merged error: 1.1b

Counts

64 → 13

Compiler

Compiled 1980 to 522 computations (73.6% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`sub-neg_binary64` `sin-sum_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 61

Calls

4 calls:

7.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
7.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series83.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
14.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4978	1251
1	4978	1251

prune73.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

Compiler

Compiled 2683 to 533 computations (80.1% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-+r+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `flip3--_binary64` `sin-mult_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 61

Calls

4 calls:

10.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
7.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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))))))

series116.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

55.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
32.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
20.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.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))))))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify85.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5161	2051

prune82.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.0b

Counts

83 → 11

Compiler

Compiled 3511 to 589 computations (83.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
0.6b	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`pow1_binary64`
4×	`log-prod_binary64` `log-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`exp-prod_binary64`
2×	`sub-neg_binary64`
1×	`flip3-+_binary64` `sin-diff_binary64` `rem-log-exp_binary64` `sin-sum_binary64` `cos-diff_binary64` `exp-sum_binary64` `cos-sum_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 45

Calls

4 calls:

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

series65.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

29.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
27.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify108.0ms (1%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4884	968
1	4884	968

prune34.0ms (0.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	57	11	68

Merged error: 0.0b

Counts

68 → 11

Compiler

Compiled 1556 to 302 computations (80.6% saved)

regimes404.0ms (3.8%)

Compiler: Compiled 2854 to 1420 computations (50.2% saved)

bsearch2.0ms (0%)

Steps

Iters	Range		Point
0	0.9806619175277544	0.9894828680852661	0.9850723928065103

Compiler

Compiled 2 to 5 computations (-150% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	141	214
1	141	214

end0.0ms (0%)

sample6.7s (63.9%)

Algorithm

1×

intervals

Results

3.5s	3554×	body	1280	valid
1.4s	2417×	body	640	valid
341.0ms	921×	body	320	valid
97.0ms	401×	body	160	valid
83.0ms	707×	body	80	valid

Compiler

Compiled 623 to 280 computations (55.1% saved)

Details

analyze2.0s (18.6%)

sample200.0ms (1.9%)

simplify36.0ms (0.3%)

prune6.0ms (0.1%)

localize21.0ms (0.2%)

rewrite23.0ms (0.2%)

series54.0ms (0.5%)

simplify104.0ms (1%)

prune99.0ms (0.9%)

localize30.0ms (0.3%)

rewrite26.0ms (0.2%)

series83.0ms (0.8%)

simplify95.0ms (0.9%)

prune73.0ms (0.7%)

localize30.0ms (0.3%)

rewrite25.0ms (0.2%)

series116.0ms (1.1%)

simplify85.0ms (0.8%)

prune82.0ms (0.8%)

localize25.0ms (0.2%)

rewrite20.0ms (0.2%)

series65.0ms (0.6%)

simplify108.0ms (1%)

prune34.0ms (0.3%)

regimes404.0ms (3.8%)

bsearch2.0ms (0%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample6.7s (63.9%)

Profiling