Details

analyze2.6s (17.2%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample262.0ms (1.7%)

Algorithm

1×

intervals

Results

198.0ms	178×	body	1024	valid
22.0ms	9×	body	2048	valid
18.0ms	31×	body	512	valid
6.0ms	16×	body	256	valid
4.0ms	22×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify184.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

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

Merged error: 14.6b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.3b	(sin.f64 (-.f64 lambda1 lambda2))
4.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_1850` `add-cbrt-cube_binary64_1825` `add-exp-log_binary64_1827` `add-sqr-sqrt_binary64_1811`
9×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
6×	`associate-r_binary64_1729` `cancel-sign-sub-inv_binary64_1755`
4×	`associate-l_binary64_1730` `pow-prod-down_binary64_1860` `cbrt-unprod_binary64_1822` `prod-exp_binary64_1838` `sin-sum_binary64_1922` `cos-sum_binary64_1923` `add-log-exp_binary64_1828`
3×	`cos-diff_binary64_1926`
2×	`sub-neg_binary64_1782` `*-commutative_binary64_1720` `sin-cos-mult_binary64_1945`
1×	`sin-diff_binary64_1925` `distribute-rgt-in_binary64_1739` `distribute-lft-in_binary64_1738` `unswap-sqr_binary64_1757` `associate-*l/_binary64_1732`

Counts

4 → 64

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series399.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
123.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
36.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4859	1102
1	4859	1102

prune123.0ms (0.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	59	17	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	17	77

Merged error: 7.4b

Counts

77 → 17

Compiler

Compiled 2688 to 610 computations (77.3% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1811`
13×	`pow1_binary64_1850` `add-cbrt-cube_binary64_1825` `add-exp-log_binary64_1827`
10×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
9×	`associate-r_binary64_1729`
7×	`associate-l_binary64_1730`
5×	`pow-prod-down_binary64_1860` `cbrt-unprod_binary64_1822` `prod-exp_binary64_1838`
4×	`cos-sum_binary64_1923` `add-log-exp_binary64_1828`
3×	`-commutative_binary64_1720` `cos-diff_binary64_1926` `cancel-sign-sub-inv_binary64_1755` `associate-l/_binary64_1732`
2×	`unswap-sqr_binary64_1757`
1×	`flip3--_binary64_1793` `distribute-rgt-in_binary64_1739` `sub-neg_binary64_1782` `sin-cos-mult_binary64_1945` `flip--_binary64_1764` `distribute-lft-in_binary64_1738`

Counts

4 → 71

Calls

4 calls:

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

series581.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
211.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
73.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5240	1458

prune133.0ms (0.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	86	14	100

Merged error: 0.1b

Counts

100 → 14

Compiler

Compiled 3560 to 637 computations (82.1% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_1850` `add-cbrt-cube_binary64_1825` `add-exp-log_binary64_1827`
18×	`pow-prod-down_binary64_1860` `cbrt-unprod_binary64_1822` `prod-exp_binary64_1838`
12×	`add-sqr-sqrt_binary64_1811`
8×	`associate-l_binary64_1730` `associate-r_binary64_1729` `*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
4×	`-commutative_binary64_1720` `sin-cos-mult_binary64_1945` `associate-l/_binary64_1732` `add-log-exp_binary64_1828`
3×	`sin-mult_binary64_1944`
2×	`cos-mult_binary64_1943` `associate-*r/_binary64_1731` `frac-times_binary64_1799` `unswap-sqr_binary64_1757`
1×	`flip3--_binary64_1793` `flip--_binary64_1764`

Counts

4 → 89

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series798.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

248.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
244.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
227.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
79.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify69.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5153	1911

prune168.0ms (1.1%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	100	15	115

Merged error: 0.0b

Counts

115 → 15

Compiler

Compiled 5557 to 845 computations (84.8% saved)

localize42.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
3.3b	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`pow1_binary64_1850`
30×	`add-cbrt-cube_binary64_1825` `add-exp-log_binary64_1827`
17×	`pow-prod-down_binary64_1860` `cbrt-unprod_binary64_1822` `prod-exp_binary64_1838`
9×	`add-sqr-sqrt_binary64_1811`
7×	`*-un-lft-identity_binary64_1789` `add-cube-cbrt_binary64_1824`
5×	`associate-l_binary64_1730` `associate-r_binary64_1729` `add-log-exp_binary64_1828`
4×	`sin-cos-mult_binary64_1945`
3×	`log-pow_binary64_1878` `*-commutative_binary64_1720` `log-prod_binary64_1875` `sin-mult_binary64_1944`
2×	`cos-mult_binary64_1943` `associate-r/_binary64_1731` `frac-times_binary64_1799` `associate-l/_binary64_1732`
1×	`exp-prod_binary64_1841` `unswap-sqr_binary64_1757` `rem-log-exp_binary64_1830` `exp-to-pow_binary64_1851`

Counts

4 → 83

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
3.0ms	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))

series890.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(log.f64 (exp.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))))
239.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
212.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
71.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4953	1664
1	4953	1664

prune129.0ms (0.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	95	15	110

Merged error: 0.0b

Counts

110 → 15

Compiler

Compiled 4694 to 529 computations (88.7% saved)

regimes257.0ms (1.7%)

Compiler: Compiled 3414 to 2006 computations (41.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	77
1	130	77

end0.0ms (0%)

sample8.2s (53.4%)

Algorithm

1×

intervals

Results

5.7s	5351×	body	1024	valid
743.0ms	1235×	body	512	valid
547.0ms	211×	body	2048	valid
148.0ms	395×	body	256	valid
144.0ms	808×	body	128	valid

Compiler

Compiled 718 to 420 computations (41.5% saved)

Details

analyze2.6s (17.2%)

sample262.0ms (1.7%)

simplify184.0ms (1.2%)

prune4.0ms (0%)

localize30.0ms (0.2%)

rewrite35.0ms (0.2%)

series399.0ms (2.6%)

simplify70.0ms (0.5%)

prune123.0ms (0.8%)

localize35.0ms (0.2%)

rewrite35.0ms (0.2%)

series581.0ms (3.8%)

simplify47.0ms (0.3%)

prune133.0ms (0.9%)

localize36.0ms (0.2%)

rewrite49.0ms (0.3%)

series798.0ms (5.2%)

simplify69.0ms (0.5%)

prune168.0ms (1.1%)

localize42.0ms (0.3%)

rewrite44.0ms (0.3%)

series890.0ms (5.8%)

simplify60.0ms (0.4%)

prune129.0ms (0.8%)

regimes257.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.2s (53.4%)

Profiling