Details

analyze2.5s (10.6%)

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
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)

sample209.0ms (0.9%)

Algorithm

1×

intervals

Results

143.0ms	160×	body	1024	valid
27.0ms	51×	body	512	valid
10.0ms	30×	body	128	valid
7.0ms	3×	body	2048	valid
4.0ms	12×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify107.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	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

Error

9.6b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.1b	(cos.f64 (-.f64 lambda1 lambda2))
1.2b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite118.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

4.5b

Rules

11×	`add-sqr-sqrt_binary64_2146` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`cancel-sign-sub-inv_binary64_2090` `associate-r_binary64_2064`
4×	`sin-sum_binary64_2257` `add-log-exp_binary64_2163` `cos-sum_binary64_2258` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-l_binary64_2065`
3×	`cos-diff_binary64_2261`
2×	`sub-neg_binary64_2117` `sin-cos-mult_binary64_2280` `*-commutative_binary64_2055`
1×	`sin-diff_binary64_2260` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-*l/_binary64_2067` `unswap-sqr_binary64_2092`

Counts

4 → 64

Calls

4 calls:

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

Compiler

Compiled 2042 to 375 computations (81.6% saved)

series665.0ms (2.8%)

Error

5.9b

Counts

4 → 54

Calls

4 calls:

385.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
101.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
58.0ms	(sin.f64 (-.f64 lambda1 lambda2))
57.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4042 to 1931 computations (52.2% saved)

simplify81.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5083	1891

prune161.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	105	13	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	13	119

Error

4.5b

Counts

119 → 13

Compiler

Compiled 3831 to 813 computations (78.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.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)))
1.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite130.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64_2146`
13×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`associate-r_binary64_2064`
7×	`associate-l_binary64_2065`
5×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`cos-sum_binary64_2258` `add-log-exp_binary64_2163`
3×	`cos-diff_binary64_2261` `cancel-sign-sub-inv_binary64_2090` `associate-l/_binary64_2067` `-commutative_binary64_2055`
2×	`sin-cos-mult_binary64_2280` `unswap-sqr_binary64_2092`
1×	`sub-neg_binary64_2117` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 72

Calls

4 calls:

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

Compiler

Compiled 2897 to 394 computations (86.4% saved)

series1.0s (4.3%)

Error

4.2b

Counts

4 → 58

Calls

4 calls:

400.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
384.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
114.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
62.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 5478 to 2647 computations (51.7% saved)

simplify78.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5048	2616

prune179.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	123	7	130
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	135	8	143

Error

0.1b

Counts

143 → 8

Compiler

Compiled 5157 to 825 computations (84% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite173.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

17×	`add-sqr-sqrt_binary64_2146`
15×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`associate-r_binary64_2064`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`associate-l_binary64_2065`
6×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
5×	`sin-cos-mult_binary64_2280`
4×	`add-log-exp_binary64_2163` `*-commutative_binary64_2055`
3×	`sin-mult_binary64_2279` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `unswap-sqr_binary64_2092`
2×	`cos-mult_binary64_2278` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 85

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

Compiler

Compiled 4145 to 512 computations (87.6% saved)

series1.4s (5.7%)

Error

0.1b

Counts

4 → 56

Calls

4 calls:

681.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
389.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
106.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
100.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 6473 to 2833 computations (56.2% saved)

simplify69.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4957	3618
1	4957	3618

prune207.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	134	7	141
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	139	10	149

Error

0.0b

Counts

149 → 10

Compiler

Compiled 6865 to 1024 computations (85.1% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))
0.2b	(.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
0.2b	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.4b	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))

rewrite370.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

87×	`pow1_binary64_2185`
54×	`associate-*r/_binary64_2066`
42×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `cos-mult_binary64_2278` `sin-mult_binary64_2279`
37×	`pow-prod-down_binary64_2195`
22×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-*l/_binary64_2067`
19×	`frac-sub_binary64_2133`
18×	`frac-times_binary64_2134`
16×	`associate-/l/_binary64_2071`
11×	`sub-div_binary64_2131`
8×	`pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
7×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
6×	`associate-r_binary64_2064`
4×	`pow-plus_binary64_2187` `add-log-exp_binary64_2163` `associate-/r/_binary64_2070`
3×	`associate-l_binary64_2065` `-commutative_binary64_2055` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `times-frac_binary64_2130` `flip3--_binary64_2128` `flip--_binary64_2099` `associate-/r_binary64_2068`
2×	`pow2_binary64_2205` `swap-sqr_binary64_2091` `sub-neg_binary64_2117` `distribute-rgt-in_binary64_2074` `cancel-sign-sub-inv_binary64_2090` `distribute-lft-in_binary64_2073`
1×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/l*_binary64_2069` `difference-of-squares_binary64_2093`

Counts

4 → 156

Calls

4 calls:

26.0ms	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
21.0ms	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))
10.0ms	(.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
9.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))

Compiler

Compiled 11897 to 1282 computations (89.2% saved)

series3.4s (14.1%)

Error

0.0b

Counts

4 → 56

Calls

4 calls:

1.8s	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1))))) (-.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
1.1s	(.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (-.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (sin.f64 lambda2) (sin.f64 lambda1)))))
169.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
158.0ms	(.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))

Compiler

Compiled 10511 to 4858 computations (53.8% saved)

simplify123.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4954	8111
1	4954	8111

prune392.0ms (1.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	212	10	222

Error

0.0b

Counts

222 → 10

Compiler

Compiled 14488 to 2933 computations (79.8% saved)

regimes2.2s (9.3%)

Accuracy

Total 0.2b remaining (79.9%)

Threshold costs 0.2b (79.9%)

Compiler

Compiled 31373 to 18980 computations (39.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	106
1	136	106

end0.0ms (0%)

sample10.2s (42.6%)

Algorithm

1×

intervals

Results

4.8s	5403×	body	1024	valid
732.0ms	1294×	body	512	valid
354.0ms	179×	body	2048	valid
127.0ms	757×	body	128	valid
125.0ms	367×	body	256	valid

Compiler

Compiled 5152 to 3106 computations (39.7% saved)

Details

analyze2.5s (10.6%)

sample209.0ms (0.9%)

simplify107.0ms (0.4%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite118.0ms (0.5%)

series665.0ms (2.8%)

simplify81.0ms (0.3%)

prune161.0ms (0.7%)

localize27.0ms (0.1%)

rewrite130.0ms (0.5%)

series1.0s (4.3%)

simplify78.0ms (0.3%)

prune179.0ms (0.7%)

localize33.0ms (0.1%)

rewrite173.0ms (0.7%)

series1.4s (5.7%)

simplify69.0ms (0.3%)

prune207.0ms (0.9%)

localize39.0ms (0.2%)

rewrite370.0ms (1.5%)

series3.4s (14.1%)

simplify123.0ms (0.5%)

prune392.0ms (1.6%)

regimes2.2s (9.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample10.2s (42.6%)

Profiling