Details

analyze3.0s (13.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1713	273
1	1713	273
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
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

Symmetry

Compiler

Compiled 25 to 18 computations (28% saved)

sample216.0ms (1%)

Algorithm

1×

intervals

Results

158.0ms	175×	body	1024	valid
19.0ms	37×	body	512	valid
12.0ms	7×	body	2048	valid
4.0ms	13×	body	256	valid
4.0ms	24×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune12.0ms (0.1%)

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

13.8b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite112.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

7.0b

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×	`cos-sum_binary64_2258` `add-log-exp_binary64_2163` `sin-sum_binary64_2257` `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` `*-commutative_binary64_2055`
1×	`sin-diff_binary64_2260` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `sin-cos-mult_binary64_2280` `associate-*l/_binary64_2067` `unswap-sqr_binary64_2092`

Counts

4 → 63

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2012 to 363 computations (82% saved)

series637.0ms (2.9%)

Error

9.6b

Counts

4 → 52

Calls

4 calls:

369.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
94.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
58.0ms	(cos.f64 (-.f64 lambda1 lambda2))
55.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3920 to 1891 computations (51.8% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5141	1760

prune159.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	100	15	115
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	15	116

Error

6.9b

Counts

116 → 15

Compiler

Compiled 3756 to 814 computations (78.3% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite120.0ms (0.6%)

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` `*-commutative_binary64_2055`
2×	`unswap-sqr_binary64_2092`
1×	`sub-neg_binary64_2117` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `sin-cos-mult_binary64_2280` `associate-*l/_binary64_2067`

Counts

4 → 69

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2635 to 424 computations (83.9% saved)

series723.0ms (3.3%)

Error

6.3b

Counts

4 → 51

Calls

4 calls:

377.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
114.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
107.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
59.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4813 to 2353 computations (51.1% saved)

simplify81.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4996	1807
1	4996	1807

prune156.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	9	5	14
Picked	1	0	1
Done	0	0	0
Total	126	9	135

Error

0.1b

Counts

135 → 9

Compiler

Compiled 4573 to 773 computations (83.1% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (cos.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))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

rewrite167.0ms (0.8%)

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`
4×	`add-log-exp_binary64_2163` `*-commutative_binary64_2055` `sin-cos-mult_binary64_2280`
3×	`sin-mult_binary64_2279` `unswap-sqr_binary64_2092` `frac-times_binary64_2134` `associate-*r/_binary64_2066`
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` `associate-*l/_binary64_2067`

Counts

4 → 82

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (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	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 3862 to 530 computations (86.3% saved)

series1.0s (4.8%)

Error

0.1b

Counts

4 → 47

Calls

4 calls:

661.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
110.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
103.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
100.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5522 to 2457 computations (55.5% saved)

simplify80.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4974	2713
1	4974	2713

prune183.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	124	5	129
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	127	11	138

Error

0.0b

Counts

138 → 11

Compiler

Compiled 6157 to 948 computations (84.6% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(/.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))))
0.3b	(.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
0.4b	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))

rewrite313.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

84×	`pow1_binary64_2185`
39×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
35×	`pow-prod-down_binary64_2195`
28×	`associate-*r/_binary64_2066`
25×	`sin-mult_binary64_2279`
24×	`cos-mult_binary64_2278`
20×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
16×	`associate-/l/_binary64_2071`
12×	`associate-*l/_binary64_2067`
10×	`add-sqr-sqrt_binary64_2146` `frac-times_binary64_2134` `frac-sub_binary64_2133`
8×	`pow-prod-up_binary64_2194` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124` `pow-sqr_binary64_2097`
6×	`sub-div_binary64_2131`
5×	`associate-l_binary64_2065` `associate-r_binary64_2064`
4×	`pow-plus_binary64_2187` `add-log-exp_binary64_2163` `associate-/r/_binary64_2070`
3×	`-commutative_binary64_2055` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `times-frac_binary64_2130` `associate-/r_binary64_2068`
2×	`pow2_binary64_2205` `swap-sqr_binary64_2091` `flip3--_binary64_2128` `flip--_binary64_2099`
1×	`frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/l*_binary64_2069` `unswap-sqr_binary64_2092`

Counts

4 → 136

Calls

4 calls:

27.0ms	(/.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))))
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)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 9987 to 1100 computations (89% saved)

series2.3s (10.5%)

Error

0.0b

Counts

4 → 45

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))))
178.0ms	(.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)))
171.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
95.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 8156 to 3429 computations (58% saved)

simplify84.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5078	5272

prune309.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	181	0	181
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	181	11	192

Error

0.0b

Counts

192 → 11

Compiler

Compiled 12007 to 2080 computations (82.7% saved)

regimes1.9s (8.9%)

Accuracy

Total 0.1b remaining (75.1%)

Threshold costs 0.1b (75.1%)

Compiler

Compiled 28865 to 18074 computations (37.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	63
1	136	63

Removed

()

end0.0ms (0%)

sample9.9s (45.7%)

Algorithm

1×

intervals

Results

4.7s	5365×	body	1024	valid
702.0ms	1262×	body	512	valid
340.0ms	167×	body	2048	valid
169.0ms	448×	body	256	valid
126.0ms	758×	body	128	valid

Compiler

Compiled 4735 to 2964 computations (37.4% saved)

Details

analyze3.0s (13.7%)

sample216.0ms (1%)

simplify22.0ms (0.1%)

prune12.0ms (0.1%)

localize19.0ms (0.1%)

rewrite112.0ms (0.5%)

series637.0ms (2.9%)

simplify80.0ms (0.4%)

prune159.0ms (0.7%)

localize32.0ms (0.1%)

rewrite120.0ms (0.6%)

series723.0ms (3.3%)

simplify81.0ms (0.4%)

prune156.0ms (0.7%)

localize32.0ms (0.1%)

rewrite167.0ms (0.8%)

series1.0s (4.8%)

simplify80.0ms (0.4%)

prune183.0ms (0.8%)

localize39.0ms (0.2%)

rewrite313.0ms (1.4%)

series2.3s (10.5%)

simplify84.0ms (0.4%)

prune309.0ms (1.4%)

regimes1.9s (8.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample9.9s (45.7%)

Profiling