Details

analyze3.7s (16.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4909	605
1	4909	605
0	5	5
1	5	5

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

Symmetry

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample220.0ms (1%)

Algorithm

1×

intervals

Results

142.0ms	118×	body	1024	valid
37.0ms	53×	body	512	valid
14.0ms	72×	body	128	valid
6.0ms	13×	body	256	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify43.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	463	55
1	463	55

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

0.1b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite128.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

12×	`add-sqr-sqrt_binary64_2146`
8×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `associate-r_binary64_2064`
2×	`sin-mult_binary64_2279` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`
1×	`diff-log_binary64_2216` `flip3--_binary64_2128` `sub-neg_binary64_2117` `flip--_binary64_2099` `cancel-sign-sub-inv_binary64_2090` `asin-acos_binary64_2304`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
4.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 2653 to 371 computations (86% saved)

series1.1s (4.7%)

Error

0.1b

Counts

4 → 48

Calls

4 calls:

421.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
388.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
128.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
70.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

Compiler

Compiled 4716 to 2149 computations (54.4% saved)

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4940	3259
1	4940	3259

prune163.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	97	9	106
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Error

0.0b

Counts

107 → 9

Compiler

Compiled 4646 to 787 computations (83.1% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)

rewrite175.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

8×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow-unpow_binary64_2201`
4×	`unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163` `cube-prod_binary64_2152`
3×	`pow-pow_binary64_2196` `pow-exp_binary64_2192` `rem-cube-cbrt_binary64_2147`
2×	`pow-to-exp_binary64_2193` `unpow3_binary64_2190` `cube-mult_binary64_2154` `sqr-pow_binary64_2096` `asin-acos_binary64_2304`
1×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `sin-mult_binary64_2279` `cube-div_binary64_2153` `cbrt-unprod_binary64_2157`

Counts

4 → 62

Calls

4 calls:

5.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
2.0ms	(pow.f64 (cos.f64 delta) 3)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 6003 to 772 computations (87.1% saved)

series1.2s (5.3%)

Error

0.0b

Counts

4 → 36

Calls

4 calls:

856.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
105.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
99.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
59.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 9004 to 2669 computations (70.4% saved)

simplify72.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4926	2422
1	4926	2422

prune233.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	98	9	107

Error

0.0b

Counts

107 → 9

Compiler

Compiled 9377 to 1294 computations (86.2% saved)

localize29.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))
0.7b	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))

rewrite114.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

10×	`add-sqr-sqrt_binary64_2146`
8×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`log-prod_binary64_2210`
4×	`log-pow_binary64_2213`
3×	`exp-prod_binary64_2176` `associate-l_binary64_2065` `associate-r_binary64_2064`
2×	`sub-neg_binary64_2117` `exp-sum_binary64_2170` `cancel-sign-sub-inv_binary64_2090`
1×	`exp-diff_binary64_2172` `log-div_binary64_2211` `rem-log-exp_binary64_2165` `diff-log_binary64_2216` `flip3--_binary64_2128` `flip--_binary64_2099` `asin-acos_binary64_2304` `sin-mult_binary64_2279` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`

Counts

4 → 57

Calls

4 calls:

6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
4.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
4.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))
4.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 2929 to 414 computations (85.9% saved)

series2.1s (9.1%)

Error

0.0b

Counts

4 → 51

Calls

4 calls:

1.1s	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))))
448.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))))
374.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1)))))))
82.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 5235 to 2425 computations (53.7% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4962	4247
1	4962	4247

prune151.0ms (0.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	108	9	117

Error

0.0b

Counts

117 → 9

Compiler

Compiled 4896 to 748 computations (84.7% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
0.4b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
5.6b	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3) 3))

rewrite277.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

22×	`cbrt-prod_binary64_2155`
14×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
11×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
8×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`pow-unpow_binary64_2201`
5×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `sqr-pow_binary64_2096`
4×	`add-log-exp_binary64_2163`
3×	`cube-div_binary64_2153` `pow-pow_binary64_2196` `pow-exp_binary64_2192` `rem-cube-cbrt_binary64_2147`
2×	`sin-mult_binary64_2279` `pow-to-exp_binary64_2193`
1×	`pow1/3_binary64_2206` `cbrt-div_binary64_2156` `rem-cbrt-cube_binary64_2148` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `asin-acos_binary64_2304`

Counts

4 → 86

Calls

4 calls:

6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
5.0ms	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3) 3))
2.0ms	(pow.f64 (cos.f64 delta) 3)
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))

Compiler

Compiled 8992 to 1384 computations (84.6% saved)

series1.9s (8.4%)

Error

0.0b

Counts

4 → 39

Calls

4 calls:

836.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3)
814.0ms	(cbrt.f64 (pow.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (.f64 (sin.f64 delta) (cos.f64 phi1))))))) 3) 3))
110.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (cos.f64 theta) (*.f64 (sin.f64 delta) (cos.f64 phi1)))))
61.0ms	(pow.f64 (cos.f64 delta) 3)

Compiler

Compiled 10009 to 3170 computations (68.3% saved)

simplify94.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4961	4188
1	4961	4188

prune317.0ms (1.4%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	124	10	134

Error

0.0b

Counts

134 → 10

Compiler

Compiled 11979 to 1647 computations (86.3% saved)

regimes1.4s (6.1%)

Accuracy

Total 0.1b remaining (71.6%)

Threshold costs 0.1b (71.6%)

Compiler

Compiled 24981 to 12117 computations (51.5% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	78	239
1	78	239

Removed

()

end0.0ms (0%)

sample9.1s (39.9%)

Algorithm

1×

intervals

Results

4.7s	3985×	body	1024	valid
991.0ms	1348×	body	512	valid
440.0ms	2115×	body	128	valid
253.0ms	541×	body	256	valid
25.0ms	11×	body	2048	valid

Compiler

Compiled 3725 to 1791 computations (51.9% saved)

Details

analyze3.7s (16.3%)

sample220.0ms (1%)

simplify43.0ms (0.2%)

prune4.0ms (0%)

localize25.0ms (0.1%)

rewrite128.0ms (0.6%)

series1.1s (4.7%)

simplify82.0ms (0.4%)

prune163.0ms (0.7%)

localize40.0ms (0.2%)

rewrite175.0ms (0.8%)

series1.2s (5.3%)

simplify72.0ms (0.3%)

prune233.0ms (1%)

localize29.0ms (0.1%)

rewrite114.0ms (0.5%)

series2.1s (9.1%)

simplify94.0ms (0.4%)

prune151.0ms (0.7%)

localize45.0ms (0.2%)

rewrite277.0ms (1.2%)

series1.9s (8.4%)

simplify94.0ms (0.4%)

prune317.0ms (1.4%)

regimes1.4s (6.1%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample9.1s (39.9%)

Profiling