Details

analyze3.7s (18.9%)

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
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

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample248.0ms (1.3%)

Algorithm

1×

intervals

Results

171.0ms	123×	body	1024	valid
35.0ms	44×	body	512	valid
16.0ms	73×	body	128	valid
7.0ms	15×	body	256	valid
3.0ms	1×	body	2048	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify206.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (36.0ms)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 66 to 46 computations (30.3% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.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))))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.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)))))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_1464`
8×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`associate-r_binary64_1382` `associate-l_binary64_1383` `add-log-exp_binary64_1481`
2×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`
1×	`cancel-sign-sub-inv_binary64_1408` `sub-neg_binary64_1435` `flip3--_binary64_1446` `flip--_binary64_1417` `diff-log_binary64_1534` `sin-cos-mult_binary64_1598` `asin-acos_binary64_1622` `sin-mult_binary64_1597`

Counts

4 → 58

Calls

4 calls:

6.0ms	(.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))))))
6.0ms	(*.f64 (sin.f64 phi1) (cos.f64 delta))
5.0ms	(-.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))))

series668.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

320.0ms	(-.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)))))))
242.0ms	(.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))))))
69.0ms	(*.f64 (sin.f64 phi1) (cos.f64 delta))
36.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	2151
1	4957	2151

prune118.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	7	71

Merged error: 0.0b

Counts

71 → 7

Compiler

Compiled 3222 to 614 computations (80.9% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite26.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`pow-unpow_binary64_1519`
4×	`cube-prod_binary64_1470` `add-log-exp_binary64_1481` `unpow-prod-down_binary64_1521`
3×	`pow-exp_binary64_1510` `rem-cube-cbrt_binary64_1465` `pow-pow_binary64_1514`
2×	`cube-mult_binary64_1472` `sqr-pow_binary64_1414` `unpow3_binary64_1508` `asin-acos_binary64_1622` `pow-to-exp_binary64_1511`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `prod-exp_binary64_1491` `cube-div_binary64_1471` `sin-mult_binary64_1597`

Counts

4 → 62

Calls

4 calls:

6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
3.0ms	(pow.f64 (cos.f64 delta) 3)
2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
1.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series774.0ms (4%)

Counts

4 → 12

Calls

4 calls:

650.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)
43.0ms	(pow.f64 (cos.f64 delta) 3)
42.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
39.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify66.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5616	1714

prune194.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	73	8	81

Merged error: 0.0b

Counts

81 → 8

Compiler

Compiled 7175 to 1038 computations (85.5% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.4b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
2.5b	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1464`
12×	`*-un-lft-identity_binary64_1442`
9×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
7×	`log-pow_binary64_1531` `add-log-exp_binary64_1481`
6×	`add-cbrt-cube_binary64_1478` `log-prod_binary64_1528` `cancel-sign-sub-inv_binary64_1408` `add-exp-log_binary64_1480`
3×	`associate-r_binary64_1382` `associate-l_binary64_1383` `associate--r+_binary64_1378`
2×	`exp-prod_binary64_1494` `exp-to-pow_binary64_1504` `distribute-lft-out--_binary64_1394`
1×	`cbrt-unprod_binary64_1475` `sub-neg_binary64_1435` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `flip--_binary64_1417` `diff-log_binary64_1534` `asin-acos_binary64_1622` `prod-exp_binary64_1491` `difference-of-squares_binary64_1411` `sin-mult_binary64_1597` `unswap-sqr_binary64_1410`

Counts

4 → 64

Calls

4 calls:

8.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
3.0ms	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.3s (6.5%)

Counts

4 → 12

Calls

4 calls:

524.0ms	(-.f64 (cos.f64 delta) (log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
440.0ms	(log.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
251.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
35.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify87.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4889	2821
1	4889	2821

prune126.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	6	6
Picked	1	0	1
Done	1	0	1
Total	75	9	84

Merged error: 0.0b

Counts

84 → 9

Compiler

Compiled 3738 to 684 computations (81.7% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.4b	(-.f64 (-.f64 (cos.f64 delta) (.f64 1/2 (.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)))))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
2.8b	(log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64_1528` `*-un-lft-identity_binary64_1442`
11×	`log-pow_binary64_1531` `add-sqr-sqrt_binary64_1464`
9×	`cancel-sign-sub-inv_binary64_1408` `add-log-exp_binary64_1481` `pow1_binary64_1503` `add-cube-cbrt_binary64_1477`
6×	`sqrt-pow1_binary64_1460` `sqrt-prod_binary64_1458` `associate--r+_binary64_1378`
5×	`add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478`
3×	`diff-log_binary64_1534`
2×	`associate--l+_binary64_1379` `sub-neg_binary64_1435` `exp-prod_binary64_1494` `asin-acos_binary64_1622` `exp-to-pow_binary64_1504` `pow1/2_binary64_1522` `distribute-lft-out--_binary64_1394`
1×	`associate--l-_binary64_1380` `rem-log-exp_binary64_1483` `flip3--_binary64_1446` `flip--_binary64_1417` `difference-of-squares_binary64_1411`

Counts

4 → 67

Calls

4 calls:

13.0ms	(-.f64 (-.f64 (cos.f64 delta) (.f64 1/2 (.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)))))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
4.0ms	(log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
1.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.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))))

series1.8s (9.1%)

Counts

4 → 12

Calls

4 calls:

1.1s	(-.f64 (-.f64 (cos.f64 delta) (.f64 1/2 (.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)))))))) (log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))))
618.0ms	(log.f64 (sqrt.f64 (exp.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
43.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
37.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify82.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4937	3568
1	4937	3568

prune142.0ms (0.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	79	9	88

Merged error: 0.0b

Counts

88 → 9

Compiler

Compiled 4935 to 736 computations (85.1% saved)

regimes612.0ms (3.2%)

Compiler: Compiled 9609 to 4830 computations (49.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	55
1	57	55

end0.0ms (0%)

sample9.0s (46.5%)

Algorithm

1×

intervals

Results

5.8s	3988×	body	1024	valid
1.1s	1359×	body	512	valid
463.0ms	2109×	body	128	valid
280.0ms	533×	body	256	valid
44.0ms	11×	body	2048	valid

Compiler

Compiled 1420 to 722 computations (49.2% saved)

Details

analyze3.7s (18.9%)

sample248.0ms (1.3%)

simplify206.0ms (1.1%)

prune4.0ms (0%)

localize32.0ms (0.2%)

rewrite25.0ms (0.1%)

series668.0ms (3.4%)

simplify77.0ms (0.4%)

prune118.0ms (0.6%)

localize47.0ms (0.2%)

rewrite26.0ms (0.1%)

series774.0ms (4%)

simplify66.0ms (0.3%)

prune194.0ms (1%)

localize35.0ms (0.2%)

rewrite28.0ms (0.1%)

series1.3s (6.5%)

simplify87.0ms (0.4%)

prune126.0ms (0.7%)

localize49.0ms (0.3%)

rewrite35.0ms (0.2%)

series1.8s (9.1%)

simplify82.0ms (0.4%)

prune142.0ms (0.7%)

regimes612.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample9.0s (46.5%)

Profiling