Details

analyze7.1s (18.6%)

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
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)

sample467.0ms (1.2%)

Algorithm

1×

intervals

Results

321.0ms	121×	body	1024	valid
74.0ms	50×	body	512	valid
27.0ms	69×	body	128	valid
15.0ms	16×	body	256	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify388.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	463	55
1	463	55

prune8.0ms (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)

localize64.0ms (0.2%)

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)))))))

rewrite50.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_772`
8×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `add-cbrt-cube_binary64_784` `*-un-lft-identity_binary64_751` `add-exp-log_binary64_786`
6×	`add-log-exp_binary64_787` `associate-l_binary64_694` `associate-r_binary64_693`
2×	`prod-exp_binary64_797` `unswap-sqr_binary64_719` `sin-mult_binary64_903` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `cbrt-unprod_binary64_781`
1×	`flip--_binary64_726` `diff-log_binary64_840` `asin-acos_binary64_928` `sub-neg_binary64_744` `flip3--_binary64_755`

Counts

4 → 57

Calls

4 calls:

12.0ms	(.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))))))
10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
8.0ms	(-.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)))))))
3.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.3s (3.6%)

Counts

4 → 12

Calls

4 calls:

656.0ms	(-.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)))))))
480.0ms	(.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))))))
134.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
78.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify190.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4857	2099
1	4857	2099

prune244.0ms (0.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 0.0b

Counts

70 → 9

Compiler

Compiled 3291 to 593 computations (82% saved)

localize77.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.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))))))) (cbrt.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))))))))
3.5b	(cbrt.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)))))))
3.5b	(cbrt.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)))))))
3.5b	(cbrt.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)))))))

rewrite67.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_809`
10×	`add-sqr-sqrt_binary64_772`
9×	`pow1/3_binary64_830`
8×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
7×	`sin-mult_binary64_903` `cbrt-prod_binary64_779` `cbrt-div_binary64_780`
6×	`add-exp-log_binary64_786`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `swap-sqr_binary64_718` `associate-l_binary64_694` `associate-r_binary64_693`
2×	`pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819`
1×	`prod-exp_binary64_797` `frac-times_binary64_761` `unswap-sqr_binary64_719` `pow-plus_binary64_811` `-commutative_binary64_684` `associate-r/_binary64_695` `cbrt-unprod_binary64_781` `pow2_binary64_829` `associate-*l/_binary64_696`

Counts

4 → 64

Calls

4 calls:

15.0ms	(.f64 (cbrt.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))))))) (cbrt.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))))))))
7.0ms	(cbrt.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)))))))
7.0ms	(cbrt.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)))))))
7.0ms	(cbrt.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)))))))

series5.2s (13.8%)

Counts

4 → 12

Calls

4 calls:

1.8s	(.f64 (cbrt.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))))))) (cbrt.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))))))))
1.2s	(cbrt.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)))))))
1.2s	(cbrt.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)))))))
1.1s	(cbrt.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)))))))

simplify151.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5058	2915

prune305.0ms (0.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	76	9	85

Merged error: 0.0b

Counts

85 → 9

Compiler

Compiled 6248 to 718 computations (88.5% saved)

localize69.0ms (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))))))
0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.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 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.8b	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.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)))))))))

rewrite46.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_772`
8×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
7×	`pow1_binary64_809`
6×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
4×	`log-prod_binary64_834` `log-pow_binary64_837`
3×	`exp-prod_binary64_800` `associate-l_binary64_694` `associate-r_binary64_693`
2×	`sub-neg_binary64_744`
1×	`prod-exp_binary64_797` `log-div_binary64_835` `rem-log-exp_binary64_789` `unswap-sqr_binary64_719` `sin-mult_binary64_903` `flip--_binary64_726` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `exp-diff_binary64_796` `diff-log_binary64_840` `cbrt-unprod_binary64_781` `asin-acos_binary64_928` `exp-sum_binary64_794` `flip3--_binary64_755`

Counts

4 → 55

Calls

4 calls:

11.0ms	(.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))))))
9.0ms	(-.f64 (cos.f64 delta) (.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)))))))
8.0ms	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.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	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series2.2s (5.8%)

Counts

4 → 12

Calls

4 calls:

1.1s	(log.f64 (exp.f64 (-.f64 (cos.f64 delta) (.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)))))))))
609.0ms	(-.f64 (cos.f64 delta) (.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)))))))
458.0ms	(.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))))))
67.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify174.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	4857	2746
1	4857	2746

prune174.0ms (0.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	67	9	76

Merged error: 0.0b

Counts

76 → 9

Compiler

Compiled 3386 to 565 computations (83.3% saved)

localize89.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.6b	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.6b	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.6b	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

rewrite51.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_779`
23×	`add-sqr-sqrt_binary64_772`
15×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
11×	`pow1_binary64_809`
9×	`pow1/3_binary64_830`
6×	`swap-sqr_binary64_718` `associate-l_binary64_694` `add-exp-log_binary64_786` `associate-r_binary64_693`
4×	`unswap-sqr_binary64_719` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
2×	`pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819`
1×	`prod-exp_binary64_797` `pow-plus_binary64_811` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `pow2_binary64_829`

Counts

4 → 73

Calls

4 calls:

13.0ms	(.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (cbrt.f64 (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	(cbrt.f64 (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	(cbrt.f64 (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	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

series3.6s (9.4%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
815.0ms	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
808.0ms	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
807.0ms	(cbrt.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

simplify179.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4937	3093
1	4937	3093

prune299.0ms (0.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	86	8	94

Merged error: 0.0b

Counts

94 → 8

Compiler

Compiled 6206 to 559 computations (91% saved)

regimes323.0ms (0.9%)

Compiler: Compiled 2210 to 1135 computations (48.6% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	129
1	63	129

end0.0ms (0%)

sample15.1s (39.8%)

Algorithm

1×

intervals

Results

10.3s	3929×	body	1024	valid
2.0s	1389×	body	512	valid
867.0ms	2149×	body	128	valid
508.0ms	525×	body	256	valid
46.0ms	8×	body	2048	valid

Compiler

Compiled 550 to 272 computations (50.5% saved)

Details

analyze7.1s (18.6%)

sample467.0ms (1.2%)

simplify388.0ms (1%)

prune8.0ms (0%)

localize64.0ms (0.2%)

rewrite50.0ms (0.1%)

series1.3s (3.6%)

simplify190.0ms (0.5%)

prune244.0ms (0.6%)

localize77.0ms (0.2%)

rewrite67.0ms (0.2%)

series5.2s (13.8%)

simplify151.0ms (0.4%)

prune305.0ms (0.8%)

localize69.0ms (0.2%)

rewrite46.0ms (0.1%)

series2.2s (5.8%)

simplify174.0ms (0.5%)

prune174.0ms (0.5%)

localize89.0ms (0.2%)

rewrite51.0ms (0.1%)

series3.6s (9.4%)

simplify179.0ms (0.5%)

prune299.0ms (0.8%)

regimes323.0ms (0.9%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample15.1s (39.8%)

Profiling