Details

analyze3.7s (19.9%)

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)

sample244.0ms (1.3%)

Algorithm

1×

intervals

Results

170.0ms	121×	body	1024	valid
32.0ms	42×	body	512	valid
16.0ms	76×	body	128	valid
8.0ms	17×	body	256	valid

Compiler

Compiled 67 to 52 computations (22.4% saved)

simplify49.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	463	55
1	463	55

prune5.0ms (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: 0.2b

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 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))))
0.5b	(-.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)))))))

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

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 (.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))))

series668.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

319.0ms	(-.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)))))))
244.0ms	(.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))))))
68.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
38.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify88.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5396	2099

prune130.0ms (0.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	10	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 0.1b

Counts

70 → 10

Compiler

Compiled 3342 to 620 computations (81.4% saved)

localize39.0ms (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))))
0.5b	(-.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)))))))))
3.2b	(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))))))))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`log-pow_binary64`
3×	`associate--r+_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`distribute-lft-out--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

7.0ms	(-.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))))

series1.2s (6.5%)

Counts

4 → 12

Calls

4 calls:

503.0ms	(-.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)))))))))
428.0ms	(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))))))))
227.0ms	(.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))))))
36.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify113.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4909	2712
1	4909	2712

prune125.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	69	11	80

Merged error: 0.1b

Counts

80 → 11

Compiler

Compiled 3624 to 715 computations (80.3% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.3b	(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) (log.f64 (pow.f64 (exp.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))))))))
3.2b	(log.f64 (pow.f64 (exp.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)))))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-prod_binary64` `add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
7×	`associate--r+_binary64` `add-exp-log_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64` `unpow-prod-down_binary64`
5×	`add-log-exp_binary64`
3×	`asin-acos_binary64` `associate-r_binary64` `rem-log-exp_binary64` `associate-l_binary64`
2×	`sin-diff_binary64` `sqr-pow_binary64` `pow-sub_binary64` `log-div_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate--r-_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 67

Calls

4 calls:

12.0ms	(-.f64 (cos.f64 delta) (log.f64 (pow.f64 (exp.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	(log.f64 (pow.f64 (exp.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))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

series1.1s (6.2%)

Counts

4 → 12

Calls

4 calls:

549.0ms	(-.f64 (cos.f64 delta) (log.f64 (pow.f64 (exp.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))))))))
485.0ms	(log.f64 (pow.f64 (exp.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)))))))
66.0ms	(*.f64 (sin.f64 theta) (sin.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))))

simplify96.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4908	2506
1	4908	2506

prune129.0ms (0.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	78	1	79
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	78	12	90

Merged error: 0.1b

Counts

90 → 12

Compiler

Compiled 4001 to 731 computations (81.7% saved)

localize49.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(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 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 1/2 (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))))))))))
3.5b	(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)))))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`log-prod_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate--r+_binary64` `log-pow_binary64` `sqrt-prod_binary64`
5×	`add-exp-log_binary64`
4×	`add-cbrt-cube_binary64`
3×	`diff-log_binary64` `sqrt-pow1_binary64`
2×	`sub-neg_binary64` `asin-acos_binary64` `distribute-lft-out--_binary64`
1×	`pow1/2_binary64` `flip3--_binary64` `associate--l-_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `flip--_binary64` `exp-to-pow_binary64` `associate--l+_binary64` `exp-prod_binary64`

Counts

4 → 58

Calls

4 calls:

12.0ms	(-.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 1/2 (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))))

series1.7s (9.3%)

Counts

4 → 12

Calls

4 calls:

1.0s	(-.f64 (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (.f64 1/2 (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))))))))))
596.0ms	(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))))
39.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5326	3286

prune131.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	2	8	10
Picked	1	0	1
Done	1	0	1
Total	71	11	82

Merged error: 0.1b

Counts

82 → 11

Compiler

Compiled 4464 to 711 computations (84.1% saved)

regimes235.0ms (1.3%)

Compiler: Compiled 3275 to 1655 computations (49.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	103	95
1	103	95

end0.0ms (0%)

sample8.3s (45.3%)

Algorithm

1×

intervals

Results

5.6s	3942×	body	1024	valid
1.1s	1308×	body	512	valid
475.0ms	2175×	body	128	valid
279.0ms	564×	body	256	valid
37.0ms	11×	body	2048	valid

Compiler

Compiled 744 to 379 computations (49.1% saved)

Details

analyze3.7s (19.9%)

sample244.0ms (1.3%)

simplify49.0ms (0.3%)

prune5.0ms (0%)

localize32.0ms (0.2%)

rewrite23.0ms (0.1%)

series668.0ms (3.6%)

simplify88.0ms (0.5%)

prune130.0ms (0.7%)

localize39.0ms (0.2%)

rewrite25.0ms (0.1%)

series1.2s (6.5%)

simplify113.0ms (0.6%)

prune125.0ms (0.7%)

localize37.0ms (0.2%)

rewrite33.0ms (0.2%)

series1.1s (6.2%)

simplify96.0ms (0.5%)

prune129.0ms (0.7%)

localize49.0ms (0.3%)

rewrite30.0ms (0.2%)

series1.7s (9.3%)

simplify75.0ms (0.4%)

prune131.0ms (0.7%)

regimes235.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample8.3s (45.3%)

Profiling