Details

analyze1.9s (16.3%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample138.0ms (1.2%)

Algorithm

1×

intervals

Results

87.0ms	136×	body	1024	valid
21.0ms	53×	body	512	valid
7.0ms	6×	body	2048	valid
6.0ms	24×	body	256	valid
4.0ms	37×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune7.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 1.0b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.6b	(sin.f64 (-.f64 lambda1 lambda2))
5.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
4×	`cos-sum_binary64_553` `sin-sum_binary64_552` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
3×	`cos-diff_binary64_556`
2×	`associate-+r+_binary64_351` `sub-neg_binary64_412`
1×	`flip3-+_binary64_422` `sin-diff_binary64_555` `distribute-rgt-in_binary64_369` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 44

Calls

4 calls:

5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series409.0ms (3.5%)

Counts

4 → 36

Calls

4 calls:

319.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
59.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
15.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify121.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4833	1529
1	4833	1529

prune100.0ms (0.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	69	11	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	11	81

Merged error: 0.8b

Counts

81 → 11

Compiler

Compiled 2290 to 453 computations (80.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_441`
7×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
5×	`cancel-sign-sub-inv_binary64_385`
4×	`cos-sum_binary64_553`
3×	`sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `associate-r_binary64_359` `distribute-lft-in_binary64_368` `associate-l_binary64_360` `cos-diff_binary64_556`
2×	`associate-+r+_binary64_351` `associate-*r/_binary64_361`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sum-log_binary64_510` `flip3--_binary64_423` `*-commutative_binary64_350` `flip-+_binary64_393` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 56

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series822.0ms (7%)

Counts

4 → 39

Calls

4 calls:

410.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
312.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
81.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify71.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5171	2443

prune112.0ms (0.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Merged error: 0.1b

Counts

106 → 12

Compiler

Compiled 3476 to 544 computations (84.3% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.7b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_441`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
6×	`add-log-exp_binary64_458` `associate-r_binary64_359` `associate-l_binary64_360`
3×	`distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368`
2×	`associate-+r+_binary64_351` `pow-prod-down_binary64_490` `sub-neg_binary64_412` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `-commutative_binary64_350` `cancel-sign-sub-inv_binary64_385`
1×	`flip3-+_binary64_422` `sin-mult_binary64_574` `sum-log_binary64_510` `flip3--_binary64_423` `flip-+_binary64_393` `flip--_binary64_394` `+-commutative_binary64_349`

Counts

4 → 63

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series1.4s (11.9%)

Counts

4 → 39

Calls

4 calls:

817.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
403.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
98.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
83.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4996	3074
1	4996	3074

prune121.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	102	12	114

Merged error: 0.1b

Counts

114 → 12

Compiler

Compiled 4420 to 609 computations (86.2% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))
0.2b	(atan2.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.7b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
5.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
6×	`*-un-lft-identity_binary64_419` `add-log-exp_binary64_458` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
4×	`cos-sum_binary64_553`
3×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-l_binary64_360` `cancel-sign-sub-inv_binary64_385` `cos-diff_binary64_556`
2×	`associate-+r+_binary64_351` `distribute-rgt-neg-out_binary64_379`
1×	`flip3-+_binary64_422` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `associate-r_binary64_359` `sum-log_binary64_510` `distribute-lft-in_binary64_368` `*-commutative_binary64_350` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

4 → 51

Calls

4 calls:

6.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
0.0ms	(atan2.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series709.0ms (6%)

Counts

4 → 39

Calls

4 calls:

320.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
288.0ms	(.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))
85.0ms	(atan2.f64 (+.f64 (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda2) (sin.f64 lambda1))) (.f64 (cos.f64 phi2) (.f64 (cos.f64 lambda1) (neg.f64 (sin.f64 lambda2))))) (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify72.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4893	2027
1	4893	2027

prune87.0ms (0.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	90	12	102

Merged error: 0.1b

Counts

102 → 12

Compiler

Compiled 3118 to 321 computations (89.7% saved)

regimes383.0ms (3.2%)

Compiler: Compiled 4809 to 3069 computations (36.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	56
1	57	56

end0.0ms (0%)

sample4.9s (41.9%)

Algorithm

1×

intervals

Results

2.8s	4506×	body	1024	valid
693.0ms	1748×	body	512	valid
202.0ms	718×	body	256	valid
162.0ms	120×	body	2048	valid
114.0ms	908×	body	128	valid

Compiler

Compiled 734 to 467 computations (36.4% saved)

Details

analyze1.9s (16.3%)

sample138.0ms (1.2%)

simplify110.0ms (0.9%)

prune7.0ms (0.1%)

localize17.0ms (0.1%)

rewrite18.0ms (0.1%)

series409.0ms (3.5%)

simplify121.0ms (1%)

prune100.0ms (0.8%)

localize25.0ms (0.2%)

rewrite24.0ms (0.2%)

series822.0ms (7%)

simplify71.0ms (0.6%)

prune112.0ms (0.9%)

localize25.0ms (0.2%)

rewrite25.0ms (0.2%)

series1.4s (11.9%)

simplify85.0ms (0.7%)

prune121.0ms (1%)

localize28.0ms (0.2%)

rewrite21.0ms (0.2%)

series709.0ms (6%)

simplify72.0ms (0.6%)

prune87.0ms (0.7%)

regimes383.0ms (3.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.9s (41.9%)

Profiling