Details

analyze2.0s (20.2%)

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)

sample145.0ms (1.5%)

Algorithm

1×

intervals

Results

91.0ms	134×	body	1024	valid
26.0ms	65×	body	512	valid
7.0ms	27×	body	256	valid
4.0ms	3×	body	2048	valid
3.0ms	27×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify120.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune8.0ms (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: 0.8b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize17.0ms (0.2%)

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)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))
2.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_3147` `cancel-sign-sub-inv_binary64_3113` `add-sqr-sqrt_binary64_3169` `add-log-exp_binary64_3186` `add-cube-cbrt_binary64_3182`
4×	`cos-sum_binary64_3281` `add-exp-log_binary64_3185` `sin-sum_binary64_3280` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
3×	`cos-diff_binary64_3284`
2×	`sub-neg_binary64_3140` `associate-+r+_binary64_3079`
1×	`flip-+_binary64_3121` `flip3-+_binary64_3150` `sin-diff_binary64_3283` `+-commutative_binary64_3077` `distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097` `sum-log_binary64_3238`

Counts

4 → 44

Calls

4 calls:

5.0ms	(sin.f64 (-.f64 lambda1 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) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series193.0ms (2%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
40.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5235	1058

prune85.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.6b

Counts

57 → 11

Compiler

Compiled 1821 to 446 computations (75.5% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_3169`
7×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
6×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208` `add-log-exp_binary64_3186`
5×	`cancel-sign-sub-inv_binary64_3113`
4×	`cos-sum_binary64_3281`
3×	`associate-r_binary64_3087` `sub-neg_binary64_3140` `cos-diff_binary64_3284` `distribute-lft-in_binary64_3096` `associate-l_binary64_3088` `distribute-rgt-in_binary64_3097`
2×	`associate-+r+_binary64_3079` `associate-*r/_binary64_3089`
1×	`*-commutative_binary64_3078` `flip--_binary64_3122` `unswap-sqr_binary64_3115` `flip-+_binary64_3121` `pow-prod-down_binary64_3218` `flip3--_binary64_3151` `flip3-+_binary64_3150` `+-commutative_binary64_3077` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `sum-log_binary64_3238`

Counts

4 → 56

Calls

4 calls:

9.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (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 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series320.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

146.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
109.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
50.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
15.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4989	1723
1	4989	1723

prune95.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	70	9	79

Merged error: 0.1b

Counts

79 → 9

Compiler

Compiled 2665 to 460 computations (82.7% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))

rewrite29.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
9×	`add-sqr-sqrt_binary64_3169`
7×	`*-un-lft-identity_binary64_3147` `add-cube-cbrt_binary64_3182`
6×	`associate-r_binary64_3087` `add-log-exp_binary64_3186`
4×	`pow-prod-down_binary64_3218` `prod-exp_binary64_3196` `cbrt-unprod_binary64_3180` `associate-l_binary64_3088`
2×	`-commutative_binary64_3078` `cancel-sign-sub-inv_binary64_3113` `sub-neg_binary64_3140` `distribute-lft-in_binary64_3096` `distribute-rgt-in_binary64_3097` `associate-r/_binary64_3089`
1×	`flip--_binary64_3122` `unswap-sqr_binary64_3115` `flip-+_binary64_3121` `associate-*l/_binary64_3090` `flip3--_binary64_3151` `flip3-+_binary64_3150` `sin-mult_binary64_3302` `+-commutative_binary64_3077` `sum-log_binary64_3238`

Counts

4 → 61

Calls

4 calls:

9.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
7.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))

series422.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
130.0ms	(+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2)))
85.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))
63.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (+.f64 (cos.f64 phi1) (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (cos.f64 phi2))) (.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (cos.f64 phi2))))

simplify71.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5022	1986

prune102.0ms (1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 0.1b

Counts

82 → 9

Compiler

Compiled 3473 to 466 computations (86.6% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))
0.6b	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
2.8b	(cos.f64 (-.f64 lambda1 lambda2))
2.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_3147` `add-sqr-sqrt_binary64_3169` `add-cube-cbrt_binary64_3182` `cbrt-prod_binary64_3178`
6×	`unpow-prod-down_binary64_3226` `cancel-sign-sub-inv_binary64_3113` `cube-prod_binary64_3175`
5×	`add-exp-log_binary64_3185` `add-cbrt-cube_binary64_3183` `pow1_binary64_3208`
4×	`cos-sum_binary64_3281` `sin-sum_binary64_3280` `add-log-exp_binary64_3186`
3×	`pow-unpow_binary64_3224`
2×	`sub-neg_binary64_3140` `sqr-pow_binary64_3119` `cube-mult_binary64_3177` `unpow3_binary64_3213`
1×	`rem-cbrt-cube_binary64_3171` `pow-exp_binary64_3215` `pow1/3_binary64_3229` `rem-cube-cbrt_binary64_3170` `pow-to-exp_binary64_3216` `sin-diff_binary64_3283` `cos-diff_binary64_3284` `pow-pow_binary64_3219`

Counts

4 → 68

Calls

4 calls:

5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))

series96.0ms (1%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3)
17.0ms	(sin.f64 (-.f64 lambda1 lambda2))
15.0ms	(cbrt.f64 (pow.f64 (cos.f64 (-.f64 lambda1 lambda2)) 3))
14.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify92.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4813	914
1	4813	914

prune84.0ms (0.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	80	9	89

Merged error: 0.1b

Counts

89 → 9

Compiler

Compiled 2140 to 657 computations (69.3% saved)

regimes436.0ms (4.5%)

Compiler: Compiled 5936 to 3482 computations (41.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	59	61
1	59	61

end0.0ms (0%)

sample5.2s (53.1%)

Algorithm

1×

intervals

Results

3.0s	4473×	body	1024	valid
723.0ms	1769×	body	512	valid
190.0ms	728×	body	256	valid
148.0ms	104×	body	2048	valid
128.0ms	926×	body	128	valid

Compiler

Compiled 898 to 527 computations (41.3% saved)

Details

analyze2.0s (20.2%)

sample145.0ms (1.5%)

simplify120.0ms (1.2%)

prune8.0ms (0.1%)

localize17.0ms (0.2%)

rewrite18.0ms (0.2%)

series193.0ms (2%)

simplify70.0ms (0.7%)

prune85.0ms (0.9%)

localize24.0ms (0.3%)

rewrite25.0ms (0.3%)

series320.0ms (3.3%)

simplify77.0ms (0.8%)

prune95.0ms (1%)

localize29.0ms (0.3%)

rewrite29.0ms (0.3%)

series422.0ms (4.3%)

simplify71.0ms (0.7%)

prune102.0ms (1%)

localize20.0ms (0.2%)

rewrite22.0ms (0.2%)

series96.0ms (1%)

simplify92.0ms (0.9%)

prune84.0ms (0.9%)

regimes436.0ms (4.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.2s (53.1%)

Profiling