Details

analyze2.1s (1.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1273	224
1	1273	224
0	4	4
1	4	4

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 (0.1%)

Algorithm

1×

intervals

Results

89.0ms	134×	body	1024	valid
23.0ms	60×	body	512	valid
7.0ms	5×	body	2048	valid
5.0ms	37×	body	128	valid
5.0ms	20×	body	256	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify27.0ms (0%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune9.0ms (0%)

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

Error

1.2b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize18.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite112.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

1.0b

Rules

12×	`sin-sum_binary64_2939` `cancel-sign-sub-inv_binary64_2772` `add-sqr-sqrt_binary64_2828`
10×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
6×	`pow1_binary64_2867` `add-log-exp_binary64_2845` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
5×	`distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755`
4×	`sub-neg_binary64_2799` `cos-sum_binary64_2940`
3×	`cos-diff_binary64_2943` `associate-l_binary64_2747` `associate-r_binary64_2746`
2×	`associate-+r+_binary64_2738`
1×	`sin-diff_binary64_2942` `sum-log_binary64_2897` `flip3-+_binary64_2809` `flip-+_binary64_2780` `+-commutative_binary64_2736` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `*-commutative_binary64_2737`

Counts

4 → 63

Calls

4 calls:

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

Compiler

Compiled 1901 to 401 computations (78.9% saved)

series617.0ms (0.5%)

Error

1.1b

Counts

4 → 54

Calls

4 calls:

312.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
156.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
49.0ms	(cos.f64 (-.f64 lambda1 lambda2))
45.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 3386 to 1693 computations (50% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5347	1915

prune143.0ms (0.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	13	117
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	13	118

Error

1.0b

Counts

118 → 13

Compiler

Compiled 3310 to 702 computations (78.8% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite111.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

13×	`add-sqr-sqrt_binary64_2828`
9×	`add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
8×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
6×	`add-log-exp_binary64_2845` `associate-l_binary64_2747` `associate-r_binary64_2746`
5×	`cancel-sign-sub-inv_binary64_2772`
4×	`cos-sum_binary64_2940`
3×	`cos-diff_binary64_2943` `sub-neg_binary64_2799` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755`
2×	`associate-+r+_binary64_2738` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `associate-r/_binary64_2748` `-commutative_binary64_2737`
1×	`sum-log_binary64_2897` `flip3-+_binary64_2809` `flip-+_binary64_2780` `+-commutative_binary64_2736` `flip3--_binary64_2810` `flip--_binary64_2781`

Counts

4 → 67

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

Compiler

Compiled 2455 to 436 computations (82.2% saved)

series905.0ms (0.8%)

Error

0.8b

Counts

4 → 55

Calls

4 calls:

347.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
325.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
110.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
58.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4394 to 2204 computations (49.8% saved)

simplify71.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5081	2362

prune153.0ms (0.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Error

0.1b

Counts

135 → 10

Compiler

Compiled 4275 to 766 computations (82.1% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite103.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

12×	`add-sqr-sqrt_binary64_2828`
8×	`pow1_binary64_2867` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `*-un-lft-identity_binary64_2806`
6×	`add-log-exp_binary64_2845` `associate-l_binary64_2747` `associate-r_binary64_2746`
3×	`distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755`
2×	`associate-+r+_binary64_2738` `pow-prod-down_binary64_2877` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `unswap-sqr_binary64_2774` `sub-neg_binary64_2799` `cancel-sign-sub-inv_binary64_2772` `associate-r/_binary64_2748` `-commutative_binary64_2737`
1×	`sum-log_binary64_2897` `flip3-+_binary64_2809` `flip-+_binary64_2780` `+-commutative_binary64_2736` `flip3--_binary64_2810` `flip--_binary64_2781`

Counts

4 → 62

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 (cos.f64 lambda1) (sin.f64 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

Compiler

Compiled 2881 to 360 computations (87.5% saved)

series1.4s (1.2%)

Error

0.1b

Counts

4 → 59

Calls

4 calls:

675.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
362.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
179.0ms	(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 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
102.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 5886 to 2542 computations (56.8% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5025	3635

prune168.0ms (0.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Error

0.1b

Counts

131 → 11

Compiler

Compiled 5264 to 791 computations (85% saved)

localize39.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))))))
0.4b	(+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3))
0.6b	(pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)
1.1b	(-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))

rewrite372.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

26×	`*-un-lft-identity_binary64_2806`
16×	`add-cube-cbrt_binary64_2841` `add-sqr-sqrt_binary64_2828` `associate-*r/_binary64_2748`
15×	`cos-mult_binary64_2960` `frac-add_binary64_2814` `times-frac_binary64_2812`
13×	`associate-/r/_binary64_2752`
9×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
8×	`add-log-exp_binary64_2845`
7×	`pow1_binary64_2867` `flip3-+_binary64_2809` `flip-+_binary64_2780`
6×	`frac-times_binary64_2816`
5×	`flip3--_binary64_2810` `flip--_binary64_2781` `sum-cubes_binary64_2807` `distribute-lft-out_binary64_2757` `associate-/l*_binary64_2751`
4×	`sin-mult_binary64_2961`
3×	`cancel-sign-sub-inv_binary64_2772` `pow-unpow_binary64_2883` `cube-div_binary64_2835` `associate-l/_binary64_2749` `associate-/r_binary64_2750`
2×	`associate--l+_binary64_2743` `pow-pow_binary64_2878` `pow-exp_binary64_2874` `rem-cube-cbrt_binary64_2829` `associate-/l/_binary64_2753`
1×	`diff-log_binary64_2898` `sub-neg_binary64_2799` `distribute-rgt-in_binary64_2756` `distribute-lft-in_binary64_2755` `unpow-prod-down_binary64_2885` `pow-prod-down_binary64_2877` `pow-to-exp_binary64_2875` `prod-exp_binary64_2855` `unpow3_binary64_2872` `cube-mult_binary64_2836` `cube-prod_binary64_2834` `cbrt-unprod_binary64_2839` `sqr-pow_binary64_2778` `sum-log_binary64_2897` `+-commutative_binary64_2736` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `frac-2neg_binary64_2817` `clear-num_binary64_2805` `div-inv_binary64_2803`

Counts

4 → 104

Calls

4 calls:

27.0ms	(/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))))))
11.0ms	(-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))
10.0ms	(+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3))
10.0ms	(pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)

Compiler

Compiled 12030 to 1565 computations (87% saved)

series1.6min (84.1%)

Error

0.1b

Counts

4 → 78

Calls

4 calls:

1.5min	(/.f64 (+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)) (+.f64 (.f64 (cos.f64 phi1) (cos.f64 phi1)) (.f64 (cos.f64 phi2) (.f64 (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))))))
6.0s	(+.f64 (pow.f64 (cos.f64 phi1) 3) (pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3))
833.0ms	(pow.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) 3)
715.0ms	(-.f64 (.f64 (cos.f64 phi2) (+.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))) (cos.f64 phi1))

Compiler

Compiled 113311 to 51283 computations (54.7% saved)

simplify552.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5331	83046

prune3.2s (2.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	179	3	182
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	182	11	193

Error

0.1b

Counts

193 → 11

Compiler

Compiled 60458 to 22658 computations (62.5% saved)

regimes1.4s (1.2%)

Accuracy

Total 0.1b remaining (65.9%)

Threshold costs 0.1b (65.9%)

Compiler

Compiled 22855 to 12253 computations (46.4% 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%)

sample6.6s (5.7%)

Algorithm

1×

intervals

Results

2.8s	4401×	body	1024	valid
731.0ms	1788×	body	512	valid
183.0ms	740×	body	256	valid
178.0ms	129×	body	2048	valid
127.0ms	942×	body	128	valid

Compiler

Compiled 3312 to 1779 computations (46.3% saved)

Details

analyze2.1s (1.8%)

sample145.0ms (0.1%)

simplify27.0ms (0%)

prune9.0ms (0%)

localize18.0ms (0%)

rewrite112.0ms (0.1%)

series617.0ms (0.5%)

simplify78.0ms (0.1%)

prune143.0ms (0.1%)

localize24.0ms (0%)

rewrite111.0ms (0.1%)

series905.0ms (0.8%)

simplify71.0ms (0.1%)

prune153.0ms (0.1%)

localize25.0ms (0%)

rewrite103.0ms (0.1%)

series1.4s (1.2%)

simplify84.0ms (0.1%)

prune168.0ms (0.1%)

localize39.0ms (0%)

rewrite372.0ms (0.3%)

series1.6min (84.1%)

simplify552.0ms (0.5%)

prune3.2s (2.8%)

regimes1.4s (1.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample6.6s (5.7%)

Profiling