Details

analyze2.1s (13.5%)

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
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample92.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	186×	body	128	valid
12.0ms	23×	body	1024	valid
10.0ms	20×	body	1024	invalid
9.0ms	27×	body	512	valid
9.0ms	86×	body	128	invalid
5.0ms	19×	body	256	valid
4.0ms	12×	body	512	invalid
2.0ms	10×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify153.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune4.0ms (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

Merged error: 35.4b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
32.5b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite95.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64`
102×	`flip3--_binary64` `flip--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`
44×	`pow1_binary64`
34×	`associate-*r/_binary64`
17×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-plus_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.7s (10.9%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
292.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5222	10334

prune618.0ms (4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 26.2b

Counts

148 → 9

Compiler

Compiled 15526 to 7014 computations (54.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
32.5b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite124.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip3--_binary64` `flip--_binary64`
196×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
98×	`associate-r/_binary64` `associate-l/_binary64`
73×	`cos-mult_binary64`
12×	`pow1_binary64` `add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `sqr-cos-a_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 192

Calls

4 calls:

31.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))

series1.5s (9.5%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
65.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
38.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify207.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4952	17738
1	4952	17738

prune807.0ms (5.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	198	6	204
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	200	13	213

Merged error: 25.7b

Counts

213 → 13

Compiler

Compiled 18397 to 7393 computations (59.8% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
0.4b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
32.5b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite82.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`flip3--_binary64` `flip--_binary64`
82×	`associate-*l/_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64` `frac-times_binary64`
32×	`associate-*r/_binary64`
19×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
8×	`associate-r_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow1_binary64` `add-cbrt-cube_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

22.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series1.7s (11.1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
279.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
62.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
28.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify117.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4978	9471
1	4978	9471

prune365.0ms (2.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	8	11
Picked	0	1	1
Done	0	1	1
Total	147	13	160

Merged error: 25.7b

Counts

160 → 13

Compiler

Compiled 10407 to 4147 computations (60.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
0.2b	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
32.5b	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-cbrt-cube_binary64`
5×	`associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `pow-pow_binary64` `prod-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unpow2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `unpow-prod-down_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 62

Calls

4 calls:

8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
7.0ms	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
6.0ms	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.9s (12.4%)

Counts

4 → 12

Calls

4 calls:

1.4s	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
326.0ms	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
185.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
31.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify54.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5064	1647

prune301.0ms (1.9%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	4	6	10
Picked	0	1	1
Done	0	2	2
Total	72	15	87

Merged error: 25.6b

Counts

87 → 15

Compiler

Compiled 6289 to 3848 computations (38.8% saved)

regimes324.0ms (2.1%)

Compiler: Compiled 2662 to 1976 computations (25.8% saved)

bsearch74.0ms (0.5%)

Steps

Iters	Range		Point
8	-5.491776192126866e+139	-2.0545810804087145e+137	-2.5518410768142865e+137

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	48
1	55	48

end0.0ms (0%)

sample3.0s (19.2%)

Algorithm

1×

intervals

Results

638.0ms	6019×	body	128	valid
433.0ms	792×	body	1024	valid
263.0ms	744×	body	512	valid
245.0ms	2413×	body	128	invalid
239.0ms	453×	body	1024	invalid
128.0ms	380×	body	512	invalid
107.0ms	439×	body	256	valid
37.0ms	165×	body	256	invalid
6.0ms	6×	body	2048	valid

Compiler

Compiled 506 to 369 computations (27.1% saved)

Details

analyze2.1s (13.5%)

sample92.0ms (0.6%)

simplify153.0ms (1%)

prune4.0ms (0%)

localize17.0ms (0.1%)

rewrite95.0ms (0.6%)

series1.7s (10.9%)

simplify105.0ms (0.7%)

prune618.0ms (4%)

localize18.0ms (0.1%)

rewrite124.0ms (0.8%)

series1.5s (9.5%)

simplify207.0ms (1.3%)

prune807.0ms (5.2%)

localize18.0ms (0.1%)

rewrite82.0ms (0.5%)

series1.7s (11.1%)

simplify117.0ms (0.8%)

prune365.0ms (2.4%)

localize20.0ms (0.1%)

rewrite35.0ms (0.2%)

series1.9s (12.4%)

simplify54.0ms (0.3%)

prune301.0ms (1.9%)

regimes324.0ms (2.1%)

bsearch74.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.0s (19.2%)

Profiling