Details

analyze3.8s (11.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5562	539
0	5	5
1	5	5

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

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample175.0ms (0.5%)

Algorithm

1×

intervals

Results

30.0ms	184×	body	128	valid
24.0ms	32×	body	1024	valid
18.0ms	71×	body	128	invalid
18.0ms	24×	body	1024	invalid
10.0ms	21×	body	512	valid
7.0ms	18×	body	256	valid
5.0ms	10×	body	512	invalid
2.0ms	6×	body	256	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify227.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (217.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	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

Error

39.4b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize32.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.0b	(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))))

rewrite436.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

39.3b

Rules

130×	`associate-*l/_binary64_3431`
97×	`flip3--_binary64_3492` `flip--_binary64_3463`
66×	`sqrt-div_binary64_3505`
64×	`frac-times_binary64_3498` `frac-add_binary64_3496`
32×	`associate-*r/_binary64_3430`
12×	`add-sqr-sqrt_binary64_3510`
9×	`*-un-lft-identity_binary64_3488`
7×	`pow1_binary64_3549` `add-cube-cbrt_binary64_3523`
6×	`add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524`
5×	`associate-l_binary64_3429`
4×	`add-log-exp_binary64_3527`
3×	`sqrt-prod_binary64_3504` `associate-r_binary64_3428`
1×	`pow1/2_binary64_3568` `sqrt-pow1_binary64_3506` `flip3-+_binary64_3491` `flip-+_binary64_3462` `rem-sqrt-square_binary64_3501` `pow-prod-down_binary64_3559` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `*-commutative_binary64_3419`

Counts

4 → 115

Calls

4 calls:

38.0ms	(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))))
13.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
10.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8305 to 2543 computations (69.4% saved)

series11.2s (32.8%)

Error

4.3b

Counts

4 → 60

Calls

4 calls:

10.4s	(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))))
411.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
37.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 16403 to 12205 computations (25.6% saved)

simplify220.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5679	13647

prune670.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	166	9	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	167	9	176

Error

4.2b

Counts

176 → 9

Compiler

Compiled 11447 to 4426 computations (61.3% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 R (-.f64 phi2 phi1))

rewrite56.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

9×	`add-sqr-sqrt_binary64_3510`
7×	`*-un-lft-identity_binary64_3488`
6×	`cancel-sign-sub-inv_binary64_3454`
5×	`add-cube-cbrt_binary64_3523` `associate-r_binary64_3428`
4×	`distribute-rgt-in_binary64_3438` `distribute-lft-in_binary64_3437`
3×	`pow1_binary64_3549` `add-exp-log_binary64_3526` `add-cbrt-cube_binary64_3524` `associate-l_binary64_3429`
2×	`sub-neg_binary64_3481` `associate-*r/_binary64_3430`
1×	`pow-prod-down_binary64_3559` `prod-exp_binary64_3537` `add-log-exp_binary64_3527` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `flip3--_binary64_3492` `flip--_binary64_3463` `difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `*-commutative_binary64_3419`

Counts

1 → 30

Calls

1 calls:

12.0ms

(*.f64 R (-.f64 phi2 phi1))

Compiler

Compiled 338 to 113 computations (66.6% saved)

series126.0ms (0.4%)

Error

4.2b

Counts

1 → 15

Calls

1 calls:

117.0ms

(*.f64 R (-.f64 phi2 phi1))

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify55.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5690	386

prune63.0ms (0.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	44	10	54

Error

4.2b

Counts

54 → 10

Compiler

Compiled 693 to 296 computations (57.3% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
5.0b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

rewrite146.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

20×	`associate-*l/_binary64_3431`
18×	`cbrt-div_binary64_3520`
11×	`pow1_binary64_3549`
10×	`add-sqr-sqrt_binary64_3510`
9×	`pow1/3_binary64_3570` `flip3--_binary64_3492` `flip--_binary64_3463`
8×	`add-cube-cbrt_binary64_3523` `*-un-lft-identity_binary64_3488`
7×	`cbrt-prod_binary64_3519`
6×	`add-exp-log_binary64_3526`
4×	`add-log-exp_binary64_3527` `add-cbrt-cube_binary64_3524` `frac-times_binary64_3498` `swap-sqr_binary64_3455` `associate-l_binary64_3429` `associate-r_binary64_3428`
2×	`pow-prod-down_binary64_3559` `pow-prod-up_binary64_3558` `pow-sqr_binary64_3461` `associate-*r/_binary64_3430`
1×	`pow2_binary64_3569` `pow-plus_binary64_3551` `prod-exp_binary64_3537` `cbrt-unprod_binary64_3521` `unswap-sqr_binary64_3456` `*-commutative_binary64_3419`

Counts

4 → 72

Calls

4 calls:

15.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
11.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
9.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
6.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 2027 to 304 computations (85% saved)

series1.5s (4.3%)

Error

4.2b

Counts

4 → 60

Calls

4 calls:

411.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
350.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
327.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
301.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))

Compiler

Compiled 5554 to 3783 computations (31.9% saved)

simplify107.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4954	2589
1	4954	2589

prune189.0ms (0.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	129	3	132
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	129	13	142

Error

4.2b

Counts

142 → 13

Compiler

Compiled 3820 to 1199 computations (68.6% saved)

localize15.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1))))
1.1b	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))) 6)
5.0b	(cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))
5.0b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

rewrite105.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

4.2b

Rules

12×	`cbrt-prod_binary64_3519`
8×	`add-cube-cbrt_binary64_3523` `cbrt-div_binary64_3520` `add-sqr-sqrt_binary64_3510` `*-un-lft-identity_binary64_3488`
7×	`unpow-prod-down_binary64_3567`
5×	`pow1_binary64_3549` `add-exp-log_binary64_3526`
4×	`pow1/3_binary64_3570` `add-log-exp_binary64_3527` `add-cbrt-cube_binary64_3524` `associate-*r/_binary64_3430`
3×	`flip3--_binary64_3492` `flip--_binary64_3463` `pow-unpow_binary64_3565`
2×	`associate-*l/_binary64_3431` `pow-pow_binary64_3560`
1×	`pow-to-exp_binary64_3557` `pow-exp_binary64_3556` `sqr-pow_binary64_3460`

Counts

4 → 58

Calls

4 calls:

9.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0ms	(cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))
4.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))) 6)
2.0ms	(cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1))))

Compiler

Compiled 1490 to 499 computations (66.5% saved)

series2.0s (5.8%)

Error

4.2b

Counts

4 → 60

Calls

4 calls:

876.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))) 6)
346.0ms	(cbrt.f64 (*.f64 R (-.f64 phi2 phi1)))
328.0ms	(cbrt.f64 (cbrt.f64 (*.f64 R (-.f64 phi2 phi1))))
309.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 5319 to 4270 computations (19.7% saved)

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5015	2511

prune191.0ms (0.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	115	3	118
Fresh	2	8	10
Picked	1	0	1
Done	0	2	2
Total	118	13	131

Error

4.2b

Counts

131 → 13

Compiler

Compiled 3023 to 1249 computations (58.7% saved)

regimes5.2s (15.3%)

Accuracy

Total 15.5b remaining (79.8%)

Threshold costs 0b (0%)

Compiler

Compiled 39734 to 25568 computations (35.7% saved)

bsearch10.0ms (0%)

Compiler: Compiled 29 to 19 computations (34.5% saved)

simplify58.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	120
1	95	120

Remove

(sort lambda1 lambda2)

Compiler

Compiled 474 to 252 computations (46.8% saved)

end0.0ms (0%)

sample7.4s (21.8%)

Algorithm

1×

intervals

Results

865.0ms	6025×	body	128	valid
558.0ms	793×	body	1024	valid
349.0ms	2417×	body	128	invalid
338.0ms	740×	body	512	valid
299.0ms	458×	body	1024	invalid
179.0ms	371×	body	512	invalid
145.0ms	436×	body	256	valid
58.0ms	186×	body	256	invalid
7.0ms	6×	body	2048	valid

Compiler

Compiled 4191 to 2704 computations (35.5% saved)

Details

analyze3.8s (11.3%)

sample175.0ms (0.5%)

simplify227.0ms (0.7%)

prune4.0ms (0%)

localize32.0ms (0.1%)

rewrite436.0ms (1.3%)

series11.2s (32.8%)

simplify220.0ms (0.6%)

prune670.0ms (2%)

localize5.0ms (0%)

rewrite56.0ms (0.2%)

series126.0ms (0.4%)

simplify55.0ms (0.2%)

prune63.0ms (0.2%)

localize9.0ms (0%)

rewrite146.0ms (0.4%)

series1.5s (4.3%)

simplify107.0ms (0.3%)

prune189.0ms (0.6%)

localize15.0ms (0%)

rewrite105.0ms (0.3%)

series2.0s (5.8%)

simplify91.0ms (0.3%)

prune191.0ms (0.6%)

regimes5.2s (15.3%)

bsearch10.0ms (0%)

simplify58.0ms (0.2%)

end0.0ms (0%)

sample7.4s (21.8%)

Profiling