Details

analyze5.5s (16.4%)

Algorithm

2×	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%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14
8.5%	90.2%	1.3%	14

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 66 to 44 computations (33.3% saved)

sample1.8s (5.5%)

Algorithm

2×

intervals

Results

41.0ms	380×	body	128	valid
27.0ms	54×	body	1024	valid
22.0ms	165×	body	128	invalid
18.0ms	50×	body	512	valid
17.0ms	34×	body	1024	invalid
7.0ms	28×	body	256	valid
6.0ms	18×	body	512	invalid
3.0ms	12×	body	256	invalid

Compiler

Compiled 11945 to 9768 computations (18.2% saved)

simplify126.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4960	49
1	4960	49

prune8.0ms (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

38.3b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
35.3b	(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))))

rewrite386.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

38.3b

Rules

130×	`associate-*l/_binary64_2067`
97×	`flip3--_binary64_2128` `flip--_binary64_2099`
66×	`sqrt-div_binary64_2141`
64×	`frac-times_binary64_2134` `frac-add_binary64_2132`
32×	`associate-*r/_binary64_2066`
12×	`add-sqr-sqrt_binary64_2146`
9×	`*-un-lft-identity_binary64_2124`
7×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`associate-l_binary64_2065`
4×	`add-log-exp_binary64_2163`
3×	`sqrt-prod_binary64_2140` `associate-r_binary64_2064`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3-+_binary64_2127` `flip-+_binary64_2098` `rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055`

Counts

4 → 115

Calls

4 calls:

20.0ms	(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))))
8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8305 to 2543 computations (69.4% saved)

series13.1s (39.4%)

Error

3.1b

Counts

4 → 71

Calls

4 calls:

12.2s	(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))))
470.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
73.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
68.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 17834 to 13137 computations (26.3% saved)

simplify134.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	6066	14551

prune576.0ms (1.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	179	7	186
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	180	7	187

Error

3.1b

Counts

187 → 7

Compiler

Compiled 12234 to 4818 computations (60.6% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

rewrite30.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

9×	`add-sqr-sqrt_binary64_2146`
7×	`*-un-lft-identity_binary64_2124`
6×	`cancel-sign-sub-inv_binary64_2090`
5×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064`
4×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
3×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-l_binary64_2065`
2×	`sub-neg_binary64_2117` `associate-*r/_binary64_2066`
1×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `flip3--_binary64_2128` `flip--_binary64_2099` `difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076` `*-commutative_binary64_2055`

Counts

1 → 30

Calls

1 calls:

7.0ms

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

Compiler

Compiled 338 to 113 computations (66.6% saved)

series152.0ms (0.5%)

Error

3.1b

Counts

1 → 15

Calls

1 calls:

145.0ms

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

Compiler

Compiled 219 to 198 computations (9.6% saved)

simplify45.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5690	386

prune47.0ms (0.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	42	10	52

Error

3.1b

Counts

52 → 10

Compiler

Compiled 755 to 344 computations (54.4% saved)

localize6.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (.f64 phi2 R) (neg.f64 (.f64 phi1 R)))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

5×	`add-log-exp_binary64_2163`
2×	`sum-log_binary64_2215`
1×	`neg-log_binary64_2217` `pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `flip3-+_binary64_2127` `*-un-lft-identity_binary64_2124` `unsub-neg_binary64_2118` `flip-+_binary64_2098` `distribute-lft-neg-in_binary64_2081` `distribute-rgt-out_binary64_2077` `neg-sub0_binary64_2119` `associate-+r-_binary64_2058` `+-commutative_binary64_2054`

Counts

1 → 15

Calls

1 calls:

5.0ms

(+.f64 (*.f64 phi2 R) (neg.f64 (*.f64 phi1 R)))

Compiler

Compiled 233 to 56 computations (76% saved)

series167.0ms (0.5%)

Error

3.1b

Counts

1 → 15

Calls

1 calls:

159.0ms

(+.f64 (*.f64 phi2 R) (neg.f64 (*.f64 phi1 R)))

Compiler

Compiled 225 to 206 computations (8.4% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5032	255

prune37.0ms (0.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	30	0	30
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	30	10	40

Error

3.1b

Counts

40 → 10

Compiler

Compiled 620 to 312 computations (49.7% 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)))
2.2b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
2.2b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
2.2b	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

rewrite109.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

3.1b

Rules

20×	`associate-*l/_binary64_2067`
18×	`cbrt-div_binary64_2156`
11×	`pow1_binary64_2185`
10×	`add-sqr-sqrt_binary64_2146`
9×	`pow1/3_binary64_2206` `flip3--_binary64_2128` `flip--_binary64_2099`
8×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
7×	`cbrt-prod_binary64_2155`
6×	`add-exp-log_binary64_2162`
4×	`add-log-exp_binary64_2163` `add-cbrt-cube_binary64_2160` `frac-times_binary64_2134` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064`
2×	`pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097` `associate-*r/_binary64_2066`
1×	`pow2_binary64_2205` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055`

Counts

4 → 72

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
5.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 2027 to 304 computations (85% saved)

series2.0s (5.8%)

Error

3.1b

Counts

4 → 71

Calls

4 calls:

478.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
457.0ms	(.f64 (cbrt.f64 (.f64 (-.f64 phi2 phi1) R)) (cbrt.f64 (*.f64 (-.f64 phi2 phi1) R)))
455.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))
432.0ms	(cbrt.f64 (*.f64 (-.f64 phi2 phi1) R))

Compiler

Compiled 6966 to 4796 computations (31.2% saved)

simplify79.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4972	3670
1	4972	3670

prune197.0ms (0.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	139	4	143
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	142	11	153

Error

3.0b

Counts

153 → 11

Compiler

Compiled 4221 to 1227 computations (70.9% saved)

regimes3.1s (9.4%)

Accuracy

Total 20.7b remaining (83.9%)

Threshold costs 0b (0%)

Compiler

Compiled 24626 to 18385 computations (25.3% saved)

bsearch5.0ms (0%)

Compiler: Compiled 3 to 6 computations (-100% saved)

simplify61.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	250
1	131	250

Compiler

Compiled 664 to 316 computations (52.4% saved)

end0.0ms (0%)

sample5.6s (16.7%)

Algorithm

1×

intervals

Results

667.0ms	5986×	body	128	valid
576.0ms	751×	body	512	valid
429.0ms	820×	body	1024	valid
282.0ms	2543×	body	128	invalid
229.0ms	459×	body	1024	invalid
131.0ms	358×	body	512	invalid
113.0ms	436×	body	256	valid
43.0ms	186×	body	256	invalid
5.0ms	7×	body	2048	valid

Compiler

Compiled 2767 to 2026 computations (26.8% saved)

Details

analyze5.5s (16.4%)

sample1.8s (5.5%)

simplify126.0ms (0.4%)

prune8.0ms (0%)

localize18.0ms (0.1%)

rewrite386.0ms (1.2%)

series13.1s (39.4%)

simplify134.0ms (0.4%)

prune576.0ms (1.7%)

localize4.0ms (0%)

rewrite30.0ms (0.1%)

series152.0ms (0.5%)

simplify45.0ms (0.1%)

prune47.0ms (0.1%)

localize6.0ms (0%)

rewrite19.0ms (0.1%)

series167.0ms (0.5%)

simplify61.0ms (0.2%)

prune37.0ms (0.1%)

localize9.0ms (0%)

rewrite109.0ms (0.3%)

series2.0s (5.8%)

simplify79.0ms (0.2%)

prune197.0ms (0.6%)

regimes3.1s (9.4%)

bsearch5.0ms (0%)

simplify61.0ms (0.2%)

end0.0ms (0%)

sample5.6s (16.7%)

Profiling