Details

analyze2.1s (1.4%)

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)

sample87.0ms (0.1%)

Algorithm

1×

intervals

Results

21.0ms	203×	body	128	valid
13.0ms	80×	body	128	invalid
8.0ms	17×	body	1024	valid
7.0ms	23×	body	512	valid
7.0ms	16×	body	1024	invalid
3.0ms	10×	body	512	invalid
3.0ms	13×	body	256	valid
1.0ms	5×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify228.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

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

40.9b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize16.0ms (0%)

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))
38.1b	(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))))

rewrite575.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

40.9b

Rules

142×	`associate-*l/_binary64_1385`
102×	`flip3--_binary64_1446` `flip--_binary64_1417`
68×	`frac-times_binary64_1452`
66×	`sqrt-div_binary64_1459`
64×	`frac-add_binary64_1450`
44×	`pow1_binary64_1503`
34×	`associate-*r/_binary64_1384`
17×	`pow-prod-down_binary64_1513`
16×	`add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478`
8×	`prod-exp_binary64_1491` `cbrt-unprod_binary64_1475`
6×	`add-sqr-sqrt_binary64_1464`
5×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `pow-prod-up_binary64_1512` `pow-sqr_binary64_1415`
3×	`sqrt-prod_binary64_1458`
2×	`pow-plus_binary64_1505`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `pow2_binary64_1523` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `associate-r_binary64_1382` `*-commutative_binary64_1373`

Counts

4 → 135

Calls

4 calls:

27.0ms	(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))))
14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.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 9145 to 2868 computations (68.6% saved)

series12.1s (8.1%)

Error

3.3b

Counts

4 → 78

Calls

4 calls:

11.1s	(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))))
550.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
45.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
42.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 22826 to 17297 computations (24.2% saved)

simplify180.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

213 → 213

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4984	16729
1	4984	16729

prune587.0ms (0.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	204	9	213
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	205	9	214

Error

3.3b

Counts

214 → 9

Compiler

Compiled 13737 to 5712 computations (58.4% saved)

localize24.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
2.9b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.9b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
38.1b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite308.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

128×	`associate-*l/_binary64_1385`
96×	`flip3--_binary64_1446` `flip--_binary64_1417`
66×	`sqrt-div_binary64_1459`
64×	`frac-times_binary64_1452` `frac-add_binary64_1450`
32×	`associate-*r/_binary64_1384`
8×	`add-sqr-sqrt_binary64_1464`
7×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
6×	`pow1_binary64_1503`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `log-pow_binary64_1531`
3×	`sqrt-prod_binary64_1458` `exp-prod_binary64_1494` `log-prod_binary64_1528`
1×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455` `rem-log-exp_binary64_1483`

Counts

4 → 108

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

Compiler

Compiled 8251 to 2688 computations (67.4% saved)

series57.9s (38.6%)

Error

3.3b

Counts

4 → 59

Calls

4 calls:

57.0s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
159.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2))))
44.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
36.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 52461 to 41347 computations (21.2% saved)

simplify188.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5584	19186

prune658.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	167	9	176

Error

3.3b

Counts

176 → 9

Compiler

Compiled 14915 to 6743 computations (54.8% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

2.9b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
2.9b	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite250.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

20×	`associate-*r/_binary64_1384` `sqrt-div_binary64_1459`
16×	`cos-mult_binary64_1596` `frac-add_binary64_1450`
12×	`flip3--_binary64_1446` `flip--_binary64_1417`
8×	`add-sqr-sqrt_binary64_1464` `frac-times_binary64_1452`
6×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `sqrt-prod_binary64_1458` `*-un-lft-identity_binary64_1442`
4×	`add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `associate-*l/_binary64_1385`
2×	`pow1/2_binary64_1522` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455`

Counts

4 → 60

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 5318 to 2438 computations (54.2% saved)

series23.2s (15.4%)

Error

3.3b

Counts

4 → 86

Calls

4 calls:

11.2s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.1s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
58.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))
50.0ms	(cos.f64 (/.f64 (+.f64 phi2 phi1) 2))

Compiler

Compiled 44636 to 33185 computations (25.7% saved)

simplify151.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5299	14230

prune845.0ms (0.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	146	9	155

Error

3.3b

Counts

155 → 9

Compiler

Compiled 15347 to 7949 computations (48.2% saved)

localize32.0ms (0%)

Local error

Found 4 expressions with local error:

38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
38.1b	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite762.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

3.3b

Rules

40×	`associate-*r/_binary64_1384` `sqrt-div_binary64_1459`
32×	`cos-mult_binary64_1596` `frac-add_binary64_1450`
24×	`flip3--_binary64_1446` `flip--_binary64_1417`
16×	`frac-times_binary64_1452`
12×	`add-sqr-sqrt_binary64_1464` `sqrt-prod_binary64_1458`
8×	`pow1_binary64_1503` `add-cube-cbrt_binary64_1477` `associate-l/_binary64_1385` `-un-lft-identity_binary64_1442`
4×	`pow1/2_binary64_1522` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-cbrt-cube_binary64_1478` `sqrt-pow1_binary64_1460` `flip3-+_binary64_1445` `flip-+_binary64_1416` `rem-sqrt-square_binary64_1455`

Counts

4 → 92

Calls

4 calls:

14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
14.0ms	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

Compiler

Compiled 14344 to 6600 computations (54% saved)

series47.6s (31.7%)

Error

3.3b

Counts

4 → 150

Calls

4 calls:

11.2s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.2s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.2s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
11.1s	(sqrt.f64 (+.f64 (.f64 (pow.f64 (-.f64 lambda1 lambda2) 2) (.f64 (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)) (cos.f64 (/.f64 (+.f64 phi2 phi1) 2)))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

Compiler

Compiled 105224 to 73639 computations (30% saved)

simplify246.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5025	28574

prune1.9s (1.3%)

Compiler: Compiled 42033 to 21149 computations (49.7% saved)

Details

analyze2.1s (1.4%)

sample87.0ms (0.1%)

simplify228.0ms (0.2%)

prune4.0ms (0%)

localize16.0ms (0%)

rewrite575.0ms (0.4%)

series12.1s (8.1%)

simplify180.0ms (0.1%)

prune587.0ms (0.4%)

localize24.0ms (0%)

rewrite308.0ms (0.2%)

series57.9s (38.6%)

simplify188.0ms (0.1%)

prune658.0ms (0.4%)

localize25.0ms (0%)

rewrite250.0ms (0.2%)

series23.2s (15.4%)

simplify151.0ms (0.1%)

prune845.0ms (0.6%)

localize32.0ms (0%)

rewrite762.0ms (0.5%)

series47.6s (31.7%)

simplify246.0ms (0.2%)

prune1.9s (1.3%)

Profiling