Details

analyze2.5s (16.7%)

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
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample215.0ms (1.4%)

Algorithm

1×

intervals

Results

149.0ms	166×	body	1024	valid
24.0ms	45×	body	512	valid
18.0ms	10×	body	2048	valid
5.0ms	13×	body	256	valid
4.0ms	22×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify116.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

14.0b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_2185` `add-sqr-sqrt_binary64_2146` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
6×	`cancel-sign-sub-inv_binary64_2090` `associate-r_binary64_2064`
4×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `prod-exp_binary64_2173` `sin-sum_binary64_2257` `cos-sum_binary64_2258` `cbrt-unprod_binary64_2157`
3×	`cos-diff_binary64_2261`
2×	`sin-cos-mult_binary64_2280` `*-commutative_binary64_2055` `sub-neg_binary64_2117`
1×	`unswap-sqr_binary64_2092` `associate-*l/_binary64_2067` `sin-diff_binary64_2260` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 64

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series207.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

111.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
61.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5363	1102

prune109.0ms (0.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	63	13	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	13	77

Error

6.6b

Counts

77 → 13

Compiler

Compiled 2571 to 527 computations (79.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2146`
13×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`associate-r_binary64_2064`
7×	`associate-l_binary64_2065`
5×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163` `cos-sum_binary64_2258`
3×	`cos-diff_binary64_2261` `cancel-sign-sub-inv_binary64_2090` `-commutative_binary64_2055` `associate-l/_binary64_2067`
2×	`unswap-sqr_binary64_2092`
1×	`flip--_binary64_2099` `sin-cos-mult_binary64_2280` `flip3--_binary64_2128` `distribute-rgt-in_binary64_2074` `sub-neg_binary64_2117` `distribute-lft-in_binary64_2073`

Counts

4 → 71

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series287.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
100.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
44.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5316	1458

prune126.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	8	4	12
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Error

0.1b

Counts

96 → 10

Compiler

Compiled 3423 to 559 computations (83.7% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2146`
15×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`associate-r_binary64_2064`
11×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
10×	`associate-l_binary64_2065`
6×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`sin-cos-mult_binary64_2280` `*-commutative_binary64_2055` `add-log-exp_binary64_2163`
3×	`unswap-sqr_binary64_2092` `associate-l/_binary64_2067` `sin-mult_binary64_2279` `associate-r/_binary64_2066` `frac-times_binary64_2134`
2×	`cos-mult_binary64_2278` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-add_binary64_2132`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`

Counts

4 → 84

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series413.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
129.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
43.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
37.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5028	2099

prune177.0ms (1.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	84	12	96
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	92	14	106

Error

0.0b

Counts

106 → 14

Compiler

Compiled 5045 to 826 computations (83.6% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
5.3b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite38.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`pow1_binary64_2185` `add-sqr-sqrt_binary64_2146`
13×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
9×	`associate-r_binary64_2064`
7×	`associate-l_binary64_2065`
5×	`pow-prod-down_binary64_2195` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`sin-cos-mult_binary64_2280` `log-pow_binary64_2213` `-commutative_binary64_2055` `log-prod_binary64_2210` `associate-l/_binary64_2067`
2×	`unswap-sqr_binary64_2092` `associate-*r/_binary64_2066` `flip3-+_binary64_2127` `frac-times_binary64_2134` `flip-+_binary64_2098`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `rem-log-exp_binary64_2165` `exp-to-pow_binary64_2186` `sin-mult_binary64_2279` `distribute-rgt-in_binary64_2074` `exp-prod_binary64_2176` `distribute-lft-in_binary64_2073`

Counts

4 → 78

Calls

4 calls:

13.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series517.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (log.f64 (exp.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
127.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
88.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4985	1961
1	4985	1961

prune113.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	91	13	104

Error

0.0b

Counts

104 → 13

Compiler

Compiled 4140 to 475 computations (88.5% saved)

regimes1.1s (7.2%)

Accuracy

Total 0.1b remaining (82.7%)

Threshold costs 0.1b (82.7%)

Compiler

Compiled 16620 to 9753 computations (41.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	63
1	136	63

end0.0ms (0%)

sample8.5s (57.2%)

Algorithm

1×

intervals

Results

5.0s	5383×	body	1024	valid
697.0ms	1264×	body	512	valid
362.0ms	194×	body	2048	valid
139.0ms	386×	body	256	valid
125.0ms	773×	body	128	valid

Compiler

Compiled 2721 to 1591 computations (41.5% saved)

Details

analyze2.5s (16.7%)

sample215.0ms (1.4%)

simplify116.0ms (0.8%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite30.0ms (0.2%)

series207.0ms (1.4%)

simplify78.0ms (0.5%)

prune109.0ms (0.7%)

localize28.0ms (0.2%)

rewrite34.0ms (0.2%)

series287.0ms (1.9%)

simplify54.0ms (0.4%)

prune126.0ms (0.8%)

localize30.0ms (0.2%)

rewrite40.0ms (0.3%)

series413.0ms (2.8%)

simplify68.0ms (0.5%)

prune177.0ms (1.2%)

localize30.0ms (0.2%)

rewrite38.0ms (0.3%)

series517.0ms (3.5%)

simplify80.0ms (0.5%)

prune113.0ms (0.8%)

regimes1.1s (7.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.5s (57.2%)

Profiling