Details

analyze2.9s (11.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1713	273
1	1713	273
0	4	4
1	4	4

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)

sample230.0ms (0.9%)

Algorithm

1×

intervals

Results

164.0ms	174×	body	1024	valid
28.0ms	50×	body	512	valid
15.0ms	7×	body	2048	valid
3.0ms	18×	body	128	valid
2.0ms	7×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune4.0ms (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

11.4b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.3b	(cos.f64 (-.f64 lambda1 lambda2))
2.3b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite113.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

5.8b

Rules

11×	`add-sqr-sqrt_binary64_2146` `pow1_binary64_2185` `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×	`sin-sum_binary64_2257` `add-log-exp_binary64_2163` `cos-sum_binary64_2258` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-l_binary64_2065`
3×	`cos-diff_binary64_2261`
2×	`sub-neg_binary64_2117` `sin-cos-mult_binary64_2280` `*-commutative_binary64_2055`
1×	`sin-diff_binary64_2260` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `associate-*l/_binary64_2067` `unswap-sqr_binary64_2092`

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))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 2066 to 344 computations (83.3% saved)

series788.0ms (3%)

Error

8.0b

Counts

4 → 61

Calls

4 calls:

405.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
188.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
59.0ms	(cos.f64 (-.f64 lambda1 lambda2))
57.0ms	(sin.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 4659 to 2181 computations (53.2% saved)

simplify91.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4957	2128
1	4957	2128

prune169.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	112	13	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	13	126

Error

5.8b

Counts

126 → 13

Compiler

Compiled 4048 to 791 computations (80.5% saved)

localize32.0ms (0.1%)

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 (cos.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.3b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite128.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

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×	`cos-sum_binary64_2258` `add-log-exp_binary64_2163`
3×	`cos-diff_binary64_2261` `cancel-sign-sub-inv_binary64_2090` `associate-l/_binary64_2067` `-commutative_binary64_2055`
2×	`unswap-sqr_binary64_2092`
1×	`sub-neg_binary64_2117` `distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `sin-cos-mult_binary64_2280` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 71

Calls

4 calls:

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

Compiler

Compiled 2860 to 402 computations (85.9% saved)

series1.1s (4.2%)

Error

5.2b

Counts

4 → 62

Calls

4 calls:

421.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
409.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
115.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
65.0ms	(cos.f64 (-.f64 lambda1 lambda2))

Compiler

Compiled 5793 to 2736 computations (52.8% saved)

simplify83.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5051	2787

prune182.0ms (0.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	127	6	133
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	137	9	146

Error

0.1b

Counts

146 → 9

Compiler

Compiled 5263 to 872 computations (83.4% saved)

localize29.0ms (0.1%)

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

rewrite178.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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×	`add-log-exp_binary64_2163` `sin-cos-mult_binary64_2280` `*-commutative_binary64_2055`
3×	`sin-mult_binary64_2279` `frac-times_binary64_2134` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `unswap-sqr_binary64_2092`
2×	`cos-mult_binary64_2278` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073` `flip3--_binary64_2128` `flip--_binary64_2099`

Counts

4 → 84

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.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))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 4101 to 514 computations (87.5% saved)

series1.4s (5.4%)

Error

0.1b

Counts

4 → 60

Calls

4 calls:

725.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
392.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
114.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
111.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

Compiler

Compiled 6948 to 3011 computations (56.7% saved)

simplify140.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4978	3834
1	4978	3834

prune224.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	138	6	144
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	145	8	153

Error

0.0b

Counts

153 → 8

Compiler

Compiled 6957 to 1017 computations (85.4% saved)

localize44.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.3b	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
0.4b	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
0.5b	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)

rewrite517.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

97×	`cos-mult_binary64_2278`
83×	`sin-mult_binary64_2279`
50×	`associate-*r/_binary64_2066` `associate-/r/_binary64_2070`
49×	`pow1_binary64_2185` `frac-add_binary64_2132`
47×	`associate-*l/_binary64_2067`
41×	`frac-times_binary64_2134`
31×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
27×	`frac-sub_binary64_2133`
19×	`pow-prod-down_binary64_2195`
15×	`sub-div_binary64_2131`
13×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
8×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
6×	`pow-unpow_binary64_2201`
4×	`pow-pow_binary64_2196` `pow-exp_binary64_2192` `add-log-exp_binary64_2163` `cube-div_binary64_2153` `rem-cube-cbrt_binary64_2147` `pow-prod-up_binary64_2194` `pow-sqr_binary64_2097`
3×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `times-frac_binary64_2130` `associate-/l/_binary64_2071` `flip3--_binary64_2128` `flip--_binary64_2099` `associate-/r*_binary64_2068`
2×	`unpow-prod-down_binary64_2203` `pow-to-exp_binary64_2193` `unpow3_binary64_2190` `cube-mult_binary64_2154` `cube-prod_binary64_2152` `sqr-pow_binary64_2096` `pow-plus_binary64_2187` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`pow2_binary64_2205` `swap-sqr_binary64_2091` `associate-l_binary64_2065` `associate-r_binary64_2064` `-commutative_binary64_2055` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/l_binary64_2069`

Counts

4 → 159

Calls

4 calls:

47.0ms	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
9.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))
5.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
5.0ms	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)

Compiler

Compiled 16187 to 2816 computations (82.6% saved)

series4.4s (16.9%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

3.6s	(/.f64 (.f64 (.f64 (cos.f64 phi2) (sin.f64 phi1)) (+.f64 (pow.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3) (pow.f64 (.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3))) (+.f64 (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (cos.f64 lambda2) (cos.f64 lambda1))) (-.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
245.0ms	(pow.f64 (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)) 3)
228.0ms	(pow.f64 (*.f64 (sin.f64 lambda2) (sin.f64 lambda1)) 3)
186.0ms	(.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (cos.f64 lambda2) (cos.f64 lambda1)))

Compiler

Compiled 12720 to 5555 computations (56.3% saved)

simplify158.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4979	12502
1	4979	12502

prune499.0ms (1.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	211	9	220

Error

0.0b

Counts

220 → 9

Compiler

Compiled 19096 to 3623 computations (81% saved)

regimes2.0s (7.8%)

Accuracy

Total 0.1b remaining (74.2%)

Threshold costs 0.1b (74.2%)

Compiler

Compiled 30164 to 18817 computations (37.6% 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%)

sample10.6s (40.5%)

Algorithm

1×

intervals

Results

4.9s	5399×	body	1024	valid
709.0ms	1279×	body	512	valid
401.0ms	202×	body	2048	valid
130.0ms	749×	body	128	valid
128.0ms	371×	body	256	valid

Compiler

Compiled 4976 to 3099 computations (37.7% saved)

Details

analyze2.9s (11.3%)

sample230.0ms (0.9%)

simplify22.0ms (0.1%)

prune4.0ms (0%)

localize20.0ms (0.1%)

rewrite113.0ms (0.4%)

series788.0ms (3%)

simplify91.0ms (0.3%)

prune169.0ms (0.6%)

localize32.0ms (0.1%)

rewrite128.0ms (0.5%)

series1.1s (4.2%)

simplify83.0ms (0.3%)

prune182.0ms (0.7%)

localize29.0ms (0.1%)

rewrite178.0ms (0.7%)

series1.4s (5.4%)

simplify140.0ms (0.5%)

prune224.0ms (0.9%)

localize44.0ms (0.2%)

rewrite517.0ms (2%)

series4.4s (16.9%)

simplify158.0ms (0.6%)

prune499.0ms (1.9%)

regimes2.0s (7.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample10.6s (40.5%)

Profiling