Details

analyze2.9s (17.3%)

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
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample256.0ms (1.5%)

Algorithm

1×

intervals

Results

164.0ms	166×	body	1024	valid
34.0ms	49×	body	512	valid
33.0ms	13×	body	2048	valid
6.0ms	16×	body	256	valid
2.0ms	12×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify188.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

prune3.0ms (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

Merged error: 16.2b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
0.3b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
6×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`cos-sum_binary64_213` `add-log-exp_binary64_118`
3×	`cancel-sign-sub-inv_binary64_45`
2×	`unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150`
1×	`sin-mult_binary64_234` `cos-diff_binary64_216` `acos-asin_binary64_260` `sub-neg_binary64_72`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series397.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
71.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
70.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4863	1492
1	4863	1492

prune371.0ms (2.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	55	14	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	14	70

Merged error: 2.8b

Counts

70 → 14

Compiler

Compiled 7246 to 4016 computations (44.6% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.3b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `add-sqr-sqrt_binary64_101` `pow1_binary64_140`
9×	`add-cube-cbrt_binary64_114` `associate-r_binary64_19` `*-un-lft-identity_binary64_79`
7×	`associate-l_binary64_20`
6×	`cos-mult_binary64_233`
5×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150`
4×	`add-log-exp_binary64_118`
3×	`sin-mult_binary64_234` `frac-times_binary64_89` `associate-r/_binary64_21` `-commutative_binary64_10`
2×	`flip-+_binary64_53` `frac-add_binary64_87` `unswap-sqr_binary64_47` `flip3-+_binary64_82`
1×	`distribute-lft-in_binary64_28` `associate-*l/_binary64_22` `acos-asin_binary64_260` `distribute-rgt-in_binary64_29`

Counts

4 → 72

Calls

4 calls:

12.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series907.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

390.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
351.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
97.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
69.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5063	2773

prune645.0ms (3.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	72	12	84
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	82	16	98

Merged error: 2.7b

Counts

98 → 16

Compiler

Compiled 14167 to 7143 computations (49.6% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
0.3b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `pow1_binary64_140`
12×	`add-sqr-sqrt_binary64_101`
10×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128` `pow-prod-down_binary64_150`
8×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
7×	`associate-l_binary64_20` `associate-r_binary64_19`
4×	`cos-mult_binary64_233` `add-log-exp_binary64_118`
3×	`*-commutative_binary64_10`
2×	`unswap-sqr_binary64_47`
1×	`sin-mult_binary64_234` `frac-times_binary64_89` `associate-l/_binary64_22` `associate-r/_binary64_21` `acos-asin_binary64_260`

Counts

4 → 70

Calls

4 calls:

10.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series732.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

330.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
243.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
94.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
64.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5016	2276

prune147.0ms (0.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	82	16	98

Merged error: 2.7b

Counts

98 → 16

Compiler

Compiled 4277 to 1108 computations (74.1% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.4b	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
0.5b	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
0.7b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite22.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
7×	`pow1_binary64_140`
6×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115` `exp-prod_binary64_131`
5×	`add-log-exp_binary64_118`
4×	`log-pow_binary64_168`
3×	`associate-l_binary64_20` `log-prod_binary64_165` `acos-asin_binary64_260` `associate-r_binary64_19`
2×	`exp-diff_binary64_127`
1×	`rem-log-exp_binary64_120` `sin-mult_binary64_234` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `log-div_binary64_166` `rem-exp-log_binary64_119`

Counts

4 → 55

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
2.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series668.0ms (4%)

Counts

4 → 12

Calls

4 calls:

330.0ms	(log.f64 (exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
190.0ms	(exp.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
78.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
70.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4864	2288
1	4864	2288

prune322.0ms (1.9%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	64	3	67
Fresh	2	12	14
Picked	1	0	1
Done	0	1	1
Total	67	16	83

Merged error: 2.7b

Counts

83 → 16

Compiler

Compiled 7669 to 3218 computations (58% saved)

regimes389.0ms (2.3%)

Compiler: Compiled 5311 to 2970 computations (44.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	53
1	33	53

end0.0ms (0%)

sample8.4s (49.7%)

Algorithm

1×

intervals

Results

5.6s	5446×	body	1024	valid
871.0ms	1463×	body	512	valid
692.0ms	285×	body	2048	valid
189.0ms	506×	body	256	valid
56.0ms	300×	body	128	valid
1.0ms	1×	body	1024	invalid
0.0ms	1×	body	256	invalid

Compiler

Compiled 769 to 432 computations (43.8% saved)

Details

analyze2.9s (17.3%)

sample256.0ms (1.5%)

simplify188.0ms (1.1%)

prune3.0ms (0%)

localize24.0ms (0.1%)

rewrite21.0ms (0.1%)

series397.0ms (2.4%)

simplify74.0ms (0.4%)

prune371.0ms (2.2%)

localize31.0ms (0.2%)

rewrite31.0ms (0.2%)

series907.0ms (5.4%)

simplify81.0ms (0.5%)

prune645.0ms (3.8%)

localize33.0ms (0.2%)

rewrite30.0ms (0.2%)

series732.0ms (4.3%)

simplify81.0ms (0.5%)

prune147.0ms (0.9%)

localize35.0ms (0.2%)

rewrite22.0ms (0.1%)

series668.0ms (4%)

simplify97.0ms (0.6%)

prune322.0ms (1.9%)

regimes389.0ms (2.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.4s (49.7%)

Profiling