Details

analyze3.0s (17.1%)

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)

sample253.0ms (1.5%)

Algorithm

1×

intervals

Results

184.0ms	178×	body	1024	valid
28.0ms	49×	body	512	valid
18.0ms	8×	body	2048	valid
5.0ms	13×	body	256	valid
2.0ms	8×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify11.0ms (0.1%)

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: 15.1b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
1.0b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `cos-sum_binary64`
3×	`cancel-sign-sub-inv_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `acos-asin_binary64` `cos-diff_binary64` `sin-mult_binary64`

Counts

4 → 57

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
6.0ms	(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)))))

series412.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

239.0ms	(.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)
75.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
65.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4862	1492
1	4862	1492

prune424.0ms (2.4%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	54	15	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	15	70

Merged error: 2.3b

Counts

70 → 15

Compiler

Compiled 8110 to 4418 computations (45.5% saved)

localize33.0ms (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 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
1.1b	(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))))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
6×	`cos-mult_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `sin-mult_binary64` `frac-times_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64`
1×	`acos-asin_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

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))))))

series943.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

418.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
344.0ms	(.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)
104.0ms	(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))))))
76.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5063	2773

prune986.0ms (5.6%)

Pruning

20 alts after pruning (19 fresh and 1 done)

	Pruned	Kept	Total
New	69	15	84
Fresh	10	4	14
Picked	0	1	1
Done	0	0	0
Total	79	20	99

Merged error: 2.2b

Counts

99 → 20

Compiler

Compiled 20870 to 11236 computations (46.2% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
1.1b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`*-commutative_binary64`
2×	`unswap-sqr_binary64` `sin-mult_binary64`
1×	`flip3-+_binary64` `acos-asin_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`

Counts

4 → 70

Calls

4 calls:

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

series934.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

410.0ms	(.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
345.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))) R)
98.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
80.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4970	2562
1	4970	2562

prune119.0ms (0.7%)

Pruning

20 alts after pruning (18 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	18	18
Picked	0	1	1
Done	0	1	1
Total	82	20	102

Merged error: 2.2b

Counts

102 → 20

Compiler

Compiled 3462 to 765 computations (77.9% saved)

localize39.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.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	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
1.1b	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
26.0b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

rewrite24.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `sin-mult_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `acos-asin_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 67

Calls

4 calls:

6.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
4.0ms	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
3.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))
2.0ms	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series634.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

326.0ms	(.f64 (acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
141.0ms	(pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)
94.0ms	(acos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) 3)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
73.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2)) 3))

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4941	2058
1	4941	2058

prune215.0ms (1.2%)

Pruning

19 alts after pruning (17 fresh and 2 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	2	15	17
Picked	1	0	1
Done	0	2	2
Total	80	19	99

Merged error: 2.2b

Counts

99 → 19

Compiler

Compiled 5225 to 1967 computations (62.4% saved)

regimes441.0ms (2.5%)

Compiler: Compiled 5745 to 3484 computations (39.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample8.5s (48.8%)

Algorithm

1×

intervals

Results

5.7s	5529×	body	1024	valid
844.0ms	1416×	body	512	valid
664.0ms	250×	body	2048	valid
189.0ms	512×	body	256	valid
56.0ms	293×	body	128	valid
2.0ms	2×	body	1024	invalid

Compiler

Compiled 849 to 517 computations (39.1% saved)

Details

analyze3.0s (17.1%)

sample253.0ms (1.5%)

simplify11.0ms (0.1%)

prune3.0ms (0%)

localize25.0ms (0.1%)

rewrite28.0ms (0.2%)

series412.0ms (2.4%)

simplify75.0ms (0.4%)

prune424.0ms (2.4%)

localize33.0ms (0.2%)

rewrite33.0ms (0.2%)

series943.0ms (5.4%)

simplify82.0ms (0.5%)

prune986.0ms (5.6%)

localize33.0ms (0.2%)

rewrite33.0ms (0.2%)

series934.0ms (5.4%)

simplify87.0ms (0.5%)

prune119.0ms (0.7%)

localize39.0ms (0.2%)

rewrite24.0ms (0.1%)

series634.0ms (3.6%)

simplify78.0ms (0.4%)

prune215.0ms (1.2%)

regimes441.0ms (2.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample8.5s (48.8%)

Profiling