Details

analyze1.9s (15.1%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample171.0ms (1.3%)

Algorithm

1×

intervals

Results

113.0ms	142×	body	1024	valid
22.0ms	49×	body	512	valid
11.0ms	6×	body	2048	valid
7.0ms	24×	body	256	valid
5.0ms	35×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify180.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	211	32
1	211	32

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: 1.6b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.9b	(sin.f64 (-.f64 lambda1 lambda2))
2.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_450`
4×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-sqr-sqrt_binary64_435`
3×	`cos-diff_binary64_548`
2×	`associate-+r+_binary64_348` `sub-neg_binary64_407`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `sin-diff_binary64_547` `+-commutative_binary64_346` `cos-sum_binary64_545` `flip-+_binary64_388` `sin-sum_binary64_544` `sum-log_binary64_502`

Counts

4 → 38

Calls

4 calls:

4.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series340.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
66.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
34.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify110.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4805	950
1	4805	950

prune85.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	39	11	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	40	11	51

Merged error: 1.3b

Counts

51 → 11

Compiler

Compiled 1695 to 441 computations (74% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
2.9b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_435`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`cos-diff_binary64_548` `sub-neg_binary64_407` `associate-l_binary64_357` `associate-r_binary64_356`
2×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `associate-+r+_binary64_348` `associate-*r/_binary64_358`
1×	`flip3--_binary64_418` `flip3-+_binary64_417` `*-commutative_binary64_347` `+-commutative_binary64_346` `prod-exp_binary64_460` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `flip-+_binary64_388` `flip--_binary64_389` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `sum-log_binary64_502`

Counts

4 → 51

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series639.0ms (5%)

Counts

4 → 12

Calls

4 calls:

293.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
223.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
91.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4974	1613
1	4974	1613

prune92.0ms (0.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	3	63
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	63	11	74

Merged error: 0.1b

Counts

74 → 11

Compiler

Compiled 2586 to 493 computations (80.9% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite26.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_435`
8×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447`
6×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356`
2×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `-commutative_binary64_347` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-+r+_binary64_348` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `associate-r/_binary64_358`
1×	`flip3--_binary64_418` `flip3-+_binary64_417` `+-commutative_binary64_346` `flip-+_binary64_388` `flip--_binary64_389` `sum-log_binary64_502` `sin-mult_binary64_566`

Counts

4 → 61

Calls

4 calls:

8.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series871.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

432.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
264.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
106.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
69.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5015	2051

prune114.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Merged error: 0.1b

Counts

84 → 11

Compiler

Compiled 3495 to 577 computations (83.5% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.6b	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))
0.7b	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64_442`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-sqr-sqrt_binary64_435`
6×	`cube-prod_binary64_439` `unpow-prod-down_binary64_490` `add-log-exp_binary64_450`
5×	`pow1_binary64_472` `add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
4×	`cube-div_binary64_440`
3×	`flip3-+_binary64_417` `pow-unpow_binary64_488` `flip-+_binary64_388`
2×	`cbrt-div_binary64_443` `cube-mult_binary64_441` `sqr-pow_binary64_386` `associate-+r+_binary64_348` `unpow3_binary64_477`
1×	`distribute-lft-in_binary64_365` `distribute-rgt-in_binary64_366` `+-commutative_binary64_346` `pow-pow_binary64_483` `pow-exp_binary64_479` `rem-cbrt-cube_binary64_437` `pow-to-exp_binary64_480` `pow1/3_binary64_493` `sum-log_binary64_502` `rem-cube-cbrt_binary64_436`

Counts

4 → 68

Calls

4 calls:

5.0ms	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)
5.0ms	(+.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	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)))

series1.9s (15.2%)

Counts

4 → 12

Calls

4 calls:

1.0s	(pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)
421.0ms	(cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3))
405.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
113.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (cbrt.f64 (pow.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))) 3)))

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5086	3358

prune106.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	79	12	91

Merged error: 0.1b

Counts

91 → 12

Compiler

Compiled 3759 to 487 computations (87% saved)

regimes218.0ms (1.7%)

Compiler: Compiled 3208 to 1576 computations (50.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	61
1	60	61

end0.0ms (0%)

sample5.6s (43.7%)

Algorithm

1×

intervals

Results

3.5s	4501×	body	1024	valid
766.0ms	1706×	body	512	valid
238.0ms	128×	body	2048	valid
205.0ms	712×	body	256	valid
130.0ms	953×	body	128	valid

Compiler

Compiled 590 to 297 computations (49.7% saved)

Details

analyze1.9s (15.1%)

sample171.0ms (1.3%)

simplify180.0ms (1.4%)

prune3.0ms (0%)

localize23.0ms (0.2%)

rewrite17.0ms (0.1%)

series340.0ms (2.7%)

simplify110.0ms (0.9%)

prune85.0ms (0.7%)

localize28.0ms (0.2%)

rewrite23.0ms (0.2%)

series639.0ms (5%)

simplify68.0ms (0.5%)

prune92.0ms (0.7%)

localize30.0ms (0.2%)

rewrite26.0ms (0.2%)

series871.0ms (6.8%)

simplify66.0ms (0.5%)

prune114.0ms (0.9%)

localize32.0ms (0.2%)

rewrite25.0ms (0.2%)

series1.9s (15.2%)

simplify70.0ms (0.5%)

prune106.0ms (0.8%)

regimes218.0ms (1.7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.6s (43.7%)

Profiling