Details

analyze2.1s (14.1%)

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
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

Compiler

Compiled 33 to 22 computations (33.3% saved)

sample86.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	191×	body	128	valid
12.0ms	75×	body	128	invalid
12.0ms	22×	body	1024	valid
9.0ms	26×	body	512	valid
8.0ms	15×	body	1024	invalid
4.0ms	17×	body	256	valid
3.0ms	9×	body	512	invalid
1.0ms	3×	body	256	invalid

Compiler

Compiled 65 to 48 computations (26.2% saved)

simplify307.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4986	49
1	4986	49

prune4.0ms (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: 42.1b

Counts

2 → 1

Compiler

Compiled 64 to 42 computations (34.4% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite90.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

142×	`associate-*l/_binary64_710`
102×	`flip--_binary64_742` `flip3--_binary64_771`
68×	`frac-times_binary64_777`
66×	`sqrt-div_binary64_784`
64×	`frac-add_binary64_775`
44×	`pow1_binary64_828`
34×	`associate-*r/_binary64_709`
17×	`pow-prod-down_binary64_838`
16×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
6×	`add-sqr-sqrt_binary64_789`
5×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
4×	`pow-prod-up_binary64_837` `add-log-exp_binary64_806` `pow-sqr_binary64_740`
3×	`sqrt-prod_binary64_783`
2×	`pow-plus_binary64_830`
1×	`associate-l_binary64_708` `pow2_binary64_848` `associate-r_binary64_707` `swap-sqr_binary64_734` `rem-sqrt-square_binary64_780` `*-commutative_binary64_698` `flip-+_binary64_741` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785`

Counts

4 → 135

Calls

4 calls:

23.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
15.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.6s (11.1%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
292.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify96.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5222	10334

prune499.0ms (3.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	9	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	139	9	148

Merged error: 25.6b

Counts

148 → 9

Compiler

Compiled 13358 to 5692 computations (57.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite114.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`flip--_binary64_742` `flip3--_binary64_771`
196×	`frac-times_binary64_777`
138×	`sqrt-div_binary64_784`
136×	`frac-add_binary64_775`
98×	`associate-r/_binary64_709` `associate-l/_binary64_710`
73×	`cos-mult_binary64_921`
12×	`pow1_binary64_828` `add-sqr-sqrt_binary64_789`
9×	`*-un-lft-identity_binary64_767` `add-cube-cbrt_binary64_802`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
4×	`add-log-exp_binary64_806`
3×	`associate-l_binary64_708` `associate-r_binary64_707` `swap-sqr_binary64_734` `sqrt-prod_binary64_783`
1×	`pow2_binary64_848` `unswap-sqr_binary64_735` `rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `pow-prod-up_binary64_837` `pow-plus_binary64_830` `prod-exp_binary64_816` `*-commutative_binary64_698` `flip-+_binary64_741` `pow1/2_binary64_847` `sqr-cos-a_binary64_916` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `pow-prod-down_binary64_838` `pow-sqr_binary64_740`

Counts

4 → 192

Calls

4 calls:

29.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
6.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.4s (9.6%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
70.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify195.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5085	17276

prune589.0ms (4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	200	4	204
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	203	10	213

Merged error: 25.6b

Counts

213 → 10

Compiler

Compiled 16986 to 6666 computations (60.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
0.3b	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (pow.f64 (-.f64 phi1 phi2) 2)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_789`
12×	`*-un-lft-identity_binary64_767`
10×	`add-exp-log_binary64_805` `add-cube-cbrt_binary64_802`
8×	`associate-r_binary64_707`
7×	`unpow-prod-down_binary64_846`
6×	`pow1_binary64_828` `add-cbrt-cube_binary64_803`
5×	`associate-l_binary64_708`
4×	`unswap-sqr_binary64_735` `add-log-exp_binary64_806`
3×	`sqr-pow_binary64_739` `prod-exp_binary64_816` `pow-unpow_binary64_844` `unpow2_binary64_832` `sqrt-prod_binary64_783`
2×	`pow-to-exp_binary64_836` `pow-exp_binary64_835` `associate-*l/_binary64_710` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `*-commutative_binary64_698` `flip-+_binary64_741` `distribute-lft-out--_binary64_719` `pow1/2_binary64_847` `flip3-+_binary64_770` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771` `pow-pow_binary64_839` `difference-of-squares_binary64_736`

Counts

4 → 71

Calls

4 calls:

19.0ms	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (pow.f64 (-.f64 phi1 phi2) 2)))
10.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)

series1.7s (11.6%)

Counts

4 → 12

Calls

4 calls:

1.4s	(sqrt.f64 (+.f64 (.f64 (-.f64 lambda1 lambda2) (.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))) (pow.f64 (-.f64 phi1 phi2) 2)))
276.0ms	(*.f64 (-.f64 lambda1 lambda2) (pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2))
59.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) 2)
27.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5042	1846

prune209.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	82	11	93

Merged error: 25.0b

Counts

93 → 11

Compiler

Compiled 4658 to 2815 computations (39.6% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
0.2b	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
2.4b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
38.8b	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_789`
10×	`pow1_binary64_828` `*-un-lft-identity_binary64_767`
9×	`add-exp-log_binary64_805`
8×	`add-cube-cbrt_binary64_802`
6×	`add-cbrt-cube_binary64_803`
5×	`associate-l_binary64_708`
4×	`add-log-exp_binary64_806`
3×	`associate-r_binary64_707` `pow-unpow_binary64_844` `sqrt-prod_binary64_783`
2×	`pow-exp_binary64_835` `prod-exp_binary64_816` `associate-*l/_binary64_710` `pow-prod-down_binary64_838` `pow-pow_binary64_839` `sqrt-div_binary64_784`
1×	`pow-to-exp_binary64_836` `unswap-sqr_binary64_735` `rem-sqrt-square_binary64_780` `cbrt-unprod_binary64_800` `sqr-pow_binary64_739` `*-commutative_binary64_698` `unpow-prod-down_binary64_846` `flip-+_binary64_741` `unpow2_binary64_832` `distribute-lft-out--_binary64_719` `pow1/2_binary64_847` `flip3-+_binary64_770` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771` `difference-of-squares_binary64_736`

Counts

4 → 62

Calls

4 calls:

8.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
7.0ms	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
6.0ms	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

series1.9s (12.7%)

Counts

4 → 12

Calls

4 calls:

1.4s	(sqrt.f64 (+.f64 (pow.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))
318.0ms	(pow.f64 (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) 2)
176.0ms	(*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
30.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5063	1647

prune219.0ms (1.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	70	4	74
Fresh	4	5	9
Picked	0	1	1
Done	0	1	1
Total	74	11	85

Merged error: 25.0b

Counts

85 → 11

Compiler

Compiled 4898 to 2906 computations (40.7% saved)

regimes411.0ms (2.8%)

Compiler: Compiled 2375 to 1750 computations (26.3% saved)

bsearch2.0ms (0%)

Compiler: Compiled 3 to 6 computations (-100% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	244	249
1	244	249

end0.0ms (0%)

sample3.0s (19.9%)

Algorithm

1×

intervals

Results

655.0ms	6053×	body	128	valid
435.0ms	811×	body	1024	valid
248.0ms	2439×	body	128	invalid
247.0ms	704×	body	512	valid
246.0ms	461×	body	1024	invalid
117.0ms	343×	body	512	invalid
109.0ms	424×	body	256	valid
42.0ms	186×	body	256	invalid
8.0ms	8×	body	2048	valid

Compiler

Compiled 552 to 362 computations (34.4% saved)

Details

analyze2.1s (14.1%)

sample86.0ms (0.6%)

simplify307.0ms (2.1%)

prune4.0ms (0%)

localize21.0ms (0.1%)

rewrite90.0ms (0.6%)

series1.6s (11.1%)

simplify96.0ms (0.6%)

prune499.0ms (3.4%)

localize19.0ms (0.1%)

rewrite114.0ms (0.8%)

series1.4s (9.6%)

simplify195.0ms (1.3%)

prune589.0ms (4%)

localize21.0ms (0.1%)

rewrite45.0ms (0.3%)

series1.7s (11.6%)

simplify80.0ms (0.5%)

prune209.0ms (1.4%)

localize20.0ms (0.1%)

rewrite33.0ms (0.2%)

series1.9s (12.7%)

simplify53.0ms (0.4%)

prune219.0ms (1.5%)

regimes411.0ms (2.8%)

bsearch2.0ms (0%)

simplify7.0ms (0%)

end0.0ms (0%)

sample3.0s (19.9%)

Profiling