Details

analyze1.6s (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
31.2%	56.2%	12.6%	9
34.3%	53%	12.6%	10
37.4%	49.9%	12.6%	11
46.8%	40.6%	12.6%	12
47.8%	39.6%	12.6%	13
49.7%	37.1%	13.2%	14

Compiler

Compiled 22 to 20 computations (9.1% saved)

sample170.0ms (0.2%)

Algorithm

1×

intervals

Results

52.0ms	54×	body	1024	invalid
40.0ms	45×	body	1024	valid
21.0ms	166×	body	128	valid
18.0ms	32×	body	512	valid
9.0ms	16×	body	512	invalid
7.0ms	6×	body	2048	valid
3.0ms	8×	body	256	invalid
2.0ms	18×	body	128	invalid
2.0ms	7×	body	256	valid

Compiler

Compiled 43 to 42 computations (2.3% saved)

simplify269.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (172.0ms)

Iter	Nodes	Cost
0	5252	34

prune2.0ms (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

Error

19.4b

Counts

2 → 1

Compiler

Compiled 21 to 19 computations (9.5% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.2b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.1b	(.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64)))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
24.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite25.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_100`
26×	`associate-l_binary64_19`
20×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`pow1_binary64_139`
6×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
2×	`-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `associate-l/_binary64_21` `pow-prod-down_binary64_149`

Counts

4 → 78

Calls

8 calls:

7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2))

series125.0ms (0.1%)

Counts

4 → 18

Calls

4 calls:

38.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
30.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0ms	(*.f64 (/.f64 angle 180) PI.f64)
28.0ms	(*.f64 (/.f64 angle 180) PI.f64)

Compiler

Compiled 684 to 612 computations (10.5% saved)

simplify107.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4922	1203
1	4922	1203

prune466.0ms (0.5%)

Pruning

59 alts after pruning (59 fresh and 0 done)

	Pruned	Kept	Total
New	37	59	96
Fresh	0	0	0
Picked	0	0	0
Done	1	0	1
Total	38	59	97

Error

18.3b

Counts

97 → 59

Compiler

Compiled 3724 to 2918 computations (21.6% saved)

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))))
0.2b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.1b	(.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64)))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2))
0.3b	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
24.4b	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
24.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_100`
30×	`times-frac_binary64_84`
26×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
25×	`associate-r_binary64_18`
16×	`associate-l_binary64_19`
14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`sqrt-prod_binary64_94`
8×	`pow1_binary64_139`
5×	`unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149`
1×	`associate-l/_binary64_21` `associate-r/_binary64_20`

Counts

4 → 88

Calls

8 calls:

10.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
3.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (*.f64 (/.f64 angle 180) PI.f64))) 2))

series191.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

70.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
59.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
32.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
29.0ms	(*.f64 (/.f64 angle 180) PI.f64)

Compiler

Compiled 858 to 786 computations (8.4% saved)

simplify81.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4977	1446
1	4977	1446

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.4b	(*.f64 (/.f64 angle 180) PI.f64)
0.2b	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
0.2b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b 1) 2))
0.2b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.2b	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_100`
16×	`associate-l_binary64_19`
15×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
14×	`add-exp-log_binary64_116`
11×	`add-cbrt-cube_binary64_114` `pow1_binary64_139`
10×	`times-frac_binary64_84`
6×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `prod-exp_binary64_127`
3×	`cbrt-unprod_binary64_111` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-pow_binary64_150`
1×	`pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `unpow-prod-down_binary64_157` `unpow2_binary64_143` `sqr-pow_binary64_50` `div-inv_binary64_75` `associate-*l/_binary64_21`

Counts

4 → 75

Calls

8 calls:

7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
5.0ms	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
4.0ms	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (*.f64 b 1) 2))

series358.0ms (0.4%)

Counts

4 → 27

Calls

4 calls:

175.0ms	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
119.0ms	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
35.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
28.0ms	(*.f64 (/.f64 angle 180) PI.f64)

Compiler

Compiled 912 to 864 computations (5.3% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	1676
1	4954	1676

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.1b	(pow.f64 (.f64 b (cos.f64 (exp.f64 (log.f64 (.f64 (/.f64 angle 180) PI.f64))))) 2)
0.1b	(.f64 b (cos.f64 (exp.f64 (log.f64 (.f64 (/.f64 angle 180) PI.f64)))))
0.0b	(log.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
2.6b	(exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64)))
11.4b	(cos.f64 (exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64))))
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_100`
13×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
10×	`times-frac_binary64_84`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
5×	`exp-prod_binary64_130`
4×	`add-log-exp_binary64_117`
3×	`associate-r_binary64_18`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-*l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `log-pow_binary64_167`
1×	`*-commutative_binary64_9` `exp-sum_binary64_124` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-exp-log_binary64_118` `div-inv_binary64_75` `log-prod_binary64_164` `exp-diff_binary64_126` `log-div_binary64_165`

Counts

4 → 61

Calls

8 calls:

7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
6.0ms	(cos.f64 (exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64))))
5.0ms	(exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64)))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(log.f64 (*.f64 (/.f64 angle 180) PI.f64))

series265.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(cos.f64 (exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64))))
94.0ms	(exp.f64 (log.f64 (*.f64 (/.f64 angle 180) PI.f64)))
29.0ms	(*.f64 (/.f64 angle 180) PI.f64)
19.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 588 to 538 computations (8.5% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4998	796
1	4998	796

localize27.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))
0.1b	(.f64 (.f64 angle angle) 1/64800)
0.0b	(pow.f64 (.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))) 2)
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))) 2))
1.6b	(pow.f64 PI.f64 4)
3.1b	(.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
11.0b	(+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
9×	`add-log-exp_binary64_117`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`add-exp-log_binary64_116` `pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114`
3×	`associate-l_binary64_19` `unpow-prod-down_binary64_157` `associate-r_binary64_18` `pow-unpow_binary64_155`
2×	`flip-+_binary64_52` `associate-+l+_binary64_11` `associate-*r/_binary64_20` `sum-log_binary64_169` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `associate-+l-_binary64_13` `distribute-lft-in_binary64_27` `*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `diff-log_binary64_170` `distribute-rgt-in_binary64_28` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`

Counts

4 → 61

Calls

8 calls:

11.0ms	(.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
10.0ms	(+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
2.0ms	(pow.f64 PI.f64 4)
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))) 2))

series642.0ms (0.7%)

Counts

4 → 27

Calls

4 calls:

401.0ms	(.f64 b (+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4)))))
201.0ms	(+.f64 (-.f64 1 (.f64 (pow.f64 PI.f64 2) (.f64 (.f64 angle angle) 1/64800))) (.f64 1/25194240000 (*.f64 (pow.f64 angle 4) (pow.f64 PI.f64 4))))
40.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(pow.f64 PI.f64 4)

Compiler

Compiled 1322 to 1155 computations (12.6% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4978	2454
1	4978	2454

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))
0.1b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2)
0.0b	(.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))
0.2b	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
11.2b	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite23.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
16×	`associate-l_binary64_19`
14×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
10×	`times-frac_binary64_84`
8×	`pow1_binary64_139`
6×	`associate-r_binary64_18`
4×	`add-log-exp_binary64_117`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `pow-prod-down_binary64_149`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `associate-*l/_binary64_21`

Counts

4 → 64

Calls

8 calls:

7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
5.0ms	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
2.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))

series227.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

105.0ms	(.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64)))
68.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
30.0ms	(*.f64 (/.f64 angle 180) PI.f64)
22.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 995 to 871 computations (12.5% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4909	1088
1	4909	1088

prune6.4s (7.3%)

Pruning

265 alts after pruning (262 fresh and 3 done)

	Pruned	Kept	Total
New	241	210	451
Fresh	2	52	54
Picked	0	0	0
Done	2	3	5
Total	245	265	510

Error

18.0b

Counts

510 → 265

Compiler

Compiled 19000 to 15053 computations (20.8% saved)

localize24.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (.f64 b (cos.f64 (.f64 angle (*.f64 PI.f64 1/180)))) 2)
0.1b	(.f64 b (cos.f64 (.f64 angle (*.f64 PI.f64 1/180))))
0.1b	(.f64 angle (.f64 PI.f64 1/180))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 angle (.f64 PI.f64 1/180)))) 2))
0.3b	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
0.3b	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
24.1b	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))
24.4b	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_116`
39×	`add-sqr-sqrt_binary64_100`
38×	`times-frac_binary64_84`
31×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
30×	`add-cbrt-cube_binary64_114`
25×	`associate-l_binary64_19`
23×	`associate-r_binary64_18`
22×	`prod-exp_binary64_127`
19×	`sqrt-prod_binary64_94`
12×	`cbrt-unprod_binary64_111`
11×	`div-exp_binary64_129` `pow1_binary64_139`
6×	`cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`
3×	`1-exp_binary64_122` `rec-exp_binary64_128` `unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `div-inv_binary64_75`
1×	`frac-times_binary64_88` `associate-*l/_binary64_21`

Counts

4 → 110

Calls

8 calls:

15.0ms	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
10.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
3.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
2.0ms	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 angle (.f64 PI.f64 1/180)))) 2))

series455.0ms (0.5%)

Counts

4 → 18

Calls

4 calls:

306.0ms	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
63.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
56.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
29.0ms	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))

Compiler

Compiled 840 to 768 computations (8.6% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4921	1729
1	4921	1729

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(pow.f64 (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))) 2)
0.2b	(*.f64 PI.f64 a)
0.2b	(.f64 angle (.f64 PI.f64 a))
0.0b	(+.f64 (pow.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) 2) (pow.f64 (.f64 b 1) 2))
0.2b	(.f64 angle (.f64 PI.f64 a))
0.2b	(*.f64 PI.f64 a)
0.3b	(pow.f64 (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))) 2)
0.3b	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))

rewrite33.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-exp-log_binary64_116` `pow1_binary64_139`
20×	`add-cbrt-cube_binary64_114`
16×	`prod-exp_binary64_127` `pow-prod-down_binary64_149`
11×	`add-sqr-sqrt_binary64_100`
10×	`cbrt-unprod_binary64_111`
9×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`associate-r_binary64_18`
4×	`pow-exp_binary64_146` `add-log-exp_binary64_117` `pow-pow_binary64_150`
3×	`*-commutative_binary64_9` `pow-unpow_binary64_155`
1×	`pow-to-exp_binary64_147` `unpow-prod-down_binary64_157` `unpow2_binary64_143` `sqr-pow_binary64_50` `unswap-sqr_binary64_46`

Counts

4 → 79

Calls

8 calls:

10.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
8.0ms	(pow.f64 (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))) 2)
5.0ms	(.f64 angle (.f64 PI.f64 a))
4.0ms	(*.f64 PI.f64 a)
0.0ms	(+.f64 (pow.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) 2) (pow.f64 (.f64 b 1) 2))

series273.0ms (0.3%)

Counts

4 → 21

Calls

4 calls:

112.0ms	(pow.f64 (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))) 2)
76.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
64.0ms	(.f64 angle (.f64 PI.f64 a))
20.0ms	(*.f64 PI.f64 a)

Compiler

Compiled 678 to 678 computations (0% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5208	1074

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 a (sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (.f64 PI.f64 (/.f64 angle (cbrt.f64 180))))))
0.3b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))) 2)
0.1b	(/.f64 angle (cbrt.f64 180))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))) 2) (pow.f64 (*.f64 b 1) 2))
0.3b	(*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))
0.5b	(.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180))))
1.0b	(*.f64 (cbrt.f64 180) (cbrt.f64 180))
24.6b	(sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))

rewrite55.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

89×	`add-exp-log_binary64_116`
47×	`prod-exp_binary64_127`
44×	`add-sqr-sqrt_binary64_100`
35×	`add-cbrt-cube_binary64_114`
29×	`associate-r_binary64_18`
28×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
26×	`cbrt-prod_binary64_109`
23×	`times-frac_binary64_84`
21×	`cbrt-unprod_binary64_111`
20×	`div-exp_binary64_129`
18×	`pow1_binary64_139`
16×	`associate-l_binary64_19`
10×	`cbrt-undiv_binary64_112`
7×	`unswap-sqr_binary64_46`
6×	`swap-sqr_binary64_45` `pow1/3_binary64_160` `1-exp_binary64_122` `rec-exp_binary64_128` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117` `associate-*r/_binary64_20`
3×	`*-commutative_binary64_9`
2×	`pow-sqr_binary64_51` `div-inv_binary64_75` `pow-prod-up_binary64_148`
1×	`pow2_binary64_159` `frac-times_binary64_88` `associate-*l/_binary64_21` `pow-plus_binary64_141`

Counts

4 → 140

Calls

8 calls:

16.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180))))
13.0ms	(*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))
7.0ms	(*.f64 (cbrt.f64 180) (cbrt.f64 180))
3.0ms	(sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))) 2) (pow.f64 (*.f64 b 1) 2))

series226.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180))))
66.0ms	(sin.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 180) (cbrt.f64 180))) (*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))))
58.0ms	(*.f64 PI.f64 (/.f64 angle (cbrt.f64 180)))
0.0ms	(*.f64 (cbrt.f64 180) (cbrt.f64 180))

Compiler

Compiled 502 to 490 computations (2.4% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4879	1803
1	4879	1803

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 a (sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)))))
0.1b	(sqrt.f64 (/.f64 angle 180))
0.1b	(sqrt.f64 (/.f64 angle 180))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
11.5b	(sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (*.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64))))
24.4b	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite12.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
6×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`

Counts

4 → 40

Calls

8 calls:

4.0ms	(sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (*.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64))))
2.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 angle 180) PI.f64))) 2))

series102.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(sin.f64 (.f64 (.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64)) (*.f64 (sqrt.f64 (/.f64 angle 180)) (sqrt.f64 PI.f64))))
35.0ms	(cos.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 577 to 502 computations (13% saved)

simplify115.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4887	634
1	4887	634

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (.f64 (sqrt.f64 a) (.f64 (sin.f64 (*.f64 (/.f64 angle 180) PI.f64)) (sqrt.f64 a))) 2)
0.1b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2)
0.0b	(.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))))
0.0b	(+.f64 (pow.f64 (.f64 (sqrt.f64 a) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (sqrt.f64 a))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))
0.2b	(/.f64 (sqrt.f64 angle) (sqrt.f64 180))
0.4b	(*.f64 (/.f64 angle 180) PI.f64)
11.2b	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

rewrite32.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`times-frac_binary64_84`
45×	`add-sqr-sqrt_binary64_100`
42×	`sqrt-prod_binary64_94`
40×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
13×	`associate-l_binary64_19`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-/l_binary64_23` `associate-/r_binary64_22` `pow1_binary64_139`
4×	`add-log-exp_binary64_117`
3×	`associate-r_binary64_18`
2×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `div-inv_binary64_75` `unswap-sqr_binary64_46`
1×	`-commutative_binary64_9` `frac-2neg_binary64_89` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `sqrt-undiv_binary64_99` `clear-num_binary64_77`

Counts

4 → 107

Calls

8 calls:

7.0ms	(*.f64 (/.f64 angle 180) PI.f64)
6.0ms	(/.f64 (sqrt.f64 angle) (sqrt.f64 180))
2.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(+.f64 (pow.f64 (.f64 (sqrt.f64 a) (.f64 (sin.f64 (.f64 (/.f64 angle 180) PI.f64)) (sqrt.f64 a))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))

series154.0ms (0.2%)

Counts

4 → 15

Calls

4 calls:

76.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
31.0ms	(*.f64 (/.f64 angle 180) PI.f64)
28.0ms	(/.f64 (sqrt.f64 angle) (sqrt.f64 180))
19.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))

Compiler

Compiled 942 to 797 computations (15.4% saved)

simplify84.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4909	1756
1	4909	1756

prune12.8s (14.6%)

Pruning

439 alts after pruning (433 fresh and 6 done)

	Pruned	Kept	Total
New	346	208	554
Fresh	32	225	257
Picked	0	0	0
Done	2	6	8
Total	380	439	819

Error

17.8b

Counts

819 → 439

Compiler

Compiled 24813 to 19999 computations (19.4% saved)

localize25.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(pow.f64 (.f64 b (pow.f64 (cos.f64 (.f64 angle (*.f64 PI.f64 1/180))) 1)) 2)
0.1b	(.f64 b (pow.f64 (cos.f64 (.f64 angle (*.f64 PI.f64 1/180))) 1))
0.1b	(.f64 angle (.f64 PI.f64 1/180))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (pow.f64 (cos.f64 (.f64 angle (.f64 PI.f64 1/180))) 1)) 2))
0.3b	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
0.3b	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
24.1b	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))
24.4b	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))

rewrite44.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_116`
39×	`add-sqr-sqrt_binary64_100`
38×	`times-frac_binary64_84`
31×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
30×	`add-cbrt-cube_binary64_114`
25×	`associate-l_binary64_19`
23×	`associate-r_binary64_18`
22×	`prod-exp_binary64_127`
19×	`sqrt-prod_binary64_94`
12×	`cbrt-unprod_binary64_111`
11×	`div-exp_binary64_129` `pow1_binary64_139`
6×	`cbrt-undiv_binary64_112`
4×	`add-log-exp_binary64_117` `pow-prod-down_binary64_149` `associate-*r/_binary64_20`
3×	`1-exp_binary64_122` `rec-exp_binary64_128` `unswap-sqr_binary64_46`
2×	`*-commutative_binary64_9` `div-inv_binary64_75`
1×	`frac-times_binary64_88` `associate-*l/_binary64_21`

Counts

4 → 110

Calls

8 calls:

15.0ms	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
10.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
3.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
3.0ms	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (pow.f64 (cos.f64 (.f64 angle (.f64 PI.f64 1/180))) 1)) 2))

series241.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

88.0ms	(.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))
71.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
51.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
32.0ms	(cos.f64 (.f64 angle (.f64 PI.f64 1/180)))

Compiler

Compiled 896 to 824 computations (8% saved)

simplify98.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4921	1729
1	4921	1729

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 a)
0.2b	(.f64 angle (.f64 PI.f64 a))
0.2b	(.f64 angle (.f64 PI.f64 a))
0.0b	(+.f64 (.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) (.f64 1/180 (.f64 angle (.f64 PI.f64 a)))) (pow.f64 (.f64 b 1) 2))
0.2b	(*.f64 PI.f64 a)
0.3b	(.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))))
0.3b	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
0.3b	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))

rewrite54.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

274×	`pow1_binary64_139`
179×	`pow-prod-down_binary64_149`
104×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
77×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
16×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148`
10×	`add-sqr-sqrt_binary64_100` `associate-l_binary64_19`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-r_binary64_18`
4×	`*-commutative_binary64_9` `add-log-exp_binary64_117` `pow-plus_binary64_141`
1×	`pow2_binary64_159` `swap-sqr_binary64_45` `unswap-sqr_binary64_46`

Counts

4 → 156

Calls

8 calls:

17.0ms	(.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))))
7.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
7.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
4.0ms	(*.f64 PI.f64 a)
0.0ms	(+.f64 (.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) (.f64 1/180 (.f64 angle (.f64 PI.f64 a)))) (pow.f64 (.f64 b 1) 2))

series336.0ms (0.4%)

Counts

4 → 21

Calls

4 calls:

147.0ms	(.f64 (.f64 1/180 (.f64 angle (.f64 PI.f64 a))) (.f64 1/180 (.f64 angle (*.f64 PI.f64 a))))
86.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
79.0ms	(.f64 1/180 (.f64 angle (*.f64 PI.f64 a)))
24.0ms	(*.f64 PI.f64 a)

Compiler

Compiled 858 to 768 computations (10.5% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4960	1959
1	4960	1959

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2)
0.1b	(pow.f64 (.f64 b (cos.f64 (.f64 (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))) 2)
0.1b	(.f64 b (cos.f64 (.f64 (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64))))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
24.0b	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
24.3b	(cos.f64 (.f64 (.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_100`
6×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `pow1/2_binary64_158`

Counts

4 → 40

Calls

8 calls:

3.0ms	(cos.f64 (.f64 (.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))
2.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 angle 180) PI.f64))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (*.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))) 2))

series65.0ms (0.1%)

Counts

4 → 12

Calls

4 calls:

33.0ms	(cos.f64 (.f64 (.f64 (/.f64 angle 180) (sqrt.f64 PI.f64)) (sqrt.f64 PI.f64)))
32.0ms	(sin.f64 (*.f64 (/.f64 angle 180) PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

Compiler

Compiled 464 to 400 computations (13.8% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5033	615

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))))
0.2b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2)
0.1b	(.f64 b (cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 angle (sqrt.f64 180))))))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2))
0.3b	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
0.3b	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
23.9b	(cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
24.4b	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-sqr-sqrt_binary64_100`
44×	`associate-r_binary64_18`
40×	`times-frac_binary64_84`
32×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`sqrt-prod_binary64_94`
14×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
2×	`-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149` `associate-r/_binary64_20`

Counts

4 → 98

Calls

8 calls:

11.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
10.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
3.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
3.0ms	(cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))) 2))

series226.0ms (0.3%)

Counts

4 → 18

Calls

4 calls:

65.0ms	(sin.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
56.0ms	(cos.f64 (.f64 (/.f64 1 (sqrt.f64 180)) (.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))))
56.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))
49.0ms	(*.f64 PI.f64 (/.f64 angle (sqrt.f64 180)))

Compiler

Compiled 1020 to 948 computations (7.1% saved)

simplify64.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5411	1665

localize28.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))
0.1b	(pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2)
0.0b	(.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180))))))
0.0b	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (.f64 (/.f64 angle 180) (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))) (cbrt.f64 PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))
1.0b	(cbrt.f64 PI.f64)
1.0b	(cbrt.f64 PI.f64)
11.2b	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
24.9b	(sin.f64 (.f64 (.f64 (/.f64 angle 180) (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))) (cbrt.f64 PI.f64)))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `cbrt-prod_binary64_109` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
2×	`pow1/3_binary64_160`

Counts

4 → 36

Calls

8 calls:

3.0ms	(sin.f64 (.f64 (.f64 (/.f64 angle 180) (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))) (cbrt.f64 PI.f64)))
2.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
1.0ms	(cbrt.f64 PI.f64)
1.0ms	(cbrt.f64 PI.f64)
0.0ms	(+.f64 (pow.f64 (.f64 a (sin.f64 (.f64 (.f64 (/.f64 angle 180) (.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))) (cbrt.f64 PI.f64)))) 2) (pow.f64 (.f64 b (cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (*.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))) 2))

series90.0ms (0.1%)

Counts

4 → 9

Calls

4 calls:

69.0ms	(cos.f64 (.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)) (.f64 PI.f64 (/.f64 (sqrt.f64 angle) (sqrt.f64 180)))))
21.0ms	(sin.f64 (.f64 (.f64 (/.f64 angle 180) (*.f64 (cbrt.f64 PI.f64) (cbrt.f64 PI.f64))) (cbrt.f64 PI.f64)))
0.0ms	(cbrt.f64 PI.f64)
0.0ms	(cbrt.f64 PI.f64)

Compiler

Compiled 519 to 438 computations (15.6% saved)

simplify54.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4955	510
1	4955	510

prune14.5s (16.5%)

Pruning

614 alts after pruning (604 fresh and 10 done)

	Pruned	Kept	Total
New	326	192	518
Fresh	16	412	428
Picked	0	0	0
Done	1	10	11
Total	343	614	957

Error

17.8b

Counts

957 → 614

Compiler

Compiled 9906 to 7057 computations (28.8% saved)

simplify688.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4983	49264
1	4983	49264

regimes9.0s (10.3%)

Compiler: Compiled 91645 to 79062 computations (13.7% saved)

bsearch0.0ms (0%)

regimes1.4s (1.6%)

Compiler: Compiled 15030 to 13419 computations (10.7% saved)

bsearch0.0ms (0%)

regimes435.0ms (0.5%)

Compiler: Compiled 4080 to 3671 computations (10% saved)

bsearch0.0ms (0%)

regimes423.0ms (0.5%)

Compiler: Compiled 3912 to 3535 computations (9.6% saved)

bsearch0.0ms (0%)

regimes415.0ms (0.5%)

Compiler: Compiled 3828 to 3459 computations (9.6% saved)

bsearch0.0ms (0%)

regimes121.0ms (0.1%)

Compiler: Compiled 892 to 856 computations (4% saved)

bsearch0.0ms (0%)

regimes171.0ms (0.2%)

Compiler: Compiled 858 to 835 computations (2.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

regimes135.0ms (0.2%)

Compiler: Compiled 526 to 535 computations (-1.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

regimes127.0ms (0.1%)

Compiler: Compiled 474 to 483 computations (-1.9% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 5 computations (-66.7% saved)

regimes45.0ms (0.1%)

Compiler: Compiled 123 to 132 computations (-7.3% saved)

bsearch226.0ms (0.3%)

Steps

Iters	Range		Point
6	3.445957875825338e+118	1.7378435998006304e+119	5.769045571076974e+118
5	-1.340047397721571e+173	-4.495375805462798e+172	-4.574094598051373e+172

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes41.0ms (0%)

Compiler: Compiled 66 to 90 computations (-36.4% saved)

bsearch220.0ms (0.3%)

Steps

Iters	Range		Point
6	3.445957875825338e+118	1.7378435998006304e+119	3.781945789741156e+118
5	-1.340047397721571e+173	-4.495375805462798e+172	-8.002931884943875e+172

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes26.0ms (0%)

Accuracy

Total 1.8b remaining (9.3%)

Threshold costs 0b (0%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch16.0ms (0%)

Compiler: Compiled 263 to 237 computations (9.9% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	145	407
1	145	407

end0.0ms (0%)

sample31.8s (36.3%)

Algorithm

1×

intervals

Results

1.4s	1543×	body	1024	valid
1.2s	1332×	body	1024	invalid
663.0ms	5133×	body	128	valid
437.0ms	741×	body	512	valid
400.0ms	666×	body	512	invalid
285.0ms	200×	body	2048	valid
127.0ms	379×	body	256	valid
114.0ms	323×	body	256	invalid
82.0ms	604×	body	128	invalid
19.0ms	4×	body	4096	valid

Compiler

Compiled 22824 to 19716 computations (13.6% saved)

Pareto

0.7323269976372251