Details

analyze1.1s (0.7%)

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
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample76.0ms (0.1%)

Algorithm

1×

intervals

Results

36.0ms	124×	body	1024	valid
8.0ms	42×	body	512	valid
5.0ms	69×	body	128	valid
3.0ms	6×	body	2048	valid
2.0ms	15×	body	256	valid

Compiler

Compiled 22 to 26 computations (-18.2% saved)

simplify95.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

4 → 4

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune3.0ms (0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1	3	4
Fresh	0	4	4
Picked	0	0	0
Done	0	0	0
Total	1	7	8

Error

15.2b

Counts

8 → 4

Compiler

Compiled 12 to 11 computations (8.3% saved)

localize9.0ms (0%)

Local error

Found 6 expressions with local error:

2.9b	(cos.f64 (+.f64 a b))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.9b	(cos.f64 (+.f64 a b))

rewrite22.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_100`
19×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
13×	`associate-r_binary64_18`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`pow1_binary64_139`
3×	`associate-l_binary64_19` `add-log-exp_binary64_117` `associate-/l_binary64_23` `associate-/r_binary64_22`
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` `pow-prod-down_binary64_149` `cos-sum_binary64_212` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

3 → 67

Calls

6 calls:

8.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
5.0ms	(cos.f64 (+.f64 a b))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))

series492.0ms (0.3%)

Counts

3 → 39

Calls

3 calls:

288.0ms	(*.f64 r (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
157.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
47.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1006 to 759 computations (24.6% saved)

simplify50.0ms (0%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4986	2320
1	4986	2320

prune482.0ms (0.3%)

Pruning

72 alts after pruning (71 fresh and 1 done)

	Pruned	Kept	Total
New	38	68	106
Fresh	0	3	3
Picked	0	0	0
Done	0	1	1
Total	38	72	110

Error

0.2b

Counts

110 → 72

Compiler

Compiled 3180 to 1453 computations (54.3% saved)

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_100`
22×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
20×	`associate-r_binary64_18`
19×	`times-frac_binary64_84`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`associate-/r/_binary64_24` `pow1_binary64_139`
7×	`sin-mult_binary64_233`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `cos-mult_binary64_232`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-sub_binary64_87` `flip3--_binary64_82` `flip--_binary64_53` `associate-/l_binary64_23` `associate-/r_binary64_22` `unswap-sqr_binary64_46` `sub-div_binary64_85`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149`
1×	`diff-log_binary64_170` `frac-2neg_binary64_89` `associate-*r/_binary64_20` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71`

Counts

4 → 100

Calls

8 calls:

13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.2s (0.8%)

Counts

4 → 49

Calls

4 calls:

611.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b)))))
332.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b))))
161.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
99.0ms	(*.f64 (sin.f64 a) (sin.f64 b))

Compiler

Compiled 1530 to 1109 computations (27.5% saved)

simplify105.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4960	4042
1	4960	4042

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 b (cos.f64 a))
0.1b	(*.f64 (/.f64 b (cos.f64 a)) r)
0.1b	(*.f64 (/.f64 b (cos.f64 a)) r)
0.1b	(/.f64 b (cos.f64 a))

rewrite13.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_100`
19×	`times-frac_binary64_84`
18×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
13×	`associate-l_binary64_19`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
4×	`pow1_binary64_139`
3×	`associate-r_binary64_18` `associate-/l_binary64_23` `associate-/r_binary64_22`
2×	`add-log-exp_binary64_117` `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` `clear-num_binary64_77`

Counts

2 → 59

Calls

4 calls:

6.0ms	(*.f64 (/.f64 b (cos.f64 a)) r)
3.0ms	(/.f64 b (cos.f64 a))
0.0ms	(*.f64 (/.f64 b (cos.f64 a)) r)
0.0ms	(/.f64 b (cos.f64 a))

series275.0ms (0.2%)

Counts

2 → 21

Calls

2 calls:

184.0ms	(*.f64 (/.f64 b (cos.f64 a)) r)
90.0ms	(/.f64 b (cos.f64 a))

Compiler

Compiled 288 to 260 computations (9.7% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4928	956
1	4928	956

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

2.9b	(cos.f64 (+.f64 a b))
0.4b	(pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(*.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.4b	(pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)
2.9b	(cos.f64 (+.f64 a b))
16.6b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3))

rewrite31.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64_84`
42×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
32×	`cbrt-prod_binary64_109`
26×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`div-inv_binary64_75` `pow1_binary64_139`
4×	`add-log-exp_binary64_117`
3×	`associate-/l_binary64_23` `associate-/r_binary64_22` `pow-unpow_binary64_155`
2×	`rem-cube-cbrt_binary64_101` `cube-mult_binary64_108` `pow-exp_binary64_146` `cbrt-undiv_binary64_112` `cube-div_binary64_107` `div-exp_binary64_129` `sqr-pow_binary64_50` `unpow3_binary64_144`
1×	`cbrt-div_binary64_110` `rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `pow1/3_binary64_160` `frac-2neg_binary64_89` `pow-pow_binary64_150` `cos-sum_binary64_212` `clear-num_binary64_77`

Counts

4 → 123

Calls

8 calls:

6.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3))
5.0ms	(pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
0.0ms	(*.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)))

series695.0ms (0.5%)

Counts

4 → 48

Calls

4 calls:

332.0ms	(pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3)
159.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
159.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))) 3))
44.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1476 to 1162 computations (21.3% saved)

simplify74.0ms (0%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5006	4002

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))
0.1b	(*.f64 1/6 (pow.f64 a 3))
0.1b	(/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))))
0.0b	(+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))))
0.3b	(.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))
2.2b	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))
2.7b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (.f64 (cos.f64 b) -1/2))))))
6.6b	(+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))

rewrite62.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100`
25×	`*-un-lft-identity_binary64_78`
23×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`associate-r_binary64_18`
20×	`pow1_binary64_139`
19×	`add-cube-cbrt_binary64_113`
13×	`times-frac_binary64_84`
12×	`cancel-sign-sub-inv_binary64_44`
11×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
10×	`pow-prod-down_binary64_149`
8×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `associate-+l+_binary64_11`
7×	`associate-l_binary64_19`
6×	`add-log-exp_binary64_117`
4×	`sub-neg_binary64_71`
3×	`-commutative_binary64_9` `unswap-sqr_binary64_46` `associate-r/_binary64_20` `distribute-lft-out_binary64_29`
2×	`flip-+_binary64_52` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `sum-log_binary64_169`

Counts

4 → 106

Calls

8 calls:

20.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (.f64 (cos.f64 b) -1/2))))))
12.0ms	(+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
10.0ms	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))
7.0ms	(.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))
0.0ms	(+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))))

series1.6s (1.1%)

Counts

4 → 47

Calls

4 calls:

988.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (.f64 (cos.f64 b) -1/2))))))
338.0ms	(+.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
184.0ms	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))
113.0ms	(.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))

Compiler

Compiled 2621 to 1967 computations (25% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4958	4513
1	4958	4513

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (sqrt.f64 r))
0.1b	(*.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (sqrt.f64 r))
0.1b	(sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.1b	(sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
0.2b	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
2.9b	(cos.f64 (+.f64 a b))
2.9b	(cos.f64 (+.f64 a b))

rewrite24.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
18×	`times-frac_binary64_84`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-/l_binary64_23` `associate-/r_binary64_22`
4×	`add-log-exp_binary64_117` `pow1_binary64_139`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `cos-sum_binary64_212` `clear-num_binary64_77`

Counts

4 → 70

Calls

8 calls:

5.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(cos.f64 (+.f64 a b))
0.0ms	(sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))

series379.0ms (0.3%)

Counts

4 → 42

Calls

4 calls:

145.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
136.0ms	(/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))
50.0ms	(cos.f64 (+.f64 a b))
48.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1858 to 1112 computations (40.2% saved)

simplify75.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4966	1962
1	4966	1962

prune11.8s (7.9%)

Pruning

359 alts after pruning (353 fresh and 6 done)

	Pruned	Kept	Total
New	364	301	665
Fresh	14	52	66
Picked	0	0	0
Done	0	6	6
Total	378	359	737

Error

0.0b

Counts

737 → 359

Compiler

Compiled 22143 to 10551 computations (52.4% saved)

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
0.1b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
0.2b	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
0.2b	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))

rewrite41.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_100`
25×	`associate-r_binary64_18`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`times-frac_binary64_84`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117`
4×	`associate-/r/_binary64_24`
3×	`distribute-lft-neg-in_binary64_35` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `associate-/l_binary64_23` `associate-/r_binary64_22` `unswap-sqr_binary64_46` `distribute-rgt-neg-in_binary64_36` `flip3-+_binary64_81`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149` `distribute-rgt-neg-out_binary64_38`
1×	`+-commutative_binary64_8` `neg-mul-1_binary64_74` `frac-2neg_binary64_89` `unsub-neg_binary64_72` `associate-*r/_binary64_20` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 101

Calls

8 calls:

11.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
7.0ms	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
6.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
6.0ms	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.4s (1%)

Counts

4 → 49

Calls

4 calls:

599.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
554.0ms	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
158.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
131.0ms	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))

Compiler

Compiled 1550 to 1129 computations (27.2% saved)

simplify89.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5231	4201

localize2.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

localize11.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b))))
0.1b	(*.f64 r (/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))))
0.0b	(sqrt.f64 (sin.f64 b))
0.0b	(sqrt.f64 (sin.f64 b))
0.1b	(*.f64 r (/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))))
0.2b	(/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b))))
0.2b	(/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))
2.9b	(cos.f64 (+.f64 a b))

rewrite116.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

526×	`times-frac_binary64_84`
304×	`add-sqr-sqrt_binary64_100`
280×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
269×	`sqrt-prod_binary64_94`
137×	`associate-r_binary64_18`
28×	`associate-/r*_binary64_22`
20×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
16×	`div-inv_binary64_75`
9×	`associate-/l*_binary64_23`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `unswap-sqr_binary64_46`
6×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117`
3×	`associate-l_binary64_19` `cbrt-unprod_binary64_111` `prod-exp_binary64_127`
2×	`frac-2neg_binary64_89` `cos-sum_binary64_212` `associate-/r/_binary64_24` `clear-num_binary64_77`
1×	`-commutative_binary64_9` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `div-sub_binary64_83`

Counts

4 → 386

Calls

8 calls:

42.0ms	(*.f64 r (/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))))
10.0ms	(/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b))))
7.0ms	(/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))
4.0ms	(cos.f64 (+.f64 a b))
0.0ms	(sqrt.f64 (sin.f64 b))

series634.0ms (0.4%)

Counts

4 → 47

Calls

4 calls:

297.0ms	(*.f64 r (/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))))
157.0ms	(/.f64 (sqrt.f64 (sin.f64 b)) (/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b))))
131.0ms	(/.f64 (cos.f64 (+.f64 a b)) (sqrt.f64 (sin.f64 b)))
50.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 1364 to 1004 computations (26.4% saved)

simplify166.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

433 → 433

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5030	12354

localize21.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))
0.1b	(*.f64 1/6 (pow.f64 a 3))
0.1b	(/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))))
0.0b	(+.f64 (cos.f64 b) (+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))))
1.5b	(exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))))
2.2b	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))
4.8b	(+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
14.4b	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))

rewrite51.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`pow1_binary64_139`
11×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `associate-*r/_binary64_20` `cancel-sign-sub-inv_binary64_44`
5×	`exp-prod_binary64_130`
4×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `log-div_binary64_165` `log-pow_binary64_167`
3×	`associate-l_binary64_19` `flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53` `pow-prod-down_binary64_149`
2×	`prod-exp_binary64_127` `log-prod_binary64_164` `exp-diff_binary64_126` `rem-log-exp_binary64_119` `sub-neg_binary64_71`
1×	`+-commutative_binary64_8` `*-commutative_binary64_9` `exp-sum_binary64_124` `cbrt-unprod_binary64_111` `flip-+_binary64_52` `rem-exp-log_binary64_118` `unswap-sqr_binary64_46` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 69

Calls

8 calls:

13.0ms	(+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
11.0ms	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))
10.0ms	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))
9.0ms	(exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))))
0.0ms	(+.f64 (cos.f64 b) (+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2))))

series1.4s (0.9%)

Counts

4 → 37

Calls

4 calls:

525.0ms	(+.f64 (exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
476.0ms	(exp.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))))
217.0ms	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a)))
179.0ms	(.f64 (sin.f64 b) (-.f64 (.f64 1/6 (pow.f64 a 3)) a))

Compiler

Compiled 2526 to 1881 computations (25.5% saved)

simplify78.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5442	2474

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 r (cbrt.f64 (.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)) (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (cos.f64 (+.f64 b a))))))
0.1b	(/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6))
0.0b	(sqrt.f64 (sin.f64 b))
0.0b	(sqrt.f64 (sin.f64 b))
0.9b	(pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)
2.9b	(cos.f64 (+.f64 b a))
2.9b	(cos.f64 (+.f64 b a))
10.6b	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)) (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (cos.f64 (+.f64 b a)))))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`unpow-prod-down_binary64_157`
5×	`add-exp-log_binary64_116` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `cbrt-prod_binary64_109`
3×	`cbrt-div_binary64_110` `pow-unpow_binary64_155`
2×	`pow1/3_binary64_160` `pow-pow_binary64_150` `cos-sum_binary64_212`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqr-pow_binary64_50` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20`

Counts

4 → 49

Calls

8 calls:

24.0ms	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)) (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (cos.f64 (+.f64 b a)))))
6.0ms	(pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)
4.0ms	(cos.f64 (+.f64 b a))
4.0ms	(cos.f64 (+.f64 b a))
0.0ms	(sqrt.f64 (sin.f64 b))

series701.0ms (0.5%)

Counts

4 → 42

Calls

4 calls:

428.0ms	(pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)
171.0ms	(cbrt.f64 (*.f64 (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (pow.f64 (cbrt.f64 (cos.f64 (+.f64 b a))) 6)) (/.f64 (pow.f64 (sqrt.f64 (sin.f64 b)) 3) (cos.f64 (+.f64 b a)))))
53.0ms	(cos.f64 (+.f64 b a))
49.0ms	(cos.f64 (+.f64 b a))

Compiler

Compiled 1890 to 1399 computations (26% saved)

simplify61.0ms (0%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4956	1506
1	4956	1506

prune22.8s (15.2%)

Pruning

637 alts after pruning (626 fresh and 11 done)

	Pruned	Kept	Total
New	480	300	780
Fresh	22	326	348
Picked	0	0	0
Done	0	11	11
Total	502	637	1139

Error

0.0b

Counts

1139 → 637

Compiler

Compiled 32810 to 15939 computations (51.4% saved)

localize17.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
0.1b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
0.2b	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
0.2b	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
0.2b	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_100`
25×	`associate-r_binary64_18`
24×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`times-frac_binary64_84`
13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`pow1_binary64_139`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117`
4×	`associate-/r/_binary64_24`
3×	`distribute-lft-neg-in_binary64_35` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `associate-/l_binary64_23` `associate-/r_binary64_22` `unswap-sqr_binary64_46` `distribute-rgt-neg-in_binary64_36` `flip3-+_binary64_81`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `div-inv_binary64_75` `pow-prod-down_binary64_149` `distribute-rgt-neg-out_binary64_38`
1×	`+-commutative_binary64_8` `neg-mul-1_binary64_74` `frac-2neg_binary64_89` `unsub-neg_binary64_72` `associate-*r/_binary64_20` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 101

Calls

8 calls:

12.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
9.0ms	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
6.0ms	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))
6.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
0.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series1.2s (0.8%)

Counts

4 → 49

Calls

4 calls:

608.0ms	(.f64 r (/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))))
335.0ms	(/.f64 (sin.f64 b) (+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))))
165.0ms	(+.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (neg.f64 (sin.f64 b))))
118.0ms	(*.f64 (sin.f64 a) (neg.f64 (sin.f64 b)))

Compiler

Compiled 1688 to 1267 computations (24.9% saved)

simplify92.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5231	4201

localize8.0ms (0%)

Local error

Found 6 expressions with local error:

6.5b	(/.f64 (.f64 b r) (+.f64 1 (.f64 (*.f64 a a) -1/2)))
0.2b	(.f64 (.f64 a a) -1/2)
0.0b	(+.f64 1 (.f64 (.f64 a a) -1/2))
0.0b	(+.f64 1 (.f64 (.f64 a a) -1/2))
0.2b	(.f64 (.f64 a a) -1/2)
6.5b	(/.f64 (.f64 b r) (+.f64 1 (.f64 (*.f64 a a) -1/2)))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`pow1_binary64_139`
7×	`add-sqr-sqrt_binary64_100`
6×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`add-log-exp_binary64_117`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
3×	`times-frac_binary64_84` `associate-r_binary64_18` `associate-/r*_binary64_22` `pow-prod-down_binary64_149`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `associate-l_binary64_19` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/l_binary64_23` `unswap-sqr_binary64_46` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

3 → 53

Calls

6 calls:

6.0ms	(/.f64 (.f64 b r) (+.f64 1 (.f64 (*.f64 a a) -1/2)))
6.0ms	(.f64 (.f64 a a) -1/2)
3.0ms	(+.f64 1 (.f64 (.f64 a a) -1/2))
0.0ms	(+.f64 1 (.f64 (.f64 a a) -1/2))
0.0ms	(/.f64 (.f64 b r) (+.f64 1 (.f64 (*.f64 a a) -1/2)))

series304.0ms (0.2%)

Counts

3 → 20

Calls

3 calls:

235.0ms	(/.f64 (.f64 b r) (+.f64 1 (.f64 (*.f64 a a) -1/2)))
42.0ms	(+.f64 1 (.f64 (.f64 a a) -1/2))
26.0ms	(.f64 (.f64 a a) -1/2)

Compiler

Compiled 417 to 390 computations (6.5% saved)

simplify67.0ms (0%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4914	1007
1	4914	1007

localize18.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(.f64 (.f64 (cos.f64 b) 1/2) a)
0.1b	(.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a)))
0.0b	(+.f64 (sin.f64 b) (.f64 (.f64 (cos.f64 b) 1/2) a))
0.0b	(-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a)))))
0.2b	(pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3)
2.6b	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (.f64 (cos.f64 b) 1/2) a))))) 3)))
18.0b	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3))

rewrite71.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`cbrt-prod_binary64_109`
74×	`add-sqr-sqrt_binary64_100`
65×	`times-frac_binary64_84`
59×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
47×	`unpow-prod-down_binary64_157` `cube-prod_binary64_106`
39×	`associate-r_binary64_18`
14×	`associate-/r/_binary64_24`
11×	`add-exp-log_binary64_116`
10×	`add-cbrt-cube_binary64_114`
7×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `unswap-sqr_binary64_46` `pow1_binary64_139`
4×	`add-log-exp_binary64_117` `sqr-pow_binary64_50`
3×	`cube-mult_binary64_108` `associate-l_binary64_19` `cube-div_binary64_107` `associate-/l_binary64_23` `associate-/r_binary64_22` `pow-unpow_binary64_155` `unpow3_binary64_144`
2×	`rem-cube-cbrt_binary64_101` `cbrt-div_binary64_110` `pow-exp_binary64_146` `cbrt-undiv_binary64_112` `div-exp_binary64_129`
1×	`-commutative_binary64_9` `rem-cbrt-cube_binary64_102` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow1/3_binary64_160` `frac-2neg_binary64_89` `pow-pow_binary64_150` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77`

Counts

4 → 186

Calls

8 calls:

25.0ms	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (.f64 (cos.f64 b) 1/2) a))))) 3)))
7.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3))
7.0ms	(pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3)
6.0ms	(/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a)))))
0.0ms	(-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))

series1.5s (1%)

Counts

4 → 47

Calls

4 calls:

569.0ms	(.f64 r (cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (.f64 (cos.f64 b) 1/2) a))))) 3)))
468.0ms	(pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3)
254.0ms	(cbrt.f64 (pow.f64 (/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a))))) 3))
246.0ms	(/.f64 (sin.f64 b) (-.f64 (cos.f64 b) (.f64 a (+.f64 (sin.f64 b) (.f64 (*.f64 (cos.f64 b) 1/2) a)))))

Compiler

Compiled 2178 to 1650 computations (24.2% saved)

simplify128.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5272	9340

localize30.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a)))) (log.f64 (+.f64 a (.f64 1/6 (pow.f64 a 3)))))
0.1b	(*.f64 1/36 (pow.f64 a 6))
0.0b	(/.f64 (sin.f64 b) (+.f64 (cos.f64 b) (+.f64 (exp.f64 (-.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a)))) (log.f64 (+.f64 a (.f64 1/6 (pow.f64 a 3)))))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))))
0.0b	(+.f64 a (*.f64 1/6 (pow.f64 a 3)))
2.6b	(+.f64 (exp.f64 (-.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a)))) (log.f64 (+.f64 a (.f64 1/6 (pow.f64 a 3)))))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
10.2b	(log.f64 (+.f64 a (*.f64 1/6 (pow.f64 a 3))))
13.0b	(-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a))
28.2b	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (*.f64 a a))))

rewrite39.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `pow1_binary64_139`
5×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `log-prod_binary64_164` `log-div_binary64_165`
3×	`rem-log-exp_binary64_119` `log-pow_binary64_167`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `associate-*r/_binary64_20` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `prod-exp_binary64_127` `diff-log_binary64_170` `pow-prod-down_binary64_149` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 51

Calls

8 calls:

16.0ms	(+.f64 (exp.f64 (-.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a)))) (log.f64 (+.f64 a (.f64 1/6 (pow.f64 a 3)))))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
7.0ms	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (*.f64 a a))))
5.0ms	(-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a))
3.0ms	(log.f64 (+.f64 a (*.f64 1/6 (pow.f64 a 3))))
0.0ms	(+.f64 a (*.f64 1/6 (pow.f64 a 3)))

series867.0ms (0.6%)

Counts

4 → 24

Calls

4 calls:

475.0ms	(+.f64 (exp.f64 (-.f64 (log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a)))) (log.f64 (+.f64 a (.f64 1/6 (pow.f64 a 3)))))) (.f64 (.f64 a a) (*.f64 (cos.f64 b) -1/2)))
232.0ms	(log.f64 (.f64 (sin.f64 b) (-.f64 (.f64 1/36 (pow.f64 a 6)) (*.f64 a a))))
116.0ms	(-.f64 (.f64 1/36 (pow.f64 a 6)) (.f64 a a))
45.0ms	(log.f64 (+.f64 a (*.f64 1/6 (pow.f64 a 3))))

Compiler

Compiled 1768 to 1350 computations (23.6% saved)

simplify62.0ms (0%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4988	1874
1	4988	1874

localize26.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 (sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b)))) (sqrt.f64 r))
0.1b	(.f64 (sqrt.f64 (.f64 (/.f64 1 (*.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b)))))) (sqrt.f64 r))
0.1b	(sqrt.f64 (/.f64 (sin.f64 b) (cos.f64 (+.f64 a b))))
0.1b	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b))))))
2.9b	(cos.f64 (+.f64 a b))
2.9b	(cos.f64 (+.f64 a b))
2.9b	(cos.f64 (+.f64 a b))
2.9b	(cos.f64 (+.f64 a b))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-log-exp_binary64_117` `add-cube-cbrt_binary64_113` `add-exp-log_binary64_116` `cos-sum_binary64_212` `*-un-lft-identity_binary64_78` `pow1_binary64_139`

Counts

4 → 32

Calls

8 calls:

5.0ms	(cos.f64 (+.f64 a b))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(cos.f64 (+.f64 a b))
4.0ms	(cos.f64 (+.f64 a b))
0.0ms	(sqrt.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 (cos.f64 (+.f64 a b))) (cbrt.f64 (cos.f64 (+.f64 a b))))) (/.f64 (sin.f64 b) (cbrt.f64 (cos.f64 (+.f64 a b))))))

series219.0ms (0.1%)

Counts

4 → 44

Calls

4 calls:

56.0ms	(cos.f64 (+.f64 a b))
55.0ms	(cos.f64 (+.f64 a b))
54.0ms	(cos.f64 (+.f64 a b))
53.0ms	(cos.f64 (+.f64 a b))

Compiler

Compiled 2704 to 1476 computations (45.4% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4974	844
1	4974	844

prune40.0s (26.7%)

Pruning

898 alts after pruning (882 fresh and 16 done)

	Pruned	Kept	Total
New	328	279	607
Fresh	18	603	621
Picked	0	0	0
Done	0	16	16
Total	346	898	1244

Error

0.0b

Counts

1244 → 898

Compiler

Compiled 14345 to 5968 computations (58.4% saved)

simplify957.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5064	62718

regimes17.0s (11.3%)

Compiler: Compiled 171692 to 109447 computations (36.3% saved)

bsearch0.0ms (0%)

regimes1.7s (1.1%)

Compiler: Compiled 14673 to 12129 computations (17.3% saved)

bsearch0.0ms (0%)

regimes1.7s (1.1%)

Compiler: Compiled 14593 to 12069 computations (17.3% saved)

bsearch0.0ms (0%)

regimes1.2s (0.8%)

Compiler: Compiled 10317 to 8899 computations (13.7% saved)

bsearch0.0ms (0%)

regimes1.0s (0.7%)

Compiler: Compiled 8728 to 7538 computations (13.6% saved)

bsearch0.0ms (0%)

regimes322.0ms (0.2%)

Compiler: Compiled 1350 to 1275 computations (5.6% saved)

bsearch95.0ms (0.1%)

Steps

Iters	Range		Point
9	1.1241052610292282e+52	1.9656918355222116e+60	1.1400914348472507e+52
11	-1.6834688190526377e+29	-6379936364.588924	-6447650229.15258

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes347.0ms (0.2%)

Compiler: Compiled 1308 to 1233 computations (5.7% saved)

bsearch69.0ms (0%)

Steps

Iters	Range		Point
9	648.5012266919995	1164791561.378084	658.9103230507245
6	-6379936364.588924	-1233449824.6021726	-1253051527.059556

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes343.0ms (0.2%)

Compiler: Compiled 1287 to 1212 computations (5.8% saved)

bsearch65.0ms (0%)

Steps

Iters	Range		Point
9	648.5012266919995	1164791561.378084	658.9103230507245
6	-6379936364.588924	-1233449824.6021726	-1253051527.059556

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes182.0ms (0.1%)

Compiler: Compiled 1266 to 1191 computations (5.9% saved)

bsearch0.0ms (0%)

regimes111.0ms (0.1%)

Compiler: Compiled 687 to 669 computations (2.6% saved)

bsearch0.0ms (0%)

regimes26.0ms (0%)

Accuracy

Total 0.3b remaining (96.3%)

Threshold costs 0.3b (96.3%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch11.0ms (0%)

Compiler: Compiled 165 to 126 computations (23.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	89	248
1	89	248

end0.0ms (0%)

sample33.3s (22.2%)

Algorithm

1×

intervals

Results

1.1s	3487×	body	1024	valid
284.0ms	1361×	body	512	valid
184.0ms	2372×	body	128	valid
123.0ms	204×	body	2048	valid
90.0ms	576×	body	256	valid
1.0ms	2×	body	1024	invalid

Compiler

Compiled 34497 to 22042 computations (36.1% saved)

Pareto

0.5067361048239761