Details

analyze499.0ms (0.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

Compiler

Compiled 16 to 9 computations (43.8% saved)

sample30.0ms (0.1%)

Algorithm

1×

intervals

Results

11.0ms	63×	body	1024	valid
6.0ms	144×	body	128	valid
5.0ms	37×	body	512	valid
1.0ms	11×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify209.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	24

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

0.3b

Counts

2 → 1

Compiler

Compiled 15 to 8 computations (46.7% saved)

localize7.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_100`
27×	`*-un-lft-identity_binary64_78`
22×	`add-cube-cbrt_binary64_113`
18×	`pow1_binary64_139`
15×	`times-frac_binary64_84`
10×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `difference-of-squares_binary64_47`
8×	`tan-quot_binary64_237`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117` `swap-sqr_binary64_45` `associate-r_binary64_18`
5×	`associate-/l*_binary64_23`
3×	`associate-/r*_binary64_22`
2×	`pow2_binary64_159` `-commutative_binary64_9` `pow-sqr_binary64_51` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-/r/_binary64_24` `associate-*r/_binary64_20` `pow-plus_binary64_141` `associate-/l/_binary64_25`
1×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `div-sub_binary64_83` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 110

Calls

8 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series413.0ms (0.7%)

Counts

4 → 23

Calls

4 calls:

214.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
72.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
67.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
60.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Compiler

Compiled 602 to 482 computations (19.9% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4936	2142
1	4936	2142

prune637.0ms (1.1%)

Pruning

76 alts after pruning (75 fresh and 1 done)

	Pruned	Kept	Total
New	58	75	133
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	58	76	134

Error

0.1b

Counts

134 → 76

Compiler

Compiled 3509 to 2287 computations (34.8% saved)

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
0.2b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
0.1b	(-.f64 -1 (pow.f64 (tan.f64 x) 2))
0.2b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
0.2b	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite43.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`add-sqr-sqrt_binary64_100`
64×	`times-frac_binary64_84` `*-un-lft-identity_binary64_78`
40×	`difference-of-sqr--1_binary64_49`
36×	`difference-of-squares_binary64_47`
26×	`add-cube-cbrt_binary64_113`
25×	`unpow-prod-down_binary64_157`
21×	`unpow2_binary64_143` `sqr-pow_binary64_50`
10×	`distribute-lft-out_binary64_29`
9×	`distribute-lft-out--_binary64_30`
8×	`associate-/l_binary64_23` `associate-/r_binary64_22` `add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `pow-unpow_binary64_155` `pow1_binary64_139`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip-+_binary64_52` `pow-pow_binary64_150` `associate-/r/_binary64_24` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `sum-log_binary64_169`

Counts

4 → 148

Calls

8 calls:

16.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
6.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
0.0ms	(-.f64 -1 (pow.f64 (tan.f64 x) 2))

series431.0ms (0.7%)

Counts

4 → 23

Calls

4 calls:

236.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (tan.f64 x) 2)))
67.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
65.0ms	(pow.f64 (tan.f64 x) 2)
62.0ms	(pow.f64 (tan.f64 x) 2)

Compiler

Compiled 586 to 514 computations (12.3% saved)

simplify107.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5184	3922

localize5.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (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 (tan.f64 x) (tan.f64 x))
0.2b	(-.f64 1 (cbrt.f64 (pow.f64 (tan.f64 x) 6)))
0.2b	(/.f64 (-.f64 1 (cbrt.f64 (pow.f64 (tan.f64 x) 6))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(-.f64 1 (cbrt.f64 (pow.f64 (tan.f64 x) 6)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.6b	(pow.f64 (tan.f64 x) 6)
11.7b	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

rewrite27.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_100`
21×	`*-un-lft-identity_binary64_78`
20×	`cbrt-prod_binary64_109`
15×	`add-cube-cbrt_binary64_113`
12×	`pow1_binary64_139`
11×	`unpow-prod-down_binary64_157`
10×	`cancel-sign-sub-inv_binary64_44`
8×	`difference-of-squares_binary64_47`
7×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
5×	`sqr-pow_binary64_50`
4×	`tan-quot_binary64_237`
3×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18` `pow-unpow_binary64_155`
1×	`pow2_binary64_159` `-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow-sqr_binary64_51` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `pow1/3_binary64_160` `frac-times_binary64_88` `pow-pow_binary64_150` `flip--_binary64_53` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `pow-plus_binary64_141` `sub-neg_binary64_71`

Counts

4 → 90

Calls

8 calls:

7.0ms	(-.f64 1 (cbrt.f64 (pow.f64 (tan.f64 x) 6)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 6)
3.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series306.0ms (0.5%)

Counts

4 → 23

Calls

4 calls:

119.0ms	(pow.f64 (tan.f64 x) 6)
64.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
64.0ms	(-.f64 1 (cbrt.f64 (pow.f64 (tan.f64 x) 6)))
59.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 6))

Compiler

Compiled 642 to 526 computations (18.1% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4878	1209
1	4878	1209

localize15.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
0.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
0.2b	(/.f64 (-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(pow.f64 (sin.f64 x) 2)

rewrite65.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

98×	`add-sqr-sqrt_binary64_100`
96×	`times-frac_binary64_84`
70×	`unpow-prod-down_binary64_157`
68×	`cancel-sign-sub-inv_binary64_44`
64×	`*-un-lft-identity_binary64_78`
45×	`add-cube-cbrt_binary64_113`
34×	`unpow2_binary64_143` `sqr-pow_binary64_50` `difference-of-squares_binary64_47`
13×	`pow1_binary64_139`
8×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `pow-unpow_binary64_155`
4×	`tan-quot_binary64_237`
3×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow-pow_binary64_150`
1×	`pow2_binary64_159` `-commutative_binary64_9` `pow-sqr_binary64_51` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `div-inv_binary64_75` `frac-times_binary64_88` `flip--_binary64_53` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `pow-plus_binary64_141` `sub-neg_binary64_71`

Counts

4 → 178

Calls

8 calls:

33.0ms	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (sin.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series214.0ms (0.4%)

Counts

4 → 23

Calls

4 calls:

86.0ms	(-.f64 1 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)))
67.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
32.0ms	(pow.f64 (sin.f64 x) 2)
29.0ms	(pow.f64 (cos.f64 x) 2)

Compiler

Compiled 692 to 556 computations (19.7% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5037	3123

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.1b	(-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
0.2b	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))

rewrite87.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

123×	`pow1_binary64_139`
37×	`pow-prod-up_binary64_148`
32×	`tan-quot_binary64_237`
26×	`*-un-lft-identity_binary64_78`
25×	`frac-times_binary64_88`
24×	`add-exp-log_binary64_116` `pow-prod-down_binary64_149`
23×	`add-cbrt-cube_binary64_114` `pow-sqr_binary64_51`
19×	`pow-plus_binary64_141`
15×	`associate-l/_binary64_21` `associate-r/_binary64_20`
14×	`pow2_binary64_159` `add-sqr-sqrt_binary64_100`
12×	`flip-+_binary64_52` `add-cube-cbrt_binary64_113` `flip3-+_binary64_81`
10×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
8×	`associate-/r/_binary64_24`
7×	`swap-sqr_binary64_45`
6×	`distribute-lft-out_binary64_29`
5×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/l*_binary64_23`
3×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `associate-/l/_binary64_25`
1×	`distribute-lft-in_binary64_27` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip3--_binary64_82` `unpow2_binary64_143` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `flip--_binary64_53` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83`

Counts

4 → 170

Calls

8 calls:

28.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
20.0ms	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
15.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
3.0ms	(pow.f64 (tan.f64 x) 2)
0.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) 1)

series570.0ms (1%)

Counts

4 → 21

Calls

4 calls:

315.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
100.0ms	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
92.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
62.0ms	(pow.f64 (tan.f64 x) 2)

Compiler

Compiled 833 to 623 computations (25.2% saved)

simplify91.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4954	2684
1	4954	2684

prune6.5s (11.1%)

Pruning

280 alts after pruning (274 fresh and 6 done)

	Pruned	Kept	Total
New	462	214	676
Fresh	10	60	70
Picked	0	0	0
Done	0	6	6
Total	472	280	752

Error

0.0b

Counts

752 → 280

Compiler

Compiled 14847 to 10034 computations (32.4% saved)

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
0.2b	(/.f64 (+.f64 1 (.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (+.f64 1 (.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.2b	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_100`
18×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
12×	`pow1_binary64_139`
9×	`times-frac_binary64_84` `add-exp-log_binary64_116`
8×	`add-cbrt-cube_binary64_114`
6×	`add-log-exp_binary64_117`
4×	`tan-quot_binary64_237`
3×	`associate-l_binary64_19` `unpow-prod-down_binary64_157` `flip-+_binary64_52` `swap-sqr_binary64_45` `associate-r_binary64_18` `associate-/l_binary64_23` `associate-/r_binary64_22` `pow-unpow_binary64_155` `flip3-+_binary64_81`
2×	`unsub-neg_binary64_72` `associate-/r/_binary64_24` `distribute-rgt-neg-out_binary64_38` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `pow2_binary64_159` `-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `pow-sqr_binary64_51` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `unpow2_binary64_143` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `div-inv_binary64_75` `frac-times_binary64_88` `pow-pow_binary64_150` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `associate-*r/_binary64_20` `clear-num_binary64_77` `div-sub_binary64_83` `pow-plus_binary64_141` `sum-log_binary64_169`

Counts

4 → 90

Calls

8 calls:

7.0ms	(/.f64 (+.f64 1 (.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
3.0ms	(pow.f64 (tan.f64 x) 2)
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series396.0ms (0.7%)

Counts

4 → 23

Calls

4 calls:

207.0ms	(/.f64 (+.f64 1 (.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
64.0ms	(pow.f64 (tan.f64 x) 2)
62.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
62.0ms	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))

Compiler

Compiled 658 to 554 computations (15.8% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5667	2049

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

12.6b	(+.f64 (.f64 2/3 (pow.f64 x 4)) (-.f64 1 (.f64 2 (*.f64 x x))))
0.1b	(*.f64 2/3 (pow.f64 x 4))
0.1b	(*.f64 2/3 (pow.f64 x 4))
12.6b	(+.f64 (.f64 2/3 (pow.f64 x 4)) (-.f64 1 (.f64 2 (*.f64 x x))))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_100`
7×	`add-log-exp_binary64_117` `associate-r_binary64_18` `add-exp-log_binary64_116`
5×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157`
3×	`associate-l_binary64_19` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
2×	`associate-+r+_binary64_10` `sqr-pow_binary64_50` `pow1_binary64_139` `sum-log_binary64_169`
1×	`+-commutative_binary64_8` `*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `associate-+r-_binary64_12` `cbrt-unprod_binary64_111` `flip-+_binary64_52` `diff-log_binary64_170` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

2 → 40

Calls

4 calls:

7.0ms	(+.f64 (.f64 2/3 (pow.f64 x 4)) (-.f64 1 (.f64 2 (*.f64 x x))))
6.0ms	(*.f64 2/3 (pow.f64 x 4))
0.0ms	(*.f64 2/3 (pow.f64 x 4))
0.0ms	(+.f64 (.f64 2/3 (pow.f64 x 4)) (-.f64 1 (.f64 2 (*.f64 x x))))

series153.0ms (0.3%)

Counts

2 → 12

Calls

2 calls:

118.0ms	(+.f64 (.f64 2/3 (pow.f64 x 4)) (-.f64 1 (.f64 2 (*.f64 x x))))
35.0ms	(*.f64 2/3 (pow.f64 x 4))

Compiler

Compiled 196 to 177 computations (9.7% saved)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4943	744
1	4943	744

localize13.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(log.f64 (tan.f64 x))
0.1b	(-.f64 1 (cbrt.f64 (exp.f64 (*.f64 6 (log.f64 (tan.f64 x))))))
0.1b	(/.f64 (-.f64 1 (cbrt.f64 (exp.f64 (.f64 6 (log.f64 (tan.f64 x)))))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(*.f64 6 (log.f64 (tan.f64 x)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.7b	(exp.f64 (*.f64 6 (log.f64 (tan.f64 x))))
5.0b	(cbrt.f64 (exp.f64 (*.f64 6 (log.f64 (tan.f64 x)))))

rewrite26.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_100`
18×	`log-prod_binary64_164`
17×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
14×	`pow1_binary64_139`
12×	`exp-sum_binary64_124`
9×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `cbrt-prod_binary64_109`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
7×	`associate-r_binary64_18`
6×	`associate-l_binary64_19` `add-log-exp_binary64_117`
4×	`tan-quot_binary64_237`
3×	`swap-sqr_binary64_45`
2×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`pow2_binary64_159` `pow-sqr_binary64_51` `rem-exp-log_binary64_118` `pow1/3_binary64_160` `frac-times_binary64_88` `exp-to-pow_binary64_140` `pow-prod-up_binary64_148` `associate-l/_binary64_21` `exp-prod_binary64_130` `associate-r/_binary64_20` `log-pow_binary64_167` `pow-plus_binary64_141`

Counts

4 → 86

Calls

8 calls:

6.0ms	(*.f64 6 (log.f64 (tan.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
4.0ms	(cbrt.f64 (exp.f64 (*.f64 6 (log.f64 (tan.f64 x)))))
3.0ms	(exp.f64 (*.f64 6 (log.f64 (tan.f64 x))))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series336.0ms (0.6%)

Counts

4 → 18

Calls

4 calls:

113.0ms	(exp.f64 (*.f64 6 (log.f64 (tan.f64 x))))
101.0ms	(*.f64 6 (log.f64 (tan.f64 x)))
67.0ms	(cbrt.f64 (exp.f64 (*.f64 6 (log.f64 (tan.f64 x)))))
55.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Compiler

Compiled 574 to 472 computations (17.8% saved)

simplify46.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5117	988

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(+.f64 (pow.f64 (tan.f64 x) 2) -1)
0.1b	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) -1) (-.f64 -1 (pow.f64 (pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2))))
0.0b	(-.f64 -1 (pow.f64 (pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.0b	(cbrt.f64 2)
1.3b	(pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))

rewrite10.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_109`
8×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`add-exp-log_binary64_116` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
3×	`unpow-prod-down_binary64_157` `pow1/3_binary64_160`
1×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `sqr-pow_binary64_50` `pow-pow_binary64_150` `pow-unpow_binary64_155`

Counts

4 → 48

Calls

8 calls:

3.0ms	(pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
1.0ms	(cbrt.f64 2)
0.0ms	(-.f64 -1 (pow.f64 (pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2))) (cbrt.f64 2)))

series142.0ms (0.2%)

Counts

4 → 3

Calls

4 calls:

142.0ms	(pow.f64 (tan.f64 x) (*.f64 (cbrt.f64 2) (cbrt.f64 2)))
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)
0.0ms	(cbrt.f64 2)

Compiler

Compiled 156 to 143 computations (8.3% saved)

simplify80.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4960	488
1	4960	488

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)))
0.1b	(sqrt.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)))
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.4b	(pow.f64 (tan.f64 x) 4)
0.4b	(pow.f64 (tan.f64 x) 4)

rewrite20.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100` `unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113` `pow-unpow_binary64_155` `*-un-lft-identity_binary64_78`
8×	`add-exp-log_binary64_116` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `add-log-exp_binary64_117` `sqr-pow_binary64_50` `pow-pow_binary64_150`
2×	`unpow2_binary64_143`

Counts

4 → 70

Calls

8 calls:

3.0ms	(pow.f64 (tan.f64 x) 4)
3.0ms	(pow.f64 (tan.f64 x) 4)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
0.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) 1)

series319.0ms (0.5%)

Counts

4 → 18

Calls

4 calls:

93.0ms	(pow.f64 (tan.f64 x) 4)
88.0ms	(pow.f64 (tan.f64 x) 4)
69.0ms	(pow.f64 (tan.f64 x) 2)
68.0ms	(pow.f64 (tan.f64 x) 2)

Compiler

Compiled 1044 to 860 computations (17.6% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5065	760

prune12.4s (21.2%)

Pruning

422 alts after pruning (411 fresh and 11 done)

	Pruned	Kept	Total
New	260	148	408
Fresh	6	263	269
Picked	0	0	0
Done	0	11	11
Total	266	422	688

Error

0.0b

Counts

688 → 422

Compiler

Compiled 17307 to 12857 computations (25.7% saved)

localize12.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
0.2b	(/.f64 (+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1)))
0.1b	(+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1))
0.2b	(/.f64 (+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1)))
0.2b	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64_78`
17×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
8×	`add-exp-log_binary64_116`
6×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `unpow-prod-down_binary64_157` `pow-unpow_binary64_155` `pow1_binary64_139`
4×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
3×	`flip-+_binary64_52` `associate-/l*_binary64_23` `flip3-+_binary64_81`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `unpow2_binary64_143` `sqr-pow_binary64_50` `pow-pow_binary64_150` `unsub-neg_binary64_72` `associate-/r/_binary64_24` `distribute-rgt-neg-out_binary64_38` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `div-sub_binary64_83` `sum-log_binary64_169`

Counts

4 → 84

Calls

8 calls:

12.0ms	(/.f64 (+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1)))
4.0ms	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
0.0ms	(+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1))

series381.0ms (0.7%)

Counts

4 → 23

Calls

4 calls:

195.0ms	(/.f64 (+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1)))) (+.f64 1 (pow.f64 (pow.f64 (tan.f64 x) 2) 1)))
66.0ms	(+.f64 1 (*.f64 (pow.f64 (tan.f64 x) 2) (neg.f64 (cbrt.f64 1))))
60.0ms	(pow.f64 (tan.f64 x) 2)
60.0ms	(pow.f64 (tan.f64 x) 2)

Compiler

Compiled 690 to 618 computations (10.4% saved)

simplify61.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4920	2166
1	4920	2166

localize4.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 4))
0.1b	(*.f64 2/3 (pow.f64 x 4))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64_100`
7×	`associate-r_binary64_18`
6×	`add-exp-log_binary64_116`
4×	`unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
3×	`add-cbrt-cube_binary64_114` `associate-l_binary64_19` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
2×	`sqr-pow_binary64_50`
1×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `pow1_binary64_139`

Counts

1 → 25

Calls

2 calls:

6.0ms	(*.f64 2/3 (pow.f64 x 4))
0.0ms	(*.f64 2/3 (pow.f64 x 4))

series35.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

35.0ms

(*.f64 2/3 (pow.f64 x 4))

Compiler

Compiled 30 to 30 computations (0% saved)

simplify66.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

28 → 28

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4886	261
1	4886	261

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 1 (/.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4) (-.f64 1 (pow.f64 (tan.f64 x) 4))))
0.1b	(-.f64 1 (pow.f64 (tan.f64 x) 4))
0.1b	(sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1))
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.2b	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4) (-.f64 1 (pow.f64 (tan.f64 x) 4)))
0.2b	(pow.f64 (tan.f64 x) 2)
0.4b	(pow.f64 (tan.f64 x) 4)
0.5b	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4)

rewrite65.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
114×	`unpow-prod-down_binary64_157`
110×	`times-frac_binary64_84`
72×	`difference-of-squares_binary64_47`
56×	`add-cube-cbrt_binary64_113`
48×	`sqrt-prod_binary64_94`
38×	`sqr-pow_binary64_50`
12×	`distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `distribute-lft-out_binary64_29`
11×	`associate-/l*_binary64_23`
10×	`associate-/r*_binary64_22`
9×	`pow-unpow_binary64_155`
8×	`pow1_binary64_139`
6×	`add-cbrt-cube_binary64_114`
5×	`pow-pow_binary64_150`
4×	`pow-exp_binary64_146` `pow-to-exp_binary64_147` `add-log-exp_binary64_117`
3×	`div-exp_binary64_129`
2×	`associate-/r/_binary64_24`
1×	`sqrt-pow2_binary64_97` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `flip3--_binary64_82` `unpow2_binary64_143` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `clear-num_binary64_77` `pow1/2_binary64_158`

Counts

4 → 206

Calls

8 calls:

19.0ms	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4) (-.f64 1 (pow.f64 (tan.f64 x) 4)))
8.0ms	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 4)
0.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) 1)

series607.0ms (1%)

Counts

4 → 22

Calls

4 calls:

297.0ms	(/.f64 (pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4) (-.f64 1 (pow.f64 (tan.f64 x) 4)))
157.0ms	(pow.f64 (sqrt.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) 4)
96.0ms	(pow.f64 (tan.f64 x) 4)
57.0ms	(pow.f64 (tan.f64 x) 2)

Compiler

Compiled 712 to 640 computations (10.1% saved)

simplify110.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5069	6660

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.2b	(-.f64 1 (*.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2)))
0.2b	(/.f64 (-.f64 1 (.f64 (cbrt.f64 (pow.f64 (tan.f64 x) 4)) (pow.f64 (cbrt.f64 (tan.f64 x)) 2))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
0.4b	(pow.f64 (tan.f64 x) 4)
0.5b	(pow.f64 (cbrt.f64 (tan.f64 x)) 2)
0.7b	(cbrt.f64 (tan.f64 x))
16.8b	(cbrt.f64 (pow.f64 (tan.f64 x) 4))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`cbrt-prod_binary64_109`
12×	`add-sqr-sqrt_binary64_100` `unpow-prod-down_binary64_157` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-exp-log_binary64_116` `pow-unpow_binary64_155` `pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
3×	`pow1/3_binary64_160` `sqr-pow_binary64_50` `pow-pow_binary64_150`
2×	`pow-exp_binary64_146` `pow-to-exp_binary64_147`
1×	`tan-quot_binary64_237` `cbrt-div_binary64_110` `unpow2_binary64_143`

Counts

4 → 66

Calls

8 calls:

4.0ms	(pow.f64 (cbrt.f64 (tan.f64 x)) 2)
3.0ms	(pow.f64 (tan.f64 x) 4)
3.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 4))
2.0ms	(cbrt.f64 (tan.f64 x))
0.0ms	(+.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series586.0ms (1%)

Counts

4 → 19

Calls

4 calls:

221.0ms	(cbrt.f64 (pow.f64 (tan.f64 x) 4))
175.0ms	(pow.f64 (cbrt.f64 (tan.f64 x)) 2)
107.0ms	(cbrt.f64 (tan.f64 x))
83.0ms	(pow.f64 (tan.f64 x) 4)

Compiler

Compiled 850 to 665 computations (21.8% saved)

simplify87.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4930	942
1	4930	942

localize23.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2))
0.1b	(-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x))))
0.1b	(+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)
0.1b	(+.f64 (pow.f64 (tan.f64 x) 2) 1)
0.2b	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)))
0.2b	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1))
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))

rewrite127.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`pow1_binary64_139`
36×	`pow-prod-up_binary64_148`
32×	`tan-quot_binary64_237`
25×	`frac-times_binary64_88`
24×	`add-exp-log_binary64_116` `pow-prod-down_binary64_149`
23×	`add-cbrt-cube_binary64_114`
22×	`pow-sqr_binary64_51`
18×	`pow-plus_binary64_141`
15×	`associate-l/_binary64_21` `associate-r/_binary64_20`
14×	`*-un-lft-identity_binary64_78`
13×	`pow2_binary64_159`
12×	`add-sqr-sqrt_binary64_100` `flip-+_binary64_52` `flip3-+_binary64_81`
10×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `add-cube-cbrt_binary64_113`
8×	`associate-/r/_binary64_24`
5×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/l*_binary64_23`
3×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155`
2×	`*-commutative_binary64_9` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `unswap-sqr_binary64_46` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `associate-/l/_binary64_25`
1×	`distribute-lft-in_binary64_27` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `flip3--_binary64_82` `swap-sqr_binary64_45` `unpow2_binary64_143` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `div-inv_binary64_75` `pow-pow_binary64_150` `flip--_binary64_53` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83`

Counts

4 → 160

Calls

8 calls:

47.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)))
40.0ms	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1))
14.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
3.0ms	(pow.f64 (sin.f64 x) 2)
0.0ms	(+.f64 (pow.f64 (tan.f64 x) 2) 1)

series674.0ms (1.2%)

Counts

4 → 22

Calls

4 calls:

381.0ms	(/.f64 (-.f64 (.f64 1 1) (.f64 (.f64 (tan.f64 x) (tan.f64 x)) (.f64 (tan.f64 x) (tan.f64 x)))) (*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)))
166.0ms	(*.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1))
93.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 x)) (*.f64 (tan.f64 x) (tan.f64 x)))
35.0ms	(pow.f64 (sin.f64 x) 2)

Compiler

Compiled 888 to 666 computations (25% saved)

simplify74.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5106	3473

prune20.5s (35%)

Pruning

652 alts after pruning (637 fresh and 15 done)

	Pruned	Kept	Total
New	365	265	630
Fresh	34	372	406
Picked	0	0	0
Done	1	15	16
Total	400	652	1052

Error

0.0b

Counts

1052 → 652

Compiler

Compiled 10764 to 7322 computations (32% saved)

simplify594.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5002	39298

regimes7.8s (13.4%)

Compiler: Compiled 75906 to 58734 computations (22.6% saved)

bsearch0.0ms (0%)

regimes287.0ms (0.5%)

Compiler: Compiled 2090 to 1753 computations (16.1% saved)

bsearch2.0ms (0%)

Compiler: Compiled 5 to 3 computations (40% saved)

regimes23.0ms (0%)

Compiler: Compiled 110 to 96 computations (12.7% saved)

bsearch3.0ms (0%)

Compiler: Compiled 31 to 26 computations (16.1% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	47
1	28	47

end0.0ms (0%)

sample1.4s (2.4%)

Algorithm

1×

intervals

Results

361.0ms	2041×	body	1024	valid
195.0ms	4463×	body	128	valid
132.0ms	970×	body	512	valid
47.0ms	518×	body	256	valid
2.0ms	8×	body	2048	valid

Compiler

Compiled 19014 to 14720 computations (22.6% saved)