Details

analyze244.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample57.0ms (0%)

Algorithm

1×

intervals

Results

29.0ms	64×	body	2048	valid
8.0ms	41×	body	1024	valid
5.0ms	42×	body	512	valid
4.0ms	83×	body	128	valid
2.0ms	24×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify110.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

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

30.6b

Counts

2 → 1

Compiler

Compiled 8 to 6 computations (25% saved)

localize12.0ms (0%)

Local error

Found 4 expressions with local error:

15.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
2.1b	(-.f64 1 (cos.f64 x))
2.1b	(-.f64 1 (cos.f64 x))
15.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite17.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
7×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`add-cube-cbrt_binary64_113`
4×	`add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `cancel-sign-sub-inv_binary64_44`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `flip--_binary64_53` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `sub-neg_binary64_71`

Counts

2 → 47

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(-.f64 1 (cos.f64 x))
0.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

series59.0ms (0.1%)

Counts

2 → 12

Calls

2 calls:

40.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
18.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 176 to 148 computations (15.9% saved)

simplify68.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6299	811

prune176.0ms (0.2%)

Pruning

36 alts after pruning (35 fresh and 1 done)

	Pruned	Kept	Total
New	24	35	59
Fresh	0	0	0
Picked	0	0	0
Done	0	1	1
Total	24	36	60

Error

0.0b

Counts

60 → 36

Compiler

Compiled 1089 to 670 computations (38.5% saved)

localize9.0ms (0%)

Local error

Found 8 expressions with local error:

15.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
0.4b	(+.f64 1 (cos.f64 x))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
15.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite42.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`*-un-lft-identity_binary64_78`
22×	`times-frac_binary64_84`
16×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
11×	`associate-/l*_binary64_23` `pow1_binary64_139`
7×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
6×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `flip3-+_binary64_81`
3×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18` `sqr-sin-a_binary64_226` `div-sub_binary64_83`
2×	`frac-2neg_binary64_89` `sin-mult_binary64_233` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `pow2_binary64_159` `*-commutative_binary64_9` `pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `pow-plus_binary64_141` `sum-log_binary64_169`

Counts

4 → 111

Calls

8 calls:

12.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))
0.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))

series191.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

81.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
60.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
32.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
17.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 488 to 380 computations (22.1% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4936	1964
1	4936	1964

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

0.4b	(.f64 (.f64 x x) 1/24)
0.4b	(.f64 (.f64 x x) 1/24)

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`add-sqr-sqrt_binary64_100` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-r_binary64_18` `pow-prod-down_binary64_149`
2×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
1×	`-commutative_binary64_9` `associate-l*_binary64_19` `add-log-exp_binary64_117` `unswap-sqr_binary64_46`

Counts

1 → 19

Calls

2 calls:

6.0ms	(.f64 (.f64 x x) 1/24)
0.0ms	(.f64 (.f64 x x) 1/24)

series29.0ms (0%)

Counts

1 → 3

Calls

1 calls:

29.0ms

(*.f64 (*.f64 x x) 1/24)

Compiler

Compiled 42 to 42 computations (0% saved)

simplify77.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5393	182

localize7.0ms (0%)

Local error

Found 6 expressions with local error:

17.7b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
0.7b	(/.f64 (cos.f64 x) (*.f64 x x))
0.7b	(/.f64 1 (*.f64 x x))
0.7b	(/.f64 1 (*.f64 x x))
0.7b	(/.f64 (cos.f64 x) (*.f64 x x))
17.7b	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))

rewrite28.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116`
18×	`times-frac_binary64_84`
17×	`*-un-lft-identity_binary64_78`
13×	`add-cbrt-cube_binary64_114`
11×	`pow1_binary64_139`
9×	`add-cube-cbrt_binary64_113`
7×	`div-inv_binary64_75` `cancel-sign-sub-inv_binary64_44`
6×	`div-exp_binary64_129` `pow-flip_binary64_152` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`add-log-exp_binary64_117`
4×	`cbrt-undiv_binary64_112` `prod-exp_binary64_127`
3×	`distribute-lft-out--_binary64_30`
2×	`cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `1-exp_binary64_122` `rec-exp_binary64_128` `associate-/r*_binary64_22` `clear-num_binary64_77` `distribute-rgt-out--_binary64_32`
1×	`pow2_binary64_159` `pow-sqr_binary64_51` `inv-pow_binary64_163` `frac-sub_binary64_87` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149` `pow-plus_binary64_141` `sub-div_binary64_85` `sub-neg_binary64_71`

Counts

3 → 84

Calls

6 calls:

11.0ms	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
5.0ms	(/.f64 1 (*.f64 x x))
5.0ms	(/.f64 (cos.f64 x) (*.f64 x x))
0.0ms	(/.f64 1 (*.f64 x x))
0.0ms	(/.f64 (cos.f64 x) (*.f64 x x))

series113.0ms (0.1%)

Counts

3 → 15

Calls

3 calls:

55.0ms	(-.f64 (/.f64 1 (.f64 x x)) (/.f64 (cos.f64 x) (.f64 x x)))
38.0ms	(/.f64 (cos.f64 x) (*.f64 x x))
19.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 260 to 213 computations (18.1% saved)

simplify86.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4983	1180
1	4983	1180

localize8.0ms (0%)

Local error

Found 8 expressions with local error:

15.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
2.2b	(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
2.1b	(-.f64 1 (cos.f64 x))
0.1b	(exp.f64 (-.f64 1 (cos.f64 x)))
0.1b	(exp.f64 (-.f64 1 (cos.f64 x)))
2.1b	(-.f64 1 (cos.f64 x))
2.2b	(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
15.7b	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))

rewrite35.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
24×	`exp-prod_binary64_130`
21×	`log-pow_binary64_167`
14×	`add-cube-cbrt_binary64_113`
10×	`times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
9×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `add-exp-log_binary64_116` `cancel-sign-sub-inv_binary64_44`
8×	`exp-sum_binary64_124`
7×	`log-prod_binary64_164` `pow1_binary64_139`
5×	`distribute-lft-out--_binary64_30`
3×	`exp-diff_binary64_126` `sub-neg_binary64_71`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `diff-log_binary64_170` `rem-exp-log_binary64_118` `log-div_binary64_165`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `rem-log-exp_binary64_119` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83`

Counts

4 → 96

Calls

8 calls:

10.0ms	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
6.0ms	(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
5.0ms	(exp.f64 (-.f64 1 (cos.f64 x)))
4.0ms	(-.f64 1 (cos.f64 x))
2.0ms	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))

series276.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

126.0ms	(/.f64 (log.f64 (exp.f64 (-.f64 1 (cos.f64 x)))) (*.f64 x x))
104.0ms	(log.f64 (exp.f64 (-.f64 1 (cos.f64 x))))
26.0ms	(exp.f64 (-.f64 1 (cos.f64 x)))
20.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 412 to 344 computations (16.5% saved)

simplify96.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4926	1454
1	4926	1454

localize10.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(+.f64 1 (sqrt.f64 (cos.f64 x)))
0.1b	(sqrt.f64 (cos.f64 x))
0.1b	(sqrt.f64 (cos.f64 x))
0.1b	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
0.1b	(+.f64 1 (sqrt.f64 (cos.f64 x)))
0.1b	(/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)
0.3b	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
2.2b	(-.f64 1 (sqrt.f64 (cos.f64 x)))

rewrite208.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

1561×	`times-frac_binary64_84`
1140×	`*-un-lft-identity_binary64_78`
1058×	`add-sqr-sqrt_binary64_100`
545×	`add-cube-cbrt_binary64_113`
280×	`sqrt-prod_binary64_94`
236×	`difference-of-squares_binary64_47`
200×	`distribute-lft-out_binary64_29`
118×	`distribute-lft-out--_binary64_30`
101×	`associate-/r*_binary64_22`
26×	`div-inv_binary64_75`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
14×	`associate-/l*_binary64_23`
8×	`add-log-exp_binary64_117`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/r/_binary64_24`
6×	`cancel-sign-sub-inv_binary64_44`
4×	`associate-/l/_binary64_25` `pow1_binary64_139`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `frac-2neg_binary64_89` `flip--_binary64_53` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `diff-log_binary64_170` `div-sub_binary64_83` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 702

Calls

8 calls:

38.0ms	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
8.0ms	(/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)
5.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
4.0ms	(+.f64 1 (sqrt.f64 (cos.f64 x)))
0.0ms	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))

series206.0ms (0.2%)

Counts

4 → 24

Calls

4 calls:

95.0ms	(/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
51.0ms	(/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)
32.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
28.0ms	(+.f64 1 (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 540 to 416 computations (23% saved)

simplify329.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

726 → 726

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4960	29568
1	4960	29568

prune11.6s (10%)

Pruning

342 alts after pruning (338 fresh and 4 done)

	Pruned	Kept	Total
New	786	316	1102
Fresh	8	22	30
Picked	0	0	0
Done	2	4	6
Total	796	342	1138

Error

Counts

1138 → 342

Compiler

Compiled 19981 to 11161 computations (44.1% saved)

localize10.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite30.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
40×	`times-frac_binary64_84`
33×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
13×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l_binary64_23` `associate-/r_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `div-inv_binary64_75` `unswap-sqr_binary64_46`
3×	`add-log-exp_binary64_117`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`tan-quot_binary64_237` `-commutative_binary64_9` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

3 → 105

Calls

6 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
5.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.0ms	(/.f64 (sin.f64 x) x)

series190.0ms (0.2%)

Counts

3 → 18

Calls

3 calls:

91.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
68.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
32.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 340 to 278 computations (18.2% saved)

simplify97.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4967	2070
1	4967	2070

localize5.0ms (0%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/24)
0.1b	(.f64 x (.f64 x 1/24))
0.1b	(.f64 x (.f64 x 1/24))
0.3b	(*.f64 x 1/24)

rewrite11.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
7×	`add-sqr-sqrt_binary64_100`
6×	`associate-l_binary64_19`
5×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-r_binary64_18` `pow-prod-down_binary64_149`
2×	`*-commutative_binary64_9` `add-log-exp_binary64_117`
1×	`unswap-sqr_binary64_46`

Counts

2 → 36

Calls

4 calls:

5.0ms	(.f64 x (.f64 x 1/24))
4.0ms	(*.f64 x 1/24)
0.0ms	(.f64 x (.f64 x 1/24))
0.0ms	(*.f64 x 1/24)

series40.0ms (0%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(.f64 x (.f64 x 1/24))
16.0ms	(*.f64 x 1/24)

Compiler

Compiled 84 to 78 computations (7.1% saved)

simplify79.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4985	296
1	4985	296

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.3b	(*.f64 (pow.f64 x 6) 1/720)
0.1b	(*.f64 1/40320 (pow.f64 x 8))
0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(+.f64 (.f64 (pow.f64 x 4) 1/24) (.f64 1/40320 (pow.f64 x 8)))
0.3b	(*.f64 (pow.f64 x 6) 1/720)
0.3b	(*.f64 (pow.f64 x 4) 1/24)
25.1b	(-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (*.f64 1/40320 (pow.f64 x 8))))
32.1b	(/.f64 (-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (.f64 1/40320 (pow.f64 x 8)))) (.f64 x x))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_100`
19×	`add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
16×	`add-log-exp_binary64_117`
14×	`associate-l_binary64_19`
13×	`add-cbrt-cube_binary64_114` `add-cube-cbrt_binary64_113`
8×	`unpow-prod-down_binary64_157` `flip-+_binary64_52` `frac-sub_binary64_87` `flip3-+_binary64_81`
7×	`prod-exp_binary64_127`
6×	`associate-r_binary64_18` `unswap-sqr_binary64_46` `associate-/l/_binary64_25`
5×	`times-frac_binary64_84` `associate-/l*_binary64_23`
4×	`diff-log_binary64_170` `sqr-pow_binary64_50` `pow1_binary64_139` `sum-log_binary64_169`
3×	`cbrt-unprod_binary64_111` `distribute-lft-out--_binary64_30` `difference-of-squares_binary64_47` `cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `flip--_binary64_53`
1×	`frac-2neg_binary64_89` `associate--l+_binary64_15` `div-inv_binary64_75` `associate--r+_binary64_14` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `sub-neg_binary64_71`

Counts

4 → 107

Calls

8 calls:

17.0ms	(/.f64 (-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (.f64 1/40320 (pow.f64 x 8)))) (.f64 x x))
14.0ms	(-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (*.f64 1/40320 (pow.f64 x 8))))
5.0ms	(*.f64 (pow.f64 x 4) 1/24)
5.0ms	(*.f64 (pow.f64 x 6) 1/720)
0.0ms	(+.f64 (.f64 (pow.f64 x 4) 1/24) (.f64 1/40320 (pow.f64 x 8)))

series203.0ms (0.2%)

Counts

4 → 22

Calls

4 calls:

74.0ms	(/.f64 (-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (.f64 1/40320 (pow.f64 x 8)))) (.f64 x x))
54.0ms	(-.f64 (+.f64 (.f64 (.f64 x x) 1/2) (.f64 (pow.f64 x 6) 1/720)) (+.f64 (.f64 (pow.f64 x 4) 1/24) (*.f64 1/40320 (pow.f64 x 8))))
43.0ms	(*.f64 (pow.f64 x 6) 1/720)
31.0ms	(*.f64 (pow.f64 x 4) 1/24)

Compiler

Compiled 592 to 468 computations (20.9% saved)

simplify88.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4903	3780
1	4903	3780

localize16.0ms (0%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1)))))
0.2b	(/.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (*.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1))))
0.2b	(*.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1))
0.1b	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1)))
0.3b	(+.f64 1 (pow.f64 (cos.f64 x) 3))
0.3b	(pow.f64 (cos.f64 x) 3)
2.1b	(+.f64 (cos.f64 x) -1)
15.6b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1))))) (*.f64 x x))

rewrite55.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

83×	`times-frac_binary64_84`
46×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
41×	`*-un-lft-identity_binary64_78`
26×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113`
23×	`associate-/l*_binary64_23`
22×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
9×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
8×	`add-log-exp_binary64_117` `distribute-lft-out_binary64_29`
6×	`associate-/r/_binary64_24`
5×	`div-inv_binary64_75` `pow1_binary64_139`
4×	`flip-+_binary64_52` `flip3-+_binary64_81`
3×	`unpow-prod-down_binary64_157` `pow-unpow_binary64_155` `cube-prod_binary64_106`
2×	`+-commutative_binary64_8` `div-sub_binary64_83` `sum-log_binary64_169`
1×	`rem-cube-cbrt_binary64_101` `cube-mult_binary64_108` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `frac-2neg_binary64_89` `sqr-pow_binary64_50` `sqr-sin-a_binary64_226` `pow-pow_binary64_150` `associate-/r*_binary64_22` `clear-num_binary64_77` `associate-/l/_binary64_25` `unpow3_binary64_144` `difference-of-sqr--1_binary64_49`

Counts

4 → 127

Calls

8 calls:

23.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1))))) (*.f64 x x))
6.0ms	(+.f64 1 (pow.f64 (cos.f64 x) 3))
4.0ms	(+.f64 (cos.f64 x) -1)
4.0ms	(pow.f64 (cos.f64 x) 3)
0.0ms	(+.f64 1 (*.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1)))

series292.0ms (0.3%)

Counts

4 → 24

Calls

4 calls:

185.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (/.f64 (+.f64 1 (pow.f64 (cos.f64 x) 3)) (+.f64 1 (.f64 (cos.f64 x) (+.f64 (cos.f64 x) -1))))) (*.f64 x x))
43.0ms	(+.f64 1 (pow.f64 (cos.f64 x) 3))
40.0ms	(pow.f64 (cos.f64 x) 3)
24.0ms	(+.f64 (cos.f64 x) -1)

Compiler

Compiled 844 to 604 computations (28.4% saved)

simplify103.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	4578
1	4965	4578

localize19.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (cos.f64 x))
0.0b	(.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
0.0b	(sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
2.2b	(-.f64 1 (sqrt.f64 (cos.f64 x)))
2.2b	(-.f64 1 (sqrt.f64 (cos.f64 x)))

rewrite21.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_100`
20×	`*-un-lft-identity_binary64_78`
12×	`sqrt-prod_binary64_94` `cancel-sign-sub-inv_binary64_44`
10×	`add-cube-cbrt_binary64_113`
8×	`add-log-exp_binary64_117` `difference-of-squares_binary64_47`
6×	`cbrt-prod_binary64_109`
4×	`add-cbrt-cube_binary64_114` `distribute-lft-out--_binary64_30` `add-exp-log_binary64_116` `pow1_binary64_139`
2×	`flip3--_binary64_82` `diff-log_binary64_170` `pow1/3_binary64_160` `flip--_binary64_53` `sub-neg_binary64_71`

Counts

4 → 68

Calls

8 calls:

5.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
5.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
0.0ms	(.f64 (/.f64 (sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)) (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 (+.f64 1 (sqrt.f64 (cos.f64 x))) (/.f64 (cbrt.f64 x) (sqrt.f64 (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))))

series235.0ms (0.2%)

Counts

4 → 18

Calls

4 calls:

85.0ms	(cbrt.f64 x)
77.0ms	(cbrt.f64 x)
39.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
34.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1000 to 652 computations (34.8% saved)

simplify93.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4868	932
1	4868	932

prune18.7s (16%)

Pruning

556 alts after pruning (548 fresh and 8 done)

	Pruned	Kept	Total
New	287	244	531
Fresh	29	304	333
Picked	0	0	0
Done	1	8	9
Total	317	556	873

Error

Counts

873 → 556

Compiler

Compiled 27630 to 17687 computations (36% saved)

localize11.0ms (0%)

Local error

Found 6 expressions with local error:

0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(*.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 (sin.f64 x) x))
0.1b	(*.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 (sin.f64 x) x))
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)

rewrite29.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
40×	`times-frac_binary64_84`
33×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
13×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l_binary64_23` `associate-/r_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `div-inv_binary64_75` `unswap-sqr_binary64_46`
3×	`add-log-exp_binary64_117`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`tan-quot_binary64_237` `-commutative_binary64_9` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

3 → 105

Calls

6 calls:

11.0ms	(*.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 (sin.f64 x) x))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)
0.0ms	(*.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 (sin.f64 x) x))
0.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)

series194.0ms (0.2%)

Counts

3 → 18

Calls

3 calls:

89.0ms	(*.f64 (/.f64 (tan.f64 (/.f64 x 2)) x) (/.f64 (sin.f64 x) x))
75.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
30.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 436 to 374 computations (14.2% saved)

simplify85.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4975	2067
1	4975	2067

localize4.0ms (0%)

Local error

Found 4 expressions with local error:

29.3b	(/.f64 (.f64 (.f64 x x) 1/2) (*.f64 x x))
0.0b	(.f64 (.f64 x x) 1/2)
0.0b	(.f64 (.f64 x x) 1/2)
29.3b	(/.f64 (.f64 (.f64 x x) 1/2) (*.f64 x x))

rewrite18.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
7×	`pow1_binary64_139`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
4×	`add-sqr-sqrt_binary64_100`
3×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `pow-prod-down_binary64_149` `*-un-lft-identity_binary64_78`
2×	`add-log-exp_binary64_117`
1×	`-commutative_binary64_9` `associate-l_binary64_19` `frac-2neg_binary64_89` `times-frac_binary64_84` `div-inv_binary64_75` `associate-/l_binary64_23` `associate-/r*_binary64_22` `unswap-sqr_binary64_46` `clear-num_binary64_77`

Counts

2 → 44

Calls

4 calls:

9.0ms	(/.f64 (.f64 (.f64 x x) 1/2) (*.f64 x x))
6.0ms	(.f64 (.f64 x x) 1/2)
0.0ms	(.f64 (.f64 x x) 1/2)
0.0ms	(/.f64 (.f64 (.f64 x x) 1/2) (*.f64 x x))

series30.0ms (0%)

Counts

2 → 6

Calls

2 calls:

25.0ms	(.f64 (.f64 x x) 1/2)
5.0ms	(/.f64 (.f64 (.f64 x x) 1/2) (*.f64 x x))

Compiler

Compiled 60 to 54 computations (10% saved)

simplify62.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4780	269
1	4780	269

localize15.0ms (0%)

Local error

Found 6 expressions with local error:

21.7b	(-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x)) (/.f64 (cos.f64 x) (*.f64 x x)))
0.7b	(/.f64 (cos.f64 x) (*.f64 x x))
0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x))
0.3b	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x))
0.7b	(/.f64 (cos.f64 x) (*.f64 x x))
21.7b	(-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x)) (/.f64 (cos.f64 x) (*.f64 x x)))

rewrite45.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_100`
43×	`times-frac_binary64_84`
29×	`add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
24×	`add-cube-cbrt_binary64_113`
22×	`add-cbrt-cube_binary64_114` `associate-r_binary64_18`
16×	`cbrt-prod_binary64_109`
9×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129`
8×	`unswap-sqr_binary64_46`
7×	`associate-l_binary64_19` `cancel-sign-sub-inv_binary64_44`
5×	`add-log-exp_binary64_117` `pow1_binary64_139`
4×	`div-inv_binary64_75`
3×	`frac-sub_binary64_87` `swap-sqr_binary64_45` `frac-times_binary64_88` `associate-/l*_binary64_23`
2×	`associate-l/_binary64_21` `associate-r/_binary64_20`
1×	`-commutative_binary64_9` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `associate-/r_binary64_22` `pow-prod-down_binary64_149` `clear-num_binary64_77` `sub-div_binary64_85` `sub-neg_binary64_71`

Counts

3 → 107

Calls

6 calls:

15.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x))
13.0ms	(-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x)) (/.f64 (cos.f64 x) (*.f64 x x)))
5.0ms	(/.f64 (cos.f64 x) (*.f64 x x))
0.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x))
0.0ms	(-.f64 (.f64 (/.f64 (.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x)) (/.f64 (cos.f64 x) (*.f64 x x)))

series117.0ms (0.1%)

Counts

3 → 15

Calls

3 calls:

55.0ms

(-.f64 (*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x)) (/.f64 (cos.f64 x) (*.f64 x x)))

42.0ms

(/.f64 (cos.f64 x) (*.f64 x x))

20.0ms

(*.f64 (/.f64 (*.f64 (cbrt.f64 1) (cbrt.f64 1)) x) (/.f64 (cbrt.f64 1) x))

Compiler

Compiled 316 to 269 computations (14.9% saved)

simplify90.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4954	1804
1	4954	1804

localize14.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(/.f64 (sin.f64 x) x)
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(/.f64 (sin.f64 x) x)
0.1b	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (/.f64 (sin.f64 x) x))) (cbrt.f64 (/.f64 (sin.f64 x) x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.3b	(*.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (/.f64 (sin.f64 x) x)))
0.4b	(cbrt.f64 (/.f64 (sin.f64 x) x))
0.4b	(cbrt.f64 (/.f64 (sin.f64 x) x))
0.4b	(cbrt.f64 (/.f64 (sin.f64 x) x))

rewrite44.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`cbrt-prod_binary64_109`
81×	`add-sqr-sqrt_binary64_100`
69×	`times-frac_binary64_84`
57×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
16×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18`
11×	`pow1_binary64_139`
9×	`pow1/3_binary64_160` `unswap-sqr_binary64_46`
7×	`cbrt-div_binary64_110` `div-inv_binary64_75`
6×	`add-exp-log_binary64_116`
4×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117`
2×	`pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149`
1×	`pow2_binary64_159` `-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-*r/_binary64_20` `pow-plus_binary64_141`

Counts

4 → 144

Calls

8 calls:

16.0ms	(*.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (/.f64 (sin.f64 x) x)))
5.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))
2.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))
2.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))
0.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (/.f64 (sin.f64 x) x))) (cbrt.f64 (/.f64 (sin.f64 x) x))) (/.f64 (tan.f64 (/.f64 x 2)) x))

series493.0ms (0.4%)

Counts

4 → 24

Calls

4 calls:

149.0ms	(*.f64 (cbrt.f64 (/.f64 (sin.f64 x) x)) (cbrt.f64 (/.f64 (sin.f64 x) x)))
118.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))
114.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))
112.0ms	(cbrt.f64 (/.f64 (sin.f64 x) x))

Compiler

Compiled 940 to 652 computations (30.6% saved)

simplify99.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5192	2943

localize20.0ms (0%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (cos.f64 x))
0.1b	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
0.1b	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
0.1b	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))
2.2b	(-.f64 1 (sqrt.f64 (cos.f64 x)))
7.7b	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
7.7b	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
7.7b	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))

rewrite128.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

522×	`times-frac_binary64_84`
415×	`add-sqr-sqrt_binary64_100`
359×	`*-un-lft-identity_binary64_78`
294×	`cbrt-prod_binary64_109`
219×	`add-cube-cbrt_binary64_113`
112×	`difference-of-squares_binary64_47`
87×	`sqrt-prod_binary64_94`
56×	`distribute-lft-out--_binary64_30`
12×	`div-inv_binary64_75`
6×	`add-log-exp_binary64_117` `cancel-sign-sub-inv_binary64_44`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
3×	`cbrt-div_binary64_110` `pow1/3_binary64_160` `associate-/r/_binary64_24`
1×	`flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `sub-neg_binary64_71`

Counts

4 → 344

Calls

8 calls:

15.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
14.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
14.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
6.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))
0.0ms	(/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x))

series622.0ms (0.5%)

Counts

4 → 24

Calls

4 calls:

197.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
195.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
191.0ms	(cbrt.f64 (/.f64 x (/.f64 (-.f64 1 (sqrt.f64 (cos.f64 x))) x)))
38.0ms	(-.f64 1 (sqrt.f64 (cos.f64 x)))

Compiler

Compiled 1444 to 1020 computations (29.4% saved)

simplify169.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

368 → 368

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4994	11722
1	4994	11722

prune43.7s (37.4%)

Pruning

822 alts after pruning (810 fresh and 12 done)

	Pruned	Kept	Total
New	538	293	831
Fresh	26	517	543
Picked	0	0	0
Done	1	12	13
Total	565	822	1387

Error

Counts

1387 → 822

Compiler

Compiled 16410 to 8187 computations (50.1% saved)

simplify903.0ms (0.8%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5343	61300

regimes5.1s (4.3%)

Compiler: Compiled 59282 to 38810 computations (34.5% saved)

bsearch0.0ms (0%)

regimes189.0ms (0.2%)

Compiler: Compiled 1423 to 1079 computations (24.2% saved)

bsearch0.0ms (0%)

regimes261.0ms (0.2%)

Compiler: Compiled 1379 to 1047 computations (24.1% saved)

bsearch35.0ms (0%)

Steps

Iters	Range		Point
8	0.0004748825009007801	0.1561988606931779	0.029652162778630416
8	-23.468369541598076	-0.0005408792989849479	-0.010448904800239387

Compiler

Compiled 1 to 1 computations (0% saved)

regimes261.0ms (0.2%)

Compiler: Compiled 1335 to 1017 computations (23.8% saved)

bsearch42.0ms (0%)

Steps

Iters	Range		Point
8	0.0004748825009007801	0.1561988606931779	0.029652162778630416
8	-23.468369541598076	-0.0005408792989849479	-0.03179237996472754

Compiler

Compiled 1 to 1 computations (0% saved)

regimes151.0ms (0.1%)

Compiler: Compiled 646 to 473 computations (26.8% saved)

bsearch34.0ms (0%)

Steps

Iters	Range		Point
8	0.0004748825009007801	0.1561988606931779	0.004961529386211527
8	-23.468369541598076	-0.0005408792989849479	-0.005849654852384069

Compiler

Compiled 1 to 1 computations (0% saved)

regimes109.0ms (0.1%)

Compiler: Compiled 416 to 315 computations (24.3% saved)

bsearch32.0ms (0%)

Steps

Iters	Range		Point
8	0.0004748825009007801	0.1561988606931779	0.004961529386211527
8	-23.468369541598076	-0.0005408792989849479	-0.005849654852384069

Compiler

Compiled 1 to 1 computations (0% saved)

regimes101.0ms (0.1%)

Compiler: Compiled 382 to 289 computations (24.3% saved)

bsearch34.0ms (0%)

Steps

Iters	Range		Point
8	0.0004748825009007801	0.1561988606931779	0.004961529386211527
8	-23.468369541598076	-0.0005408792989849479	-0.005849654852384069

Compiler

Compiled 1 to 1 computations (0% saved)

regimes55.0ms (0%)

Compiler: Compiled 161 to 119 computations (26.1% saved)

bsearch31.0ms (0%)

Steps

Iters	Range		Point
9	0.1561988606931779	1038961.7268039496	3.4232957165348683
8	-23.468369541598076	-0.0005408792989849479	-3.4738830732676806

Compiler

Compiled 1 to 1 computations (0% saved)

regimes24.0ms (0%)

Compiler: Compiled 16 to 18 computations (-12.5% saved)

bsearch47.0ms (0%)

Steps

Iters	Range		Point
11	2.6345068941681076e+57	2.374462003234296e+80	8.710248358228808e+76
7	-1.5070357225576596e+77	-2.442624934988681e+75	-5.182845402085625e+76

Compiler

Compiled 1 to 1 computations (0% saved)

regimes9.0ms (0%)

Accuracy

Total 0.1b remaining (100%)

Threshold costs 0.1b (100%)

Compiler

Compiled 4 to 6 computations (-50% saved)

bsearch12.0ms (0%)

Compiler: Compiled 231 to 168 computations (27.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	147	306
1	147	306

end0.0ms (0%)

sample28.8s (24.7%)

Algorithm

1×

intervals

Results

901.0ms	2013×	body	2048	valid
233.0ms	1118×	body	1024	valid
196.0ms	1521×	body	512	valid
106.0ms	2568×	body	128	valid
65.0ms	698×	body	256	valid
32.0ms	82×	body	4096	valid

Compiler

Compiled 30195 to 19821 computations (34.4% saved)

Pareto

0.6676641899099861