Details

analyze333.0ms (7.8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12
0	1	1
1	1	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)

sample50.0ms (1.2%)

Algorithm

1×

intervals

Results

24.0ms	59×	body	2048	valid
7.0ms	33×	body	1024	valid
7.0ms	58×	body	512	valid
3.0ms	82×	body	128	valid
2.0ms	21×	body	256	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify22.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

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

Merged error: 29.8b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 1 (cos.f64 x))
13.8b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite15.0ms (0.4%)

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

2 calls:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series47.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

36.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
11.0ms	(-.f64 1 (cos.f64 x))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6395	715

prune62.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	45	8	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	8	54

Merged error: 0.0b

Counts

54 → 8

Compiler

Compiled 793 to 429 computations (45.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))
13.8b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite40.0ms (0.9%)

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

4 calls:

11.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
8.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series137.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
48.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
15.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
7.0ms	(+.f64 1 (cos.f64 x))

simplify72.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4963	1781
1	4963	1781

prune114.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	125	6	131

Merged error: 0b

Counts

131 → 6

Compiler

Compiled 2165 to 1091 computations (49.6% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
0.2b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-exp-log_binary64_116`
31×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100`
28×	`times-frac_binary64_84`
26×	`associate-l_binary64_19` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
22×	`prod-exp_binary64_127`
12×	`cbrt-unprod_binary64_111` `div-exp_binary64_129`
10×	`pow1_binary64_139`
7×	`cbrt-undiv_binary64_112`
6×	`tan-quot_binary64_237` `frac-times_binary64_88` `associate-*r/_binary64_20`
4×	`associate-r_binary64_18` `associate-*l/_binary64_21` `pow-prod-down_binary64_149`
3×	`add-log-exp_binary64_117` `1-exp_binary64_122` `div-inv_binary64_75` `associate-/l_binary64_23` `rec-exp_binary64_128` `associate-/r_binary64_22`
2×	`*-commutative_binary64_9` `unswap-sqr_binary64_46`
1×	`frac-2neg_binary64_89` `clear-num_binary64_77`

Counts

3 → 110

Calls

3 calls:

13.0ms	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
8.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series182.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

82.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
79.0ms	(.f64 (/.f64 1 x) (.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))))
19.0ms	(/.f64 (sin.f64 x) x)

simplify95.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4992	1994
1	4992	1994

prune101.0ms (2.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	119	6	125

Merged error: 0b

Counts

125 → 6

Compiler

Compiled 2160 to 1188 computations (45% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) x)
0.6b	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
14.5b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
14.5b	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))

rewrite45.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`pow1_binary64_139`
32×	`sqrt-pow1_binary64_96`
30×	`sqrt-div_binary64_95`
22×	`pow-prod-down_binary64_149`
19×	`frac-times_binary64_88`
18×	`add-sqr-sqrt_binary64_100`
16×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
13×	`associate-l/_binary64_21` `associate-r/_binary64_20`
12×	`pow1/2_binary64_158`
10×	`pow-prod-up_binary64_148`
9×	`times-frac_binary64_84`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`sqrt-prod_binary64_94` `pow-sqr_binary64_51`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117` `swap-sqr_binary64_45` `associate-r_binary64_18`
3×	`associate-/l_binary64_23` `associate-/r_binary64_22`
1×	`pow2_binary64_159` `*-commutative_binary64_9` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `frac-2neg_binary64_89` `sqrt-unprod_binary64_98` `div-inv_binary64_75` `rem-square-sqrt_binary64_90` `unswap-sqr_binary64_46` `clear-num_binary64_77` `pow-plus_binary64_141`

Counts

4 → 119

Calls

4 calls:

16.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
5.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
5.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
4.0ms	(/.f64 (sin.f64 x) x)

series306.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
106.0ms	(sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x)))
69.0ms	(.f64 (sqrt.f64 (.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))) (sqrt.f64 (*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))))
22.0ms	(/.f64 (sin.f64 x) x)

simplify96.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4933	2155
1	4933	2155

prune174.0ms (4.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	131	6	137

Merged error: 0b

Counts

137 → 6

Compiler

Compiled 3099 to 1758 computations (43.3% saved)

regimes107.0ms (2.5%)

Compiler: Compiled 1077 to 764 computations (29.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample2.1s (49.9%)

Algorithm

1×

intervals

Results

857.0ms	1998×	body	2048	valid
224.0ms	1106×	body	1024	valid
186.0ms	1493×	body	512	valid
94.0ms	2526×	body	128	valid
66.0ms	756×	body	256	valid
46.0ms	121×	body	4096	valid

Compiler

Compiled 508 to 363 computations (28.5% saved)

Details

analyze333.0ms (7.8%)

sample50.0ms (1.2%)

simplify22.0ms (0.5%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite15.0ms (0.4%)

series47.0ms (1.1%)

simplify66.0ms (1.5%)

prune62.0ms (1.5%)

localize9.0ms (0.2%)

rewrite40.0ms (0.9%)

series137.0ms (3.2%)

simplify72.0ms (1.7%)

prune114.0ms (2.7%)

localize10.0ms (0.2%)

rewrite34.0ms (0.8%)

series182.0ms (4.3%)

simplify95.0ms (2.2%)

prune101.0ms (2.4%)

localize11.0ms (0.3%)

rewrite45.0ms (1%)

series306.0ms (7.2%)

simplify96.0ms (2.2%)

prune174.0ms (4.1%)

regimes107.0ms (2.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.1s (49.9%)

Profiling