Details

analyze1.2s (10.8%)

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)

sample66.0ms (0.6%)

Algorithm

1×

intervals

Results

29.0ms	75×	body	1024	valid
12.0ms	137×	body	128	valid
9.0ms	34×	body	512	valid
2.0ms	10×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify550.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (257.0ms)

Iter	Nodes	Cost
0	5717	24

prune17.0ms (0.2%)

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: 0.3b

Counts

2 → 1

Compiler

Compiled 30 to 16 computations (46.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

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))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

14.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
13.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
11.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series1.2s (10.2%)

Counts

4 → 12

Calls

4 calls:

664.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
184.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
172.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
140.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify141.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5715	1997

prune333.0ms (2.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	12	122

Merged error: 0.1b

Counts

122 → 12

Compiler

Compiled 2717 to 1587 computations (41.6% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (sin.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)
0.3b	(pow.f64 (cos.f64 x) 2)

rewrite35.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

5.0ms	(pow.f64 (sin.f64 x) 2)
5.0ms	(pow.f64 (sin.f64 x) 2)
5.0ms	(pow.f64 (cos.f64 x) 2)
5.0ms	(pow.f64 (cos.f64 x) 2)

series182.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(pow.f64 (sin.f64 x) 2)
47.0ms	(pow.f64 (sin.f64 x) 2)
44.0ms	(pow.f64 (cos.f64 x) 2)
43.0ms	(pow.f64 (cos.f64 x) 2)

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5233	660

prune226.0ms (2%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	84	12	96

Merged error: 0.1b

Counts

96 → 12

Compiler

Compiled 2464 to 1620 computations (34.3% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))

rewrite133.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64`
116×	`add-sqr-sqrt_binary64`
96×	`times-frac_binary64`
72×	`difference-of-squares_binary64`
55×	`log-pow_binary64`
54×	`exp-prod_binary64`
44×	`add-cube-cbrt_binary64`
25×	`distribute-lft-out_binary64`
24×	`unpow-prod-down_binary64`
20×	`unpow2_binary64` `sqr-pow_binary64`
12×	`associate-/l*_binary64`
9×	`distribute-lft-out--_binary64`
8×	`add-exp-log_binary64`
7×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-cbrt-cube_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `associate-/r/_binary64`
3×	`log-prod_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `associate-/l/_binary64` `pow-pow_binary64` `div-sub_binary64` `div-inv_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `log-div_binary64` `flip--_binary64`

Counts

4 → 184

Calls

4 calls:

45.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
30.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
6.0ms	(pow.f64 (tan.f64 x) 2)
6.0ms	(pow.f64 (tan.f64 x) 2)

series2.3s (20.7%)

Counts

4 → 12

Calls

4 calls:

1.5s	(log.f64 (exp.f64 (/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))))
632.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
129.0ms	(pow.f64 (tan.f64 x) 2)
119.0ms	(pow.f64 (tan.f64 x) 2)

simplify176.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5159	4308

prune518.0ms (4.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	192	4	196
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	195	13	208

Merged error: 0.0b

Counts

208 → 13

Compiler

Compiled 4916 to 3531 computations (28.2% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite65.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
7×	`add-exp-log_binary64`
6×	`associate-/r*_binary64` `add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
5×	`pow1_binary64`
4×	`associate-/l*_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `diff-log_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `sqr-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 94

Calls

4 calls:

23.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
7.0ms	(-.f64 1 (tan.f64 x))
7.0ms	(+.f64 1 (tan.f64 x))
6.0ms	(pow.f64 (tan.f64 x) 2)

series735.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

438.0ms	(/.f64 (+.f64 (pow.f64 (tan.f64 x) 2) 1) (-.f64 1 (tan.f64 x)))
131.0ms	(pow.f64 (tan.f64 x) 2)
85.0ms	(-.f64 1 (tan.f64 x))
82.0ms	(+.f64 1 (tan.f64 x))

simplify186.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	5041	1981

prune210.0ms (1.8%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	104	15	119

Merged error: 0.0b

Counts

119 → 15

Compiler

Compiled 2424 to 1573 computations (35.1% saved)

regimes216.0ms (1.9%)

Compiler: Compiled 1280 to 976 computations (23.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	36
1	30	36

end0.0ms (0%)

sample2.6s (22.7%)

Algorithm

1×

intervals

Results

782.0ms	2034×	body	1024	valid
332.0ms	4451×	body	128	valid
257.0ms	1027×	body	512	valid
84.0ms	481×	body	256	valid
5.0ms	7×	body	2048	valid

Compiler

Compiled 470 to 356 computations (24.3% saved)

Details

analyze1.2s (10.8%)

sample66.0ms (0.6%)

simplify550.0ms (4.9%)

prune17.0ms (0.2%)

localize18.0ms (0.2%)

rewrite64.0ms (0.6%)

series1.2s (10.2%)

simplify141.0ms (1.2%)

prune333.0ms (2.9%)

localize25.0ms (0.2%)

rewrite35.0ms (0.3%)

series182.0ms (1.6%)

simplify93.0ms (0.8%)

prune226.0ms (2%)

localize23.0ms (0.2%)

rewrite133.0ms (1.2%)

series2.3s (20.7%)

simplify176.0ms (1.6%)

prune518.0ms (4.6%)

localize21.0ms (0.2%)

rewrite65.0ms (0.6%)

series735.0ms (6.5%)

simplify186.0ms (1.6%)

prune210.0ms (1.8%)

regimes216.0ms (1.9%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.6s (22.7%)

Profiling