Details

analyze679.0ms (9.9%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	65×	body	1024	valid
7.0ms	26×	body	512	valid
6.0ms	143×	body	128	valid
2.0ms	22×	body	256	valid

Compiler

Compiled 31 to 18 computations (41.9% saved)

simplify309.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (143.0ms)

Iter	Nodes	Cost
0	5717	24

prune4.0ms (0.1%)

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)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite34.0ms (0.5%)

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:

7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))

series632.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
103.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
94.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
77.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5715	1997

prune190.0ms (2.8%)

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: 0.0b

Counts

122 → 12

Compiler

Compiled 2705 to 1579 computations (41.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite73.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
15×	`difference-of-squares_binary64`
12×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
5×	`distribute-lft-out_binary64`
4×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 96

Calls

4 calls:

53.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)

series797.0ms (11.7%)

Counts

4 → 12

Calls

4 calls:

558.0ms	(-.f64 (/.f64 1 (+.f64 (pow.f64 (tan.f64 x) 2) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
84.0ms	(pow.f64 (tan.f64 x) 2)
77.0ms	(pow.f64 (tan.f64 x) 2)
77.0ms	(pow.f64 (tan.f64 x) 2)

simplify98.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4989	2346
1	4989	2346

prune192.0ms (2.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	5	108
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	108	12	120

Merged error: 0.0b

Counts

120 → 12

Compiler

Compiled 3159 to 2239 computations (29.1% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite93.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
30×	`times-frac_binary64`
15×	`difference-of-squares_binary64`
12×	`unpow-prod-down_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow-unpow_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `unpow2_binary64` `sqr-pow_binary64` `distribute-lft-out--_binary64`
4×	`distribute-lft-out_binary64` `add-cbrt-cube_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `div-inv_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 87

Calls

4 calls:

73.0ms	(-.f64 (/.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)

series753.0ms (11%)

Counts

4 → 12

Calls

4 calls:

580.0ms	(-.f64 (/.f64 1 (+.f64 (/.f64 (pow.f64 (sin.f64 x) 2) (pow.f64 (cos.f64 x) 2)) 1)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1)))
81.0ms	(pow.f64 (tan.f64 x) 2)
66.0ms	(pow.f64 (tan.f64 x) 2)
25.0ms	(pow.f64 (sin.f64 x) 2)

simplify78.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5110	2814

prune199.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	99	12	111

Merged error: 0.0b

Counts

111 → 12

Compiler

Compiled 3655 to 2514 computations (31.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.5b	(pow.f64 (tan.f64 x) 4)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
30×	`difference-of-squares_binary64`
28×	`add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64`
13×	`pow1_binary64`
12×	`sqr-pow_binary64`
11×	`distribute-lft-out_binary64`
10×	`add-exp-log_binary64` `associate-/l*_binary64`
8×	`add-cbrt-cube_binary64`
6×	`pow-unpow_binary64`
5×	`distribute-lft-out--_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `tan-quot_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

15.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 4)
3.0ms	(pow.f64 (tan.f64 x) 2)

series648.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

385.0ms	(/.f64 (-.f64 1 (pow.f64 (tan.f64 x) 4)) (+.f64 (pow.f64 (tan.f64 x) 2) 1))
117.0ms	(pow.f64 (tan.f64 x) 4)
80.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
65.0ms	(pow.f64 (tan.f64 x) 2)

simplify76.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5297	3002

prune213.0ms (3.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	144	2	146
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	145	13	158

Merged error: 0.0b

Counts

158 → 13

Compiler

Compiled 4109 to 2580 computations (37.2% saved)

regimes113.0ms (1.6%)

Compiler: Compiled 1188 to 898 computations (24.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	35	39
1	35	39

end0.0ms (0%)

sample1.4s (21%)

Algorithm

1×

intervals

Results

412.0ms	1984×	body	1024	valid
187.0ms	4514×	body	128	valid
128.0ms	963×	body	512	valid
48.0ms	534×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 442 to 334 computations (24.4% saved)

Details

analyze679.0ms (9.9%)

sample39.0ms (0.6%)

simplify309.0ms (4.5%)

prune4.0ms (0.1%)

localize16.0ms (0.2%)

rewrite34.0ms (0.5%)

series632.0ms (9.2%)

simplify81.0ms (1.2%)

prune190.0ms (2.8%)

localize9.0ms (0.1%)

rewrite73.0ms (1.1%)

series797.0ms (11.7%)

simplify98.0ms (1.4%)

prune192.0ms (2.8%)

localize18.0ms (0.3%)

rewrite93.0ms (1.4%)

series753.0ms (11%)

simplify78.0ms (1.1%)

prune199.0ms (2.9%)

localize13.0ms (0.2%)

rewrite41.0ms (0.6%)

series648.0ms (9.5%)

simplify76.0ms (1.1%)

prune213.0ms (3.1%)

regimes113.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.4s (21%)

Profiling