Details

analyze2.2s (15.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
0%	100%	0%	4
0%	100%	0%	5
0%	100%	0%	6
0%	100%	0%	7
0%	100%	0%	8
0%	100%	0%	9
0%	100%	0%	10
0%	100%	0%	11
0%	100%	0%	12
0%	100%	0%	13
0.1%	99.9%	0%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample269.0ms (1.9%)

Algorithm

1×

intervals

Results

197.0ms	55×	body	2048	valid
37.0ms	93×	body	1024	valid
14.0ms	56×	body	512	valid
5.0ms	30×	body	256	valid
2.0ms	1×	body	4096	valid
2.0ms	21×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify186.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune6.0ms (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

29.0b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize17.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
0.8b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (sin.f64 x))

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
14×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`add-log-exp_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

3 → 84

Calls

3 calls:

17.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
10.0ms	(-.f64 x (sin.f64 x))
7.0ms	(-.f64 x (tan.f64 x))

series181.0ms (1.3%)

Counts

3 → 9

Calls

3 calls:

84.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
53.0ms	(-.f64 x (tan.f64 x))
44.0ms	(-.f64 x (sin.f64 x))

simplify99.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	6199	1847

prune91.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	3	94

Error

Counts

94 → 3

Compiler

Compiled 1614 to 339 computations (79% saved)

localize18.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
0.8b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
0.8b	(-.f64 x (tan.f64 x))
0.8b	(-.f64 x (tan.f64 x))

rewrite80.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`*-un-lft-identity_binary64`
61×	`add-sqr-sqrt_binary64`
48×	`times-frac_binary64`
27×	`add-cube-cbrt_binary64` `cancel-sign-sub-inv_binary64`
21×	`distribute-lft-out--_binary64`
15×	`difference-of-squares_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r*_binary64`
4×	`pow1_binary64` `div-inv_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `distribute-rgt-out--_binary64` `associate-/l*_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sub-div_binary64` `frac-sub_binary64`

Counts

4 → 118

Calls

4 calls:

50.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
7.0ms	(-.f64 x (tan.f64 x))
6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (tan.f64 x))

series354.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

167.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
81.0ms	(-.f64 x (tan.f64 x))
58.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
48.0ms	(-.f64 x (tan.f64 x))

simplify100.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4947	2684
1	4947	2684

prune147.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	130	3	133

Error

Counts

133 → 3

Compiler

Compiled 2815 to 493 computations (82.5% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 9/40)
16.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64`
10×	`associate-r_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`prod-exp_binary64`
4×	`cbrt-unprod_binary64` `associate-l_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64`
3×	`pow-prod-down_binary64` `cancel-sign-sub-inv_binary64`
2×	`diff-log_binary64` `sqr-pow_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 60

Calls

3 calls:

19.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
10.0ms	(.f64 (.f64 x x) 9/40)
6.0ms	(*.f64 27/2800 (pow.f64 x 4))

series75.0ms (0.5%)

Counts

3 → 9

Calls

3 calls:

30.0ms	(*.f64 27/2800 (pow.f64 x 4))
26.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
19.0ms	(.f64 (.f64 x x) 9/40)

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5451	873

prune93.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	69	3	72

Error

Counts

72 → 3

Compiler

Compiled 1196 to 870 computations (27.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (sin.f64 x) 2)
0.8b	(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
0.8b	(-.f64 x (tan.f64 x))
15.2b	(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x)))

rewrite71.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
36×	`add-sqr-sqrt_binary64`
28×	`times-frac_binary64`
25×	`difference-of-squares_binary64`
22×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64`
11×	`cancel-sign-sub-inv_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64` `unpow2_binary64` `sqr-pow_binary64`
7×	`add-exp-log_binary64` `associate-/l*_binary64`
6×	`add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`associate-/r*_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `pow-exp_binary64`

Counts

4 → 113

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x)))
11.0ms	(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
6.0ms	(-.f64 x (tan.f64 x))
6.0ms	(pow.f64 (sin.f64 x) 2)

series247.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

88.0ms	(-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2))
80.0ms	(/.f64 (-.f64 (*.f64 x x) (pow.f64 (sin.f64 x) 2)) (+.f64 x (sin.f64 x)))
50.0ms	(-.f64 x (tan.f64 x))
28.0ms	(pow.f64 (sin.f64 x) 2)

simplify143.0ms (1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4947	2224
1	4947	2224

prune136.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	125	3	128

Error

Counts

128 → 3

Compiler

Compiled 2885 to 872 computations (69.8% saved)

regimes87.0ms (0.6%)

Accuracy

Total 0.0b remaining (36.9%)

Threshold costs 0.0b (36.9%)

Compiler

Compiled 276 to 192 computations (30.4% saved)

bsearch88.0ms (0.6%)

Steps

Iters	Range		Point
11	5.127669329324241e-05	29186608049147348.0	0.031920716483614116
10	-63.439410214120024	-2.2751728216128456e-14	-0.027623021734207834

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	96	55
1	96	55

end0.0ms (0%)

sample9.0s (64.9%)

Algorithm

1×

intervals

Results

6.1s	2078×	body	2048	valid
1.6s	2996×	body	1024	valid
405.0ms	1505×	body	512	valid
142.0ms	734×	body	256	valid
119.0ms	79×	body	4096	valid
67.0ms	608×	body	128	valid

Compiler

Compiled 174 to 121 computations (30.5% saved)

Details

analyze2.2s (15.6%)

sample269.0ms (1.9%)

simplify186.0ms (1.3%)

prune6.0ms (0%)

localize17.0ms (0.1%)

rewrite47.0ms (0.3%)

series181.0ms (1.3%)

simplify99.0ms (0.7%)

prune91.0ms (0.7%)

localize18.0ms (0.1%)

rewrite80.0ms (0.6%)

series354.0ms (2.6%)

simplify100.0ms (0.7%)

prune147.0ms (1.1%)

localize16.0ms (0.1%)

rewrite39.0ms (0.3%)

series75.0ms (0.5%)

simplify72.0ms (0.5%)

prune93.0ms (0.7%)

localize24.0ms (0.2%)

rewrite71.0ms (0.5%)

series247.0ms (1.8%)

simplify143.0ms (1%)

prune136.0ms (1%)

regimes87.0ms (0.6%)

bsearch88.0ms (0.6%)

simplify6.0ms (0%)

end0.0ms (0%)

sample9.0s (64.9%)

Profiling