Details

analyze1.6s (14.6%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14
0	1	1
1	1	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)

sample174.0ms (1.6%)

Algorithm

1×

intervals

Results

116.0ms	67×	body	2048	valid
26.0ms	85×	body	1024	valid
10.0ms	55×	body	512	valid
4.0ms	4×	body	4096	valid
3.0ms	26×	body	256	valid
1.0ms	19×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	1005	14
1	1005	14

prune4.0ms (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

33.5b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite102.0ms (1%)

Algorithm

1×	rewrite-expression-head

Error

32.6b

Rules

45×	`add-sqr-sqrt_binary64` `*-un-lft-identity_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×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64` `associate-/r_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`pow1_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `associate-/l/_binary64` `associate-/r/_binary64`
1×	`div-exp_binary64` `cbrt-undiv_binary64` `frac-2neg_binary64` `div-sub_binary64` `clear-num_binary64` `div-inv_binary64`

Counts

3 → 84

Calls

3 calls:

15.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
3.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 1513 to 300 computations (80.2% saved)

series241.0ms (2.3%)

Error

0.0b

Counts

3 → 27

Calls

3 calls:

103.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
63.0ms	(-.f64 x (tan.f64 x))
41.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1028 to 643 computations (37.5% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4950	2216
1	4950	2216

prune88.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	3	112

Error

Counts

112 → 3

Compiler

Compiled 1902 to 466 computations (75.5% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 9/40 (.f64 x x))
0.3b	(*.f64 27/112000 (pow.f64 x 6))
14.1b	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
18.2b	(+.f64 (.f64 27/112000 (pow.f64 x 6)) (-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))))

rewrite163.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

4 → 78

Calls

4 calls:

12.0ms	(+.f64 (.f64 27/112000 (pow.f64 x 6)) (-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))))
11.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(.f64 9/40 (.f64 x x))
5.0ms	(*.f64 27/112000 (pow.f64 x 6))

Compiler

Compiled 2202 to 1669 computations (24.2% saved)

series180.0ms (1.7%)

Error

Counts

4 → 19

Calls

4 calls:

50.0ms	(+.f64 (.f64 27/112000 (pow.f64 x 6)) (-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (.f64 27/2800 (pow.f64 x 4)))))
45.0ms	(*.f64 27/112000 (pow.f64 x 6))
42.0ms	(-.f64 (.f64 9/40 (.f64 x x)) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
28.0ms	(.f64 9/40 (.f64 x x))

Compiler

Compiled 695 to 602 computations (13.4% saved)

simplify78.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4941	1533
1	4941	1533

prune126.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	97	3	100

Error

Counts

100 → 3

Compiler

Compiled 2228 to 1701 computations (23.7% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
0.0b	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite257.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Error

Rules

218×	`times-frac_binary64`
202×	`add-sqr-sqrt_binary64` `*-un-lft-identity_binary64`
94×	`add-cube-cbrt_binary64`
54×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64` `flip3--_binary64` `flip--_binary64` `div-exp_binary64` `associate-/l*_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64`
2×	`diff-log_binary64` `sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `frac-2neg_binary64` `clear-num_binary64` `associate-/l/_binary64`
1×	`inv-pow_binary64` `pow-flip_binary64` `div-sub_binary64`

Counts

4 → 232

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
11.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 5463 to 1537 computations (71.9% saved)

series331.0ms (3.1%)

Error

Counts

4 → 39

Calls

4 calls:

104.0ms	(/.f64 1 (/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x))))
94.0ms	(/.f64 (-.f64 x (tan.f64 x)) (-.f64 x (sin.f64 x)))
61.0ms	(-.f64 x (tan.f64 x))
32.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1656 to 1073 computations (35.2% saved)

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Counts

271 → 271

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5035	6935

prune212.0ms (2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	271	0	271
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	271	3	274

Error

Counts

274 → 3

Compiler

Compiled 5544 to 1344 computations (75.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sqrt.f64 (-.f64 x (tan.f64 x))) (sqrt.f64 (-.f64 x (tan.f64 x))))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (tan.f64 x))
2.1b	(-.f64 x (sin.f64 x))

rewrite132.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

43×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
30×	`sqrt-prod_binary64`
19×	`pow1_binary64`
15×	`add-cube-cbrt_binary64`
12×	`sqrt-div_binary64` `swap-sqr_binary64`
10×	`add-log-exp_binary64`
9×	`flip3--_binary64` `flip--_binary64` `cancel-sign-sub-inv_binary64` `distribute-lft-out--_binary64`
8×	`pow1/2_binary64` `sqrt-pow1_binary64` `associate-l_binary64` `associate-r_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`frac-times_binary64` `unswap-sqr_binary64`
3×	`diff-log_binary64` `sub-neg_binary64` `pow-prod-down_binary64` `pow-sqr_binary64`
2×	`rem-sqrt-square_binary64` `associate-l/_binary64` `associate-r/_binary64`
1×	`pow2_binary64` `pow-plus_binary64` `prod-exp_binary64` `cbrt-unprod_binary64` `sqrt-unprod_binary64` `sqr-abs_binary64` `rem-square-sqrt_binary64` `*-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

14.0ms	(*.f64 (sqrt.f64 (-.f64 x (tan.f64 x))) (sqrt.f64 (-.f64 x (tan.f64 x))))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

Compiler

Compiled 2756 to 502 computations (81.8% saved)

series238.0ms (2.2%)

Error

Counts

4 → 30

Calls

4 calls:

65.0ms	(-.f64 x (tan.f64 x))
62.0ms	(-.f64 x (tan.f64 x))
52.0ms	(*.f64 (sqrt.f64 (-.f64 x (tan.f64 x))) (sqrt.f64 (-.f64 x (tan.f64 x))))
33.0ms	(-.f64 x (sin.f64 x))

Compiler

Compiled 1333 to 761 computations (42.9% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4887	1700
1	4887	1700

prune104.0ms (1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	144	3	147

Error

Counts

147 → 3

Compiler

Compiled 2699 to 597 computations (77.9% saved)

regimes129.0ms (1.2%)

Accuracy

Total 0.0b remaining (43.8%)

Threshold costs 0.0b (43.8%)

Compiler

Compiled 883 to 562 computations (36.4% saved)

bsearch60.0ms (0.6%)

Steps

Iters	Range		Point
11	2.1635373518452178e-13	442486531866.3032	0.0865345537426781
9	-7017.91898440024	-0.02197677467267197	-0.08693418950050123

Compiler

Compiled 1 to 1 computations (0% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	95	71
1	95	71

end0.0ms (0%)

sample6.1s (57.4%)

Algorithm

1×

intervals

Results

3.8s	2000×	body	2048	valid
1.0s	3008×	body	1024	valid
291.0ms	1509×	body	512	valid
142.0ms	127×	body	4096	valid
95.0ms	734×	body	256	valid
48.0ms	622×	body	128	valid

Compiler

Compiled 474 to 301 computations (36.5% saved)

Details

analyze1.6s (14.6%)

sample174.0ms (1.6%)

simplify77.0ms (0.7%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite102.0ms (1%)

series241.0ms (2.3%)

simplify68.0ms (0.6%)

prune88.0ms (0.8%)

localize13.0ms (0.1%)

rewrite163.0ms (1.5%)

series180.0ms (1.7%)

simplify78.0ms (0.7%)

prune126.0ms (1.2%)

localize8.0ms (0.1%)

rewrite257.0ms (2.4%)

series331.0ms (3.1%)

simplify111.0ms (1%)

prune212.0ms (2%)

localize9.0ms (0.1%)

rewrite132.0ms (1.2%)

series238.0ms (2.2%)

simplify68.0ms (0.6%)

prune104.0ms (1%)

regimes129.0ms (1.2%)

bsearch60.0ms (0.6%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.1s (57.4%)

Profiling