Details

analyze1.4s (14.7%)

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)

sample163.0ms (1.8%)

Algorithm

1×

intervals

Results

97.0ms	69×	body	2048	valid
35.0ms	102×	body	1024	valid
9.0ms	8×	body	4096	valid
8.0ms	41×	body	512	valid
2.0ms	16×	body	256	valid
2.0ms	20×	body	128	valid

Compiler

Compiled 19 to 14 computations (26.3% saved)

simplify182.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

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

Merged error: 34.7b

Counts

2 → 1

Compiler

Compiled 18 to 12 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite26.0ms (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:

9.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
6.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series152.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

66.0ms	(/.f64 (-.f64 x (sin.f64 x)) (-.f64 x (tan.f64 x)))
52.0ms	(-.f64 x (tan.f64 x))
34.0ms	(-.f64 x (sin.f64 x))

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	6199	1847

prune79.0ms (0.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.0b

Counts

94 → 4

Compiler

Compiled 1618 to 344 computations (78.7% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 27/2800 (pow.f64 x 4))
0.3b	(.f64 (.f64 x x) 9/40)
15.3b	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))

rewrite27.0ms (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:

8.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
6.0ms	(*.f64 27/2800 (pow.f64 x 4))
6.0ms	(.f64 (.f64 x x) 9/40)

series71.0ms (0.8%)

Counts

3 → 9

Calls

3 calls:

29.0ms	(-.f64 (.f64 (.f64 x x) 9/40) (+.f64 1/2 (*.f64 27/2800 (pow.f64 x 4))))
24.0ms	(*.f64 27/2800 (pow.f64 x 4))
18.0ms	(.f64 (.f64 x x) 9/40)

simplify58.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5451	873

prune69.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	69	4	73

Merged error: 0.0b

Counts

73 → 4

Compiler

Compiled 1214 to 882 computations (27.3% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (tan.f64 x))
1.5b	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))

rewrite60.0ms (0.7%)

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:

34.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (tan.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series299.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(-.f64 (/.f64 x (-.f64 x (tan.f64 x))) (/.f64 (sin.f64 x) (-.f64 x (tan.f64 x))))
63.0ms	(/.f64 (sin.f64 x) (-.f64 x (tan.f64 x)))
51.0ms	(-.f64 x (tan.f64 x))
47.0ms	(-.f64 x (tan.f64 x))

simplify75.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4947	2684
1	4947	2684

prune100.0ms (1.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	130	4	134

Merged error: 0.0b

Counts

134 → 4

Compiler

Compiled 2806 to 487 computations (82.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x (tan.f64 x)))
0.1b	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
1.4b	(-.f64 x (tan.f64 x))
1.4b	(-.f64 x (sin.f64 x))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
47×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
26×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`
17×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
5×	`associate-/r_binary64` `associate-l*_binary64`
4×	`associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
3×	`unswap-sqr_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64` `-commutative_binary64`

Counts

4 → 123

Calls

4 calls:

15.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
6.0ms	(/.f64 1 (-.f64 x (tan.f64 x)))
4.0ms	(-.f64 x (sin.f64 x))
4.0ms	(-.f64 x (tan.f64 x))

series183.0ms (2%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(*.f64 (-.f64 x (sin.f64 x)) (/.f64 1 (-.f64 x (tan.f64 x))))
50.0ms	(-.f64 x (tan.f64 x))
44.0ms	(/.f64 1 (-.f64 x (tan.f64 x)))
25.0ms	(-.f64 x (sin.f64 x))

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4931	2187
1	4931	2187

prune98.0ms (1.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	135	4	139

Merged error: 0.0b

Counts

139 → 4

Compiler

Compiled 2345 to 741 computations (68.4% saved)

regimes87.0ms (0.9%)

Compiler: Compiled 489 to 317 computations (35.2% saved)

bsearch56.0ms (0.6%)

Steps

Iters	Range		Point
11	1.2142740521310512e-09	40015538968.081276	0.030611731145775405
9	-0.37058326659578555	-2.5138101129751348e-08	-0.027204265308962153

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	67
1	97	67

end0.0ms (0%)

sample5.9s (63.5%)

Algorithm

1×

intervals

Results

3.8s	1985×	body	2048	valid
1.0s	3042×	body	1024	valid
265.0ms	1478×	body	512	valid
111.0ms	109×	body	4096	valid
95.0ms	723×	body	256	valid
64.0ms	663×	body	128	valid

Compiler

Compiled 269 to 171 computations (36.4% saved)

Details

analyze1.4s (14.7%)

sample163.0ms (1.8%)

simplify182.0ms (2%)

prune4.0ms (0%)

localize8.0ms (0.1%)

rewrite26.0ms (0.3%)

series152.0ms (1.6%)

simplify81.0ms (0.9%)

prune79.0ms (0.9%)

localize8.0ms (0.1%)

rewrite27.0ms (0.3%)

series71.0ms (0.8%)

simplify58.0ms (0.6%)

prune69.0ms (0.7%)

localize8.0ms (0.1%)

rewrite60.0ms (0.7%)

series299.0ms (3.2%)

simplify75.0ms (0.8%)

prune100.0ms (1.1%)

localize8.0ms (0.1%)

rewrite40.0ms (0.4%)

series183.0ms (2%)

simplify66.0ms (0.7%)

prune98.0ms (1.1%)

regimes87.0ms (0.9%)

bsearch56.0ms (0.6%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (63.5%)

Profiling