Details

analyze1.7s (15.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	93.6%	6.4%	8
9.4%	84.3%	6.4%	9
14.8%	75.7%	9.5%	10
16%	71.4%	12.6%	11
20.9%	65.7%	13.4%	12
24.2%	60.5%	15.3%	13
24.8%	58.6%	16.6%	14

Compiler

Compiled 28 to 24 computations (14.3% saved)

sample138.0ms (1.2%)

Algorithm

1×

intervals

Results

57.0ms	61×	body	1280	valid
29.0ms	45×	body	640	valid
19.0ms	128×	body	80	valid
9.0ms	29×	body	80	invalid
7.0ms	16×	body	320	valid
2.0ms	6×	body	160	valid
1.0ms	5×	body	80	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify331.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (190.0ms)

Iter	Nodes	Cost
0	4665	32
1	4665	32

prune14.0ms (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: 12.7b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 F (sin.f64 B))
5.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite250.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`times-frac_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64` `associate-l_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`associate-/r_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 119

Calls

4 calls:

217.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
18.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
5.0ms	(/.f64 x (tan.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

series736.0ms (6.4%)

Counts

4 → 12

Calls

4 calls:

280.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
237.0ms	(/.f64 x (tan.f64 B))
114.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
104.0ms	(/.f64 F (sin.f64 B))

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5163	2585

prune211.0ms (1.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	120	11	131
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	122	11	133

Merged error: 0.0b

Counts

133 → 11

Compiler

Compiled 3883 to 1867 computations (51.9% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
0.3b	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
25×	`associate-r_binary64` `unpow-prod-down_binary64`
22×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
10×	`associate-/l*_binary64`
9×	`sqr-pow_binary64`
7×	`pow1_binary64` `div-exp_binary64`
6×	`associate-/r*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `cbrt-undiv_binary64` `associate-l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `pow-pow_binary64` `associate-/r/_binary64` `tan-quot_binary64` `-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

19.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
16.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
11.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
5.0ms	(/.f64 x (tan.f64 B))

series819.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (sin.f64 B)))
240.0ms	(/.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2) (sin.f64 B))
216.0ms	(/.f64 x (tan.f64 B))
96.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify189.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4935	4002
1	4935	4002

prune235.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	153	12	165

Merged error: 0.0b

Counts

165 → 12

Compiler

Compiled 5000 to 2656 computations (46.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 F (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
5.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite47.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
26×	`associate-l_binary64`
25×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
10×	`associate-r_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `associate-/r_binary64` `cbrt-undiv_binary64` `associate-/l_binary64` `div-inv_binary64` `pow-exp_binary64`
2×	`associate-l/_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 123

Calls

4 calls:

18.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
9.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
4.0ms	(/.f64 F (sin.f64 B))

series636.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

274.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
173.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
98.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
91.0ms	(/.f64 F (sin.f64 B))

simplify171.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4943	2706
1	4943	2706

prune183.0ms (1.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	133	2	135
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	135	12	147

Merged error: 0.0b

Counts

147 → 12

Compiler

Compiled 4387 to 1905 computations (56.6% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 F (sin.f64 B))
0.3b	(/.f64 1 (/.f64 (tan.f64 B) x))
5.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
18.0b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite49.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
78×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
31×	`add-exp-log_binary64`
16×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
13×	`associate-l_binary64`
11×	`div-exp_binary64`
8×	`unpow-prod-down_binary64`
7×	`associate-r_binary64` `div-inv_binary64`
6×	`pow1_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l*_binary64`
5×	`cbrt-undiv_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`cbrt-unprod_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64`
1×	`pow-pow_binary64` `associate-/r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 167

Calls

4 calls:

18.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
10.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
8.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
4.0ms	(/.f64 F (sin.f64 B))

series633.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

266.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
176.0ms	(/.f64 1 (/.f64 (tan.f64 B) x))
100.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
91.0ms	(/.f64 F (sin.f64 B))

simplify191.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4937	3477
1	4937	3477

prune236.0ms (2.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	179	12	191

Merged error: 0.0b

Counts

191 → 12

Compiler

Compiled 5304 to 2523 computations (52.4% saved)

regimes108.0ms (0.9%)

Compiler: Compiled 852 to 666 computations (21.8% saved)

bsearch185.0ms (1.6%)

Steps

Iters	Range		Point
9	0.18628361777479926	83489.93999905977	54677.39711774091
9	-6.998522250784078e+46	-1.9647977373106593e+41	-1.0580176342636273e+42

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	99	100
1	99	100

end0.0ms (0%)

sample4.1s (35.7%)

Algorithm

1×

intervals

Results

1.6s	1730×	body	1280	valid
869.0ms	1416×	body	640	valid
555.0ms	3900×	body	80	valid
278.0ms	646×	body	320	valid
105.0ms	692×	body	80	invalid
91.0ms	308×	body	160	valid
15.0ms	143×	body	80	nan
1.0ms	1×	body	1280	invalid

Compiler

Compiled 375 to 279 computations (25.6% saved)

Details

analyze1.7s (15.2%)

sample138.0ms (1.2%)

simplify331.0ms (2.9%)

prune14.0ms (0.1%)

localize22.0ms (0.2%)

rewrite250.0ms (2.2%)

series736.0ms (6.4%)

simplify111.0ms (1%)

prune211.0ms (1.8%)

localize20.0ms (0.2%)

rewrite58.0ms (0.5%)

series819.0ms (7.1%)

simplify189.0ms (1.7%)

prune235.0ms (2.1%)

localize21.0ms (0.2%)

rewrite47.0ms (0.4%)

series636.0ms (5.6%)

simplify171.0ms (1.5%)

prune183.0ms (1.6%)

localize23.0ms (0.2%)

rewrite49.0ms (0.4%)

series633.0ms (5.5%)

simplify191.0ms (1.7%)

prune236.0ms (2.1%)

regimes108.0ms (0.9%)

bsearch185.0ms (1.6%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample4.1s (35.7%)

Profiling