Details

analyze1.7s (12.5%)

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)

sample97.0ms (0.7%)

Algorithm

1×

intervals

Results

43.0ms	75×	body	1024	valid
16.0ms	131×	body	128	valid
14.0ms	37×	body	512	valid
3.0ms	13×	body	256	valid
3.0ms	22×	body	128	invalid

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify235.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune9.0ms (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

Error

11.3b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.1b	(/.f64 F (sin.f64 B))
5.7b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.7b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite213.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

44×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64` `*-un-lft-identity_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×	`prod-exp_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `associate-/r_binary64`
5×	`pow1_binary64` `div-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64`
1×	`pow-pow_binary64` `associate-l/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 115

Calls

4 calls:

14.0ms	(.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)
3.0ms	(/.f64 x (tan.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series908.0ms (6.6%)

Error

0.1b

Counts

4 → 43

Calls

4 calls:

337.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
212.0ms	(/.f64 x (tan.f64 B))
202.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
97.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3384 to 2458 computations (27.4% saved)

simplify97.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4919	3354
1	4919	3354

prune230.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	147	11	158
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	11	160

Error

0.0b

Counts

160 → 11

Compiler

Compiled 4672 to 2295 computations (50.9% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
5.7b	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
17.7b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
17.7b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

rewrite465.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`add-exp-log_binary64`
58×	`add-sqr-sqrt_binary64`
47×	`prod-exp_binary64`
44×	`unpow-prod-down_binary64`
28×	`sqrt-prod_binary64`
25×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
23×	`associate-l_binary64`
18×	`add-cbrt-cube_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `unswap-sqr_binary64`
12×	`sqr-pow_binary64` `swap-sqr_binary64`
11×	`associate-r_binary64`
10×	`div-exp_binary64` `times-frac_binary64`
8×	`pow1_binary64`
7×	`cbrt-unprod_binary64`
4×	`add-log-exp_binary64` `sqrt-div_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `flip3-+_binary64` `flip-+_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `cbrt-undiv_binary64` `*-commutative_binary64`
1×	`associate-*l/_binary64` `div-inv_binary64` `pow2_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`

Counts

4 → 150

Calls

4 calls:

22.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
19.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))
6.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
6.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

Compiler

Compiled 7593 to 4488 computations (40.9% saved)

series811.0ms (5.9%)

Error

0.0b

Counts

4 → 52

Calls

4 calls:

353.0ms	(.f64 (/.f64 F (sin.f64 B)) (.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2)))
129.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
128.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
125.0ms	(.f64 (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F)))) -1/2) (pow.f64 (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))) -1/2))

Compiler

Compiled 4822 to 3546 computations (26.5% saved)

simplify121.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4942	5944
1	4942	5944

prune362.0ms (2.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	202	11	213

Error

0.0b

Counts

213 → 11

Compiler

Compiled 7468 to 4198 computations (43.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x)))))) (sin.f64 B))
0.3b	(.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))))))
0.3b	(/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x)))))
17.7b	(sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))))

rewrite257.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

49×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
38×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64`
26×	`sqrt-prod_binary64`
24×	`associate-r_binary64`
20×	`add-cbrt-cube_binary64`
11×	`div-exp_binary64`
9×	`pow1_binary64` `associate-/r*_binary64`
8×	`prod-exp_binary64`
6×	`sqrt-div_binary64` `cbrt-undiv_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `associate-/r/_binary64` `associate-/l*_binary64` `cbrt-unprod_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `pow-flip_binary64` `1-exp_binary64` `rec-exp_binary64` `div-inv_binary64` `associate-l_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `frac-2neg_binary64` `clear-num_binary64` `un-div-inv_binary64` `associate-*r/_binary64` `associate-/l/_binary64`
1×	`rem-sqrt-square_binary64` `inv-pow_binary64` `pow-prod-down_binary64` `*-commutative_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))))))
13.0ms	(/.f64 (.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x)))))) (sin.f64 B))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x)))))
6.0ms	(sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))))

Compiler

Compiled 4761 to 2739 computations (42.5% saved)

series758.0ms (5.5%)

Error

0.0b

Counts

4 → 50

Calls

4 calls:

317.0ms	(/.f64 (.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x)))))) (sin.f64 B))
145.0ms	(.f64 F (/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (*.f64 2 x))))))
122.0ms	(/.f64 1 (sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x)))))
114.0ms	(sqrt.f64 (+.f64 (.f64 F F) (+.f64 2 (.f64 2 x))))

Compiler

Compiled 3790 to 2839 computations (25.1% saved)

simplify108.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4935	4651
1	4935	4651

prune267.0ms (1.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	188	11	199

Error

0.0b

Counts

199 → 11

Compiler

Compiled 5661 to 3194 computations (43.6% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))))
0.2b	(/.f64 F (.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
17.7b	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

rewrite154.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

23×	`add-sqr-sqrt_binary64`
18×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`times-frac_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`sqrt-div_binary64` `associate-/l_binary64` `associate-r*_binary64`
4×	`add-log-exp_binary64` `associate-r/_binary64` `associate-/r_binary64`
3×	`flip3-+_binary64` `flip-+_binary64` `div-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `associate-l_binary64`
2×	`prod-exp_binary64` `cbrt-unprod_binary64` `frac-2neg_binary64` `clear-num_binary64` `div-inv_binary64` `unswap-sqr_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-prod-down_binary64` `*-commutative_binary64` `tan-quot_binary64`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/.f64 F (.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
10.0ms	(.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))
3.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 2709 to 1367 computations (49.5% saved)

series951.0ms (6.9%)

Error

0.0b

Counts

4 → 54

Calls

4 calls:

326.0ms	(/.f64 F (.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))))))
256.0ms	(.f64 (sin.f64 B) (sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F)))))
189.0ms	(/.f64 x (tan.f64 B))
114.0ms	(sqrt.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))))

Compiler

Compiled 4108 to 2839 computations (30.9% saved)

simplify92.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4941	3309
1	4941	3309

prune171.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	4	4	8
Picked	1	0	1
Done	0	2	2
Total	145	10	155

Error

0.0b

Counts

155 → 10

Compiler

Compiled 3905 to 1941 computations (50.3% saved)

regimes852.0ms (6.2%)

Accuracy

Total 0.2b remaining (92.4%)

Threshold costs 0.2b (92.4%)

Compiler

Compiled 8996 to 6824 computations (24.1% saved)

bsearch103.0ms (0.7%)

Steps

Iters	Range		Point
9	844656197646805.5	2.617711100231379e+22	858337087626449.4
3	-2.139687726879464e+18	-1.7712338408992847e+18	-1.794262208773046e+18

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	71
1	53	71

end0.0ms (0%)

sample4.7s (34.2%)

Algorithm

1×

intervals

Results

1.2s	2231×	body	1024	valid
513.0ms	4086×	body	128	valid
405.0ms	1087×	body	512	valid
146.0ms	589×	body	256	valid
89.0ms	708×	body	128	invalid
9.0ms	100×	body	128	nan
6.0ms	7×	body	2048	valid
2.0ms	3×	body	1024	invalid

Compiler

Compiled 2308 to 1745 computations (24.4% saved)

Details

analyze1.7s (12.5%)

sample97.0ms (0.7%)

simplify235.0ms (1.7%)

prune9.0ms (0.1%)

localize20.0ms (0.1%)

rewrite213.0ms (1.5%)

series908.0ms (6.6%)

simplify97.0ms (0.7%)

prune230.0ms (1.7%)

localize24.0ms (0.2%)

rewrite465.0ms (3.4%)

series811.0ms (5.9%)

simplify121.0ms (0.9%)

prune362.0ms (2.6%)

localize17.0ms (0.1%)

rewrite257.0ms (1.9%)

series758.0ms (5.5%)

simplify108.0ms (0.8%)

prune267.0ms (1.9%)

localize15.0ms (0.1%)

rewrite154.0ms (1.1%)

series951.0ms (6.9%)

simplify92.0ms (0.7%)

prune171.0ms (1.2%)

regimes852.0ms (6.2%)

bsearch103.0ms (0.7%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.7s (34.2%)

Profiling