Details

analyze1.8s (11.6%)

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)

sample103.0ms (0.7%)

Algorithm

1×

intervals

Results

37.0ms	63×	body	1024	valid
22.0ms	46×	body	512	valid
17.0ms	130×	body	128	valid
4.0ms	17×	body	256	valid
3.0ms	22×	body	128	invalid
1.0ms	5×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify238.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (131.0ms)

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

12.7b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 x (tan.f64 B))
5.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite222.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

8.9b

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:

15.0ms	(.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)
4.0ms	(/.f64 F (sin.f64 B))
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 3459 to 1606 computations (53.6% saved)

series1.1s (7%)

Error

0.2b

Counts

4 → 53

Calls

4 calls:

412.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
253.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
207.0ms	(/.f64 x (tan.f64 B))
96.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4535 to 3291 computations (27.4% saved)

simplify141.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (103.0ms)

Iter	Nodes	Cost
0	4917	3964
1	4917	3964

prune259.0ms (1.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	153	15	168
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	155	15	170

Error

0.0b

Counts

170 → 15

Compiler

Compiled 5247 to 2636 computations (49.8% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 x (tan.f64 B))
0.2b	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
0.4b	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
14.1b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite268.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
54×	`times-frac_binary64`
45×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
25×	`unpow-prod-down_binary64` `associate-r_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` `prod-exp_binary64` `unswap-sqr_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `associate-l_binary64`
2×	`frac-2neg_binary64` `clear-num_binary64` `cbrt-unprod_binary64`
1×	`pow-pow_binary64` `pow-prod-down_binary64` `associate-r/_binary64` `-commutative_binary64` `tan-quot_binary64` `associate-/r/_binary64`

Counts

4 → 138

Calls

4 calls:

15.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
10.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
7.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 4662 to 2467 computations (47.1% saved)

series1.3s (8.9%)

Error

0.0b

Counts

4 → 63

Calls

4 calls:

418.0ms	(.f64 F (/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (sin.f64 B)))
399.0ms	(/.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2) (sin.f64 B))
224.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
192.0ms	(/.f64 x (tan.f64 B))

Compiler

Compiled 5730 to 4219 computations (26.4% saved)

simplify119.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4940	6160
1	4940	6160

prune326.0ms (2.2%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	200	1	201
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	200	16	216

Error

0.0b

Counts

216 → 16

Compiler

Compiled 6874 to 3744 computations (45.5% saved)

localize23.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
0.9b	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
14.1b	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)

rewrite184.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

44×	`add-sqr-sqrt_binary64`
24×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64` `*-un-lft-identity_binary64`
22×	`associate-r_binary64`
18×	`add-exp-log_binary64` `cbrt-prod_binary64`
9×	`unpow-prod-down_binary64` `unswap-sqr_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`prod-exp_binary64`
5×	`pow1_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `pow-to-exp_binary64` `pow-exp_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `pow1/3_binary64`
1×	`pow-pow_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 94

Calls

4 calls:

19.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
6.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)

Compiler

Compiled 3793 to 1676 computations (55.8% saved)

series1.0s (6.9%)

Error

0.0b

Counts

4 → 38

Calls

4 calls:

566.0ms	(.f64 (pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (*.f64 F F))) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
239.0ms	(pow.f64 (+.f64 (.f64 2 x) (+.f64 2 (.f64 F F))) -1/2)
86.0ms	(cbrt.f64 F)
73.0ms	(cbrt.f64 F)

Compiler

Compiled 4699 to 3435 computations (26.9% saved)

simplify108.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4917	3790
1	4917	3790

prune234.0ms (1.5%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	132	16	148

Error

0.0b

Counts

148 → 16

Compiler

Compiled 5520 to 2666 computations (51.7% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.2b	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
5.5b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
14.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite186.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

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

Counts

4 → 108

Calls

4 calls:

15.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
5.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
3.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 3591 to 1519 computations (57.7% saved)

series974.0ms (6.4%)

Error

0.0b

Counts

4 → 53

Calls

4 calls:

409.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
233.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
152.0ms	(/.f64 (*.f64 x (cos.f64 B)) (sin.f64 B))
93.0ms	(/.f64 F (sin.f64 B))

Compiler

Compiled 4844 to 3356 computations (30.7% saved)

simplify86.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4921	3921
1	4921	3921

prune208.0ms (1.4%)

Pruning

16 alts after pruning (13 fresh and 3 done)

	Pruned	Kept	Total
New	161	0	161
Fresh	0	13	13
Picked	0	1	1
Done	0	2	2
Total	161	16	177

Error

0.0b

Counts

177 → 16

Compiler

Compiled 5126 to 2275 computations (55.6% saved)

regimes971.0ms (6.4%)

Accuracy

Total 0.2b remaining (94.4%)

Threshold costs 0.2b (94.4%)

Compiler

Compiled 10244 to 7724 computations (24.6% saved)

bsearch133.0ms (0.9%)

Steps

Iters	Range		Point
9	93377.45930867748	91104182791494.83	222155469.19471267
6	-2.1439379544603723e+21	-2.7777855668128547e+20	-5.93455159894269e+20

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	77
1	81	77

end0.0ms (0%)

sample5.1s (33.5%)

Algorithm

1×

intervals

Results

1.3s	2226×	body	1024	valid
536.0ms	4138×	body	128	valid
424.0ms	1092×	body	512	valid
145.0ms	536×	body	256	valid
84.0ms	647×	body	128	invalid
12.0ms	115×	body	128	nan
8.0ms	8×	body	2048	valid

Compiler

Compiled 2624 to 1974 computations (24.8% saved)

Details

analyze1.8s (11.6%)

sample103.0ms (0.7%)

simplify238.0ms (1.6%)

prune9.0ms (0.1%)

localize19.0ms (0.1%)

rewrite222.0ms (1.5%)

series1.1s (7%)

simplify141.0ms (0.9%)

prune259.0ms (1.7%)

localize21.0ms (0.1%)

rewrite268.0ms (1.8%)

series1.3s (8.9%)

simplify119.0ms (0.8%)

prune326.0ms (2.2%)

localize23.0ms (0.2%)

rewrite184.0ms (1.2%)

series1.0s (6.9%)

simplify108.0ms (0.7%)

prune234.0ms (1.5%)

localize19.0ms (0.1%)

rewrite186.0ms (1.2%)

series974.0ms (6.4%)

simplify86.0ms (0.6%)

prune208.0ms (1.4%)

regimes971.0ms (6.4%)

bsearch133.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.1s (33.5%)

Profiling