Details

analyze1.7s (18.1%)

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)

sample91.0ms (1%)

Algorithm

1×

intervals

Results

38.0ms	67×	body	1024	valid
18.0ms	137×	body	128	valid
12.0ms	30×	body	512	valid
6.0ms	22×	body	256	valid
3.0ms	23×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 55 to 50 computations (9.1% saved)

simplify235.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4666	32
1	4666	32

prune8.0ms (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: 14.2b

Counts

2 → 2

Compiler

Compiled 69 to 57 computations (17.4% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 F (sin.f64 B))
0.1b	(/.f64 x (tan.f64 B))
9.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite44.0ms (0.5%)

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

series401.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
117.0ms	(/.f64 x (tan.f64 B))
80.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
48.0ms	(/.f64 F (sin.f64 B))

simplify84.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4933	2525
1	4933	2525

prune198.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	115	12	127
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	117	12	129

Merged error: 0.0b

Counts

129 → 12

Compiler

Compiled 3841 to 1851 computations (51.8% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (tan.f64 B))
0.2b	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
0.3b	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

12.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))
12.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
9.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
4.0ms	(/.f64 x (tan.f64 B))

series372.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(/.f64 (.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2)) (sin.f64 B))
117.0ms	(/.f64 x (tan.f64 B))
62.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
52.0ms	(.f64 F (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2))

simplify81.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4978	2141
1	4978	2141

prune137.0ms (1.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	105	12	117

Merged error: 0.0b

Counts

117 → 12

Compiler

Compiled 3119 to 1673 computations (46.4% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 F)
0.6b	(cbrt.f64 F)
2.8b	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

18.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
8.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)
1.0ms	(cbrt.f64 F)
1.0ms	(cbrt.f64 F)

series440.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(.f64 (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 2 x)) -1/2) (/.f64 (cbrt.f64 F) (sin.f64 B)))
81.0ms	(cbrt.f64 F)
78.0ms	(cbrt.f64 F)
60.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 2 x)) -1/2)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5226	2549

prune168.0ms (1.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	105	13	118

Merged error: 0.0b

Counts

118 → 13

Compiler

Compiled 4266 to 1978 computations (53.6% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 x (sin.f64 B))
0.2b	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
9.3b	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
17.1b	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)

rewrite45.0ms (0.5%)

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`
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 → 119

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)
7.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
3.0ms	(/.f64 x (sin.f64 B))

series347.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

149.0ms	(.f64 (/.f64 F (sin.f64 B)) (pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (*.f64 x 2)) -1/2))
81.0ms	(*.f64 (/.f64 x (sin.f64 B)) (cos.f64 B))
65.0ms	(pow.f64 (+.f64 (+.f64 (.f64 F F) 2) (.f64 x 2)) -1/2)
52.0ms	(/.f64 x (sin.f64 B))

simplify90.0ms (1%)

Algorithm

1×	egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4945	2641
1	4945	2641

prune162.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	4	6	10
Picked	0	1	1
Done	0	2	2
Total	134	10	144

Merged error: 0.0b

Counts

144 → 10

Compiler

Compiled 4046 to 1704 computations (57.9% saved)

regimes536.0ms (5.7%)

Compiler: Compiled 5720 to 4288 computations (25% saved)

bsearch64.0ms (0.7%)

Steps

Iters	Range		Point
5	2.7923783560514696e+20	7.830620008482902e+20	2.8254526638305755e+20
2	-31549673031.68364	-27264041820.589233	-27799745721.976036

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	99	103
1	99	103

end0.0ms (0%)

sample4.0s (42.2%)

Algorithm

1×

intervals

Results

1.2s	2221×	body	1024	valid
530.0ms	4113×	body	128	valid
405.0ms	1090×	body	512	valid
143.0ms	569×	body	256	valid
83.0ms	677×	body	128	invalid
11.0ms	109×	body	128	nan
7.0ms	7×	body	2048	valid

Compiler

Compiled 1510 to 1121 computations (25.8% saved)

Details

analyze1.7s (18.1%)

sample91.0ms (1%)

simplify235.0ms (2.5%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

rewrite44.0ms (0.5%)

series401.0ms (4.3%)

simplify84.0ms (0.9%)

prune198.0ms (2.1%)

localize20.0ms (0.2%)

rewrite44.0ms (0.5%)

series372.0ms (3.9%)

simplify81.0ms (0.9%)

prune137.0ms (1.5%)

localize25.0ms (0.3%)

rewrite40.0ms (0.4%)

series440.0ms (4.7%)

simplify66.0ms (0.7%)

prune168.0ms (1.8%)

localize19.0ms (0.2%)

rewrite45.0ms (0.5%)

series347.0ms (3.7%)

simplify90.0ms (1%)

prune162.0ms (1.7%)

regimes536.0ms (5.7%)

bsearch64.0ms (0.7%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (42.2%)

Profiling