Details

analyze986.0ms (18.6%)

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
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

Compiler

Compiled 16 to 13 computations (18.8% saved)

sample43.0ms (0.8%)

Algorithm

1×

intervals

Results

16.0ms	256×	body	128	valid
10.0ms	118×	body	128	invalid
4.0ms	81×	body	128	nan

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify208.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	5019	19

prune4.0ms (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

2.4b

Counts

2 → 2

Compiler

Compiled 41 to 34 computations (17.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 a (pow.f64 k m))
0.0b	(*.f64 k (+.f64 k 10))
2.4b	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-exp-log_binary64_2162`
17×	`add-sqr-sqrt_binary64_2146`
12×	`*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
11×	`associate-r_binary64_2064`
10×	`add-cube-cbrt_binary64_2159`
7×	`prod-exp_binary64_2173`
6×	`associate-l_binary64_2065`
5×	`pow1_binary64_2185`
4×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203` `div-exp_binary64_2175`
3×	`associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `times-frac_binary64_2130` `cbrt-unprod_binary64_2157`
2×	`cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `pow-exp_binary64_2192` `-commutative_binary64_2055` `sqr-pow_binary64_2096` `pow-to-exp_binary64_2193` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `associate-/l*_binary64_2069` `distribute-lft-out_binary64_2075` `distribute-rgt-in_binary64_2074` `div-inv_binary64_2121` `distribute-lft-in_binary64_2073` `frac-2neg_binary64_2135`

Counts

3 → 73

Calls

3 calls:

7.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
7.0ms	(*.f64 k (+.f64 k 10))
6.0ms	(*.f64 a (pow.f64 k m))

series215.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

132.0ms	(/.f64 (.f64 a (pow.f64 k m)) (+.f64 1 (.f64 k (+.f64 k 10))))
57.0ms	(*.f64 a (pow.f64 k m))
26.0ms	(*.f64 k (+.f64 k 10))

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4956	1226
1	4956	1226

prune78.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Error

2.3b

Counts

84 → 4

Compiler

Compiled 1595 to 863 computations (45.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
0.1b	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
13.1b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
13.1b	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

rewrite72.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`add-sqr-sqrt_binary64_2146`
110×	`times-frac_binary64_2130`
64×	`sqrt-prod_binary64_2140`
61×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
48×	`associate-r_binary64_2064`
30×	`add-exp-log_binary64_2162`
24×	`unpow-prod-down_binary64_2203` `associate-l_binary64_2065`
21×	`unswap-sqr_binary64_2092`
18×	`add-cbrt-cube_binary64_2160`
12×	`sqr-pow_binary64_2096`
11×	`div-exp_binary64_2175`
10×	`sqrt-div_binary64_2141`
8×	`pow1_binary64_2185` `prod-exp_binary64_2173`
6×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
5×	`cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
3×	`associate-/l*_binary64_2069` `div-inv_binary64_2121`
2×	`sqrt-pow1_binary64_2142` `pow-exp_binary64_2192` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `pow-to-exp_binary64_2193`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l/_binary64_2067` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `frac-2neg_binary64_2135`

Counts

4 → 188

Calls

4 calls:

37.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
5.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

series233.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

138.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 1 (.f64 k (+.f64 k 10))))) (/.f64 (pow.f64 k m) (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))))
66.0ms	(/.f64 a (sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10)))))
15.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))
14.0ms	(sqrt.f64 (+.f64 1 (*.f64 k (+.f64 k 10))))

simplify176.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4928	6633
1	4928	6633

prune337.0ms (6.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	200	0	200
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	200	4	204

Error

2.3b

Counts

204 → 4

Compiler

Compiled 6879 to 4544 computations (33.9% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 a (pow.f64 k m))
0.0b	(*.f64 k (+.f64 k 10))
0.1b	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
2.4b	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-exp-log_binary64_2162`
36×	`times-frac_binary64_2130`
34×	`add-sqr-sqrt_binary64_2146`
29×	`*-un-lft-identity_binary64_2124`
27×	`add-cube-cbrt_binary64_2159`
26×	`div-exp_binary64_2175`
22×	`add-cbrt-cube_binary64_2160`
16×	`prod-exp_binary64_2173`
11×	`associate-r_binary64_2064`
8×	`associate-/r*_binary64_2068`
7×	`cbrt-undiv_binary64_2158` `pow1_binary64_2185`
6×	`associate-/l_binary64_2069` `associate-l*_binary64_2065` `div-inv_binary64_2121`
5×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193` `1-exp_binary64_2168` `rec-exp_binary64_2174`
4×	`unswap-sqr_binary64_2092` `unpow-prod-down_binary64_2203` `add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
2×	`clear-num_binary64_2123` `-commutative_binary64_2055` `sqr-pow_binary64_2096` `associate-r/_binary64_2066` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`
1×	`pow-prod-down_binary64_2195` `associate-/r/_binary64_2070` `distribute-lft-out_binary64_2075` `distribute-rgt-in_binary64_2074` `pow-flip_binary64_2198` `inv-pow_binary64_2209` `distribute-lft-in_binary64_2073`

Counts

4 → 135

Calls

4 calls:

9.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
8.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
7.0ms	(*.f64 k (+.f64 k 10))
5.0ms	(*.f64 a (pow.f64 k m))

series308.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m)))
107.0ms	(/.f64 1 (/.f64 (+.f64 1 (.f64 k (+.f64 k 10))) (.f64 a (pow.f64 k m))))
59.0ms	(*.f64 a (pow.f64 k m))
27.0ms	(*.f64 k (+.f64 k 10))

simplify130.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4921	2954
1	4921	2954

prune144.0ms (2.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	147	4	151

Error

0.0b

Counts

151 → 4

Compiler

Compiled 3120 to 1834 computations (41.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
0.6b	(cbrt.f64 a)
0.6b	(cbrt.f64 a)
2.4b	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-exp-log_binary64_2162`
18×	`prod-exp_binary64_2173`
16×	`add-cbrt-cube_binary64_2160`
9×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `cbrt-prod_binary64_2155` `*-un-lft-identity_binary64_2124` `div-exp_binary64_2175`
8×	`cbrt-unprod_binary64_2157`
5×	`cbrt-undiv_binary64_2158`
4×	`pow1_binary64_2185` `add-log-exp_binary64_2163`
3×	`associate-/r*_binary64_2068` `pow1/3_binary64_2206` `times-frac_binary64_2130`
2×	`associate-/r/_binary64_2070` `pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
1×	`clear-num_binary64_2123` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 66

Calls

4 calls:

13.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)

series399.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

162.0ms	(/.f64 (.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (.f64 (pow.f64 k m) (cbrt.f64 a))) (+.f64 1 (.f64 k (+.f64 k 10))))
80.0ms	(cbrt.f64 a)
80.0ms	(cbrt.f64 a)
76.0ms	(cbrt.f64 a)

simplify62.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4999	1161
1	4999	1161

prune70.0ms (1.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	78	4	82

Error

0.0b

Counts

82 → 4

Compiler

Compiled 1722 to 813 computations (52.8% saved)

regimes120.0ms (2.3%)

Accuracy

Total 0.2b remaining (61.1%)

Threshold costs 0.2b (61.1%)

Compiler

Compiled 1084 to 846 computations (22% saved)

bsearch13.0ms (0.3%)

Steps

Iters	Range		Point
3	5.166458792131295e-17	6.447403773807031e-17	5.218508833152239e-17

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	74
1	42	74

end0.0ms (0%)

sample1.5s (28.5%)

Algorithm

1×

intervals

Results

520.0ms	8000×	body	128	valid
277.0ms	3214×	body	128	invalid
97.0ms	2019×	body	128	nan

Compiler

Compiled 327 to 251 computations (23.2% saved)

Details

analyze986.0ms (18.6%)

sample43.0ms (0.8%)

simplify208.0ms (3.9%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite25.0ms (0.5%)

series215.0ms (4.1%)

simplify59.0ms (1.1%)

prune78.0ms (1.5%)

localize11.0ms (0.2%)

rewrite72.0ms (1.4%)

series233.0ms (4.4%)

simplify176.0ms (3.3%)

prune337.0ms (6.4%)

localize13.0ms (0.2%)

rewrite40.0ms (0.7%)

series308.0ms (5.8%)

simplify130.0ms (2.4%)

prune144.0ms (2.7%)

localize14.0ms (0.3%)

rewrite22.0ms (0.4%)

series399.0ms (7.5%)

simplify62.0ms (1.2%)

prune70.0ms (1.3%)

regimes120.0ms (2.3%)

bsearch13.0ms (0.3%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.5s (28.5%)

Profiling