Details

analyze517.0ms (11.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample20.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify205.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	514	22
1	514	22

prune2.0ms (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: 26.1b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.8b	(-.f64 (.f64 b c) (.f64 a d))
25.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`times-frac_binary64_2149`
7×	`add-log-exp_binary64_2182`
5×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`pow1_binary64_2204` `associate-/r_binary64_2087` `associate-/l_binary64_2088`
2×	`flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `flip3-+_binary64_2146` `flip-+_binary64_2117` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `sum-log_binary64_2234` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

3 → 55

Calls

3 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series330.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

204.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
86.0ms	(-.f64 (.f64 b c) (.f64 a d))
40.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify69.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6309	1462

prune308.0ms (7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	53	11	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	11	65

Merged error: 25.3b

Counts

65 → 11

Compiler

Compiled 7549 to 3186 computations (57.8% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b c) (.f64 a d))
14.5b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2165`
21×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
18×	`sqrt-prod_binary64_2159` `times-frac_binary64_2149`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `associate-/r*_binary64_2087` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series426.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
83.0ms	(-.f64 (.f64 b c) (.f64 a d))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5026	2374

prune207.0ms (4.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Merged error: 23.8b

Counts

109 → 12

Compiler

Compiled 5744 to 1884 computations (67.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b c) (.f64 a d))
25.7b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary64_2160`
10×	`add-sqr-sqrt_binary64_2165`
9×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`associate-/r/_binary64_2089` `add-cube-cbrt_binary64_2178` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-un-lft-identity_binary64_2143`
6×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `sqrt-prod_binary64_2159`
4×	`frac-times_binary64_2153`
3×	`associate-/l*_binary64_2088` `times-frac_binary64_2149`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `flip--_binary64_2118` `flip3--_binary64_2147` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `sqrt-pow1_binary64_2161` `div-exp_binary64_2194` `associate-/l/_binary64_2090`
1×	`diff-log_binary64_2235` `clear-num_binary64_2142` `associate-/r*_binary64_2087` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `cancel-sign-sub-inv_binary64_2109` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 74

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series376.0ms (8.5%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
90.0ms	(-.f64 (.f64 b c) (.f64 a d))
47.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
41.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify73.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6050	1690

prune83.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	86	12	98

Merged error: 23.8b

Counts

98 → 12

Compiler

Compiled 2665 to 489 computations (81.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b c) (.f64 a d))
14.5b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.8b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2165`
21×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
18×	`sqrt-prod_binary64_2159` `times-frac_binary64_2149`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `associate-/r*_binary64_2087` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series414.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
83.0ms	(-.f64 (.f64 b c) (.f64 a d))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify70.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5026	2374

prune104.0ms (2.4%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	98	12	110

Merged error: 23.8b

Counts

110 → 12

Compiler

Compiled 3661 to 735 computations (79.9% saved)

regimes131.0ms (3%)

Compiler: Compiled 1157 to 805 computations (30.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	82
1	62	82

end0.0ms (0%)

sample819.0ms (18.6%)

Algorithm

1×

intervals

Results

334.0ms	8000×	body	128	valid
22.0ms	470×	body	128	invalid

Compiler

Compiled 321 to 198 computations (38.3% saved)

Details

analyze517.0ms (11.7%)

sample20.0ms (0.5%)

simplify205.0ms (4.7%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite22.0ms (0.5%)

series330.0ms (7.5%)

simplify69.0ms (1.6%)

prune308.0ms (7%)

localize12.0ms (0.3%)

rewrite33.0ms (0.7%)

series426.0ms (9.7%)

simplify67.0ms (1.5%)

prune207.0ms (4.7%)

localize13.0ms (0.3%)

rewrite39.0ms (0.9%)

series376.0ms (8.5%)

simplify73.0ms (1.7%)

prune83.0ms (1.9%)

localize15.0ms (0.3%)

rewrite33.0ms (0.7%)

series414.0ms (9.4%)

simplify70.0ms (1.6%)

prune104.0ms (2.4%)

regimes131.0ms (3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample819.0ms (18.6%)

Profiling