Details

analyze519.0ms (13.5%)

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
1.0ms	13×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify101.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	16	22
1	16	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: 25.1b

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))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
24.6b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite20.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
7×	`add-log-exp_binary64_2163`
5×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
4×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`associate-/l_binary64_2069` `pow1_binary64_2185` `associate-/r_binary64_2068`
2×	`associate-/r/_binary64_2070` `sum-log_binary64_2215` `+-commutative_binary64_2054` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

3 → 53

Calls

3 calls:

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

series149.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
37.0ms	(+.f64 (.f64 a c) (.f64 b d))
20.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify68.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5571	1420

prune68.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	56	6	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	6	63

Merged error: 24.4b

Counts

63 → 6

Compiler

Compiled 1535 to 270 computations (82.4% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
14.6b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2146`
21×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
18×	`sqrt-prod_binary64_2140` `times-frac_binary64_2130`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
3×	`associate-/l*_binary64_2069`
2×	`associate-/r/_binary64_2070` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 84

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series213.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
38.0ms	(+.f64 (.f64 a c) (.f64 b d))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
24.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify63.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5230	2326

prune95.0ms (2.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	92	10	102

Merged error: 22.4b

Counts

102 → 10

Compiler

Compiled 3354 to 470 computations (86% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
14.6b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.4b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite66.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2146`
76×	`times-frac_binary64_2130`
53×	`*-un-lft-identity_binary64_2124`
47×	`sqrt-prod_binary64_2140` `add-cube-cbrt_binary64_2159`
28×	`add-exp-log_binary64_2162`
24×	`associate-l_binary64_2065` `associate-r_binary64_2064`
18×	`add-cbrt-cube_binary64_2160`
15×	`unswap-sqr_binary64_2092`
10×	`sqrt-div_binary64_2141`
9×	`div-exp_binary64_2175`
8×	`pow1_binary64_2185` `prod-exp_binary64_2173`
6×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068` `flip3-+_binary64_2127` `flip-+_binary64_2098`
5×	`cbrt-undiv_binary64_2158`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
3×	`associate-/l*_binary64_2069` `div-inv_binary64_2121`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `1-exp_binary64_2168` `associate-/l/_binary64_2071` `rec-exp_binary64_2174`
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 → 160

Calls

4 calls:

28.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
9.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b 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)))

series297.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
111.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
29.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
22.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify103.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4969	5537
1	4969	5537

prune153.0ms (4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	172	10	182

Merged error: 22.4b

Counts

182 → 10

Compiler

Compiled 6197 to 900 computations (85.5% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.2b	(+.f64 (.f64 a c) (.f64 b d))
0.6b	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
24.3b	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))

rewrite34.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_2146`
21×	`*-un-lft-identity_binary64_2124`
20×	`add-cube-cbrt_binary64_2159` `times-frac_binary64_2130`
17×	`add-exp-log_binary64_2162`
15×	`associate-r_binary64_2064`
11×	`add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`pow1_binary64_2185`
6×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`associate-/r/_binary64_2070` `prod-exp_binary64_2173` `div-exp_binary64_2175`
3×	`unswap-sqr_binary64_2092` `associate-/l_binary64_2069` `associate-/r_binary64_2068` `associate-l_binary64_2065`
2×	`cbrt-undiv_binary64_2158` `sum-log_binary64_2215` `associate-*l/_binary64_2067` `+-commutative_binary64_2054` `frac-times_binary64_2134` `1-exp_binary64_2168` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `un-div-inv_binary64_2122` `-commutative_binary64_2055` `pow-flip_binary64_2198` `associate-r/_binary64_2066` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 97

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
5.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 a c) (.f64 b d))

series181.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(.f64 (+.f64 (.f64 a c) (.f64 b d)) (/.f64 1 (+.f64 (.f64 c c) (*.f64 d d))))
40.0ms	(+.f64 (.f64 a c) (.f64 b d))
24.0ms	(/.f64 1 (+.f64 (.f64 c c) (.f64 d d)))
20.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify87.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4960	2169
1	4960	2169

prune79.0ms (2.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	109	10	119

Merged error: 22.4b

Counts

119 → 10

Compiler

Compiled 2551 to 524 computations (79.5% saved)

regimes312.0ms (8.1%)

Compiler: Compiled 4212 to 2296 computations (45.5% saved)

bsearch2.0ms (0.1%)

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

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	80
1	24	80

end0.0ms (0%)

sample1.1s (29.4%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
21.0ms	453×	body	128	invalid

Compiler

Compiled 907 to 484 computations (46.6% saved)

Details

analyze519.0ms (13.5%)

sample20.0ms (0.5%)

simplify101.0ms (2.6%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite20.0ms (0.5%)

series149.0ms (3.9%)

simplify68.0ms (1.8%)

prune68.0ms (1.8%)

localize11.0ms (0.3%)

rewrite32.0ms (0.8%)

series213.0ms (5.5%)

simplify63.0ms (1.6%)

prune95.0ms (2.5%)

localize15.0ms (0.4%)

rewrite66.0ms (1.7%)

series297.0ms (7.7%)

simplify103.0ms (2.7%)

prune153.0ms (4%)

localize11.0ms (0.3%)

rewrite34.0ms (0.9%)

series181.0ms (4.7%)

simplify87.0ms (2.3%)

prune79.0ms (2.1%)

regimes312.0ms (8.1%)

bsearch2.0ms (0.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (29.4%)

Profiling