Details

analyze558.0ms (11.1%)

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)

sample21.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify169.0ms (3.4%)

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%)

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: 23.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (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))
23.1b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite23.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
9×	`times-frac_binary64_2105`
7×	`add-log-exp_binary64_2135`
5×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
4×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`pow1_binary64_2157` `associate-/r_binary64_2045` `associate-/l_binary64_2046`
2×	`associate-/l/_binary64_2048` `sum-log_binary64_2187` `associate-/r/_binary64_2047` `+-commutative_binary64_2031`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `div-inv_binary64_2096`

Counts

3 → 53

Calls

3 calls:

10.0ms	(/.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))

series302.0ms (6%)

Counts

3 → 9

Calls

3 calls:

187.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (+.f64 (.f64 c c) (.f64 d d)))
73.0ms	(+.f64 (.f64 a c) (.f64 b d))
42.0ms	(+.f64 (.f64 c c) (.f64 d d))

simplify60.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5263	1420

prune78.0ms (1.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	54	8	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	9	63

Merged error: 22.7b

Counts

63 → 9

Compiler

Compiled 1625 to 302 computations (81.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 a c) (.f64 b d))
15.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2120`
21×	`add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
18×	`times-frac_binary64_2105` `sqrt-prod_binary64_2114`
6×	`add-cbrt-cube_binary64_2132` `pow1_binary64_2157` `add-log-exp_binary64_2135` `associate-/r*_binary64_2045` `sqrt-div_binary64_2115` `add-exp-log_binary64_2134`
5×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
3×	`associate-/l*_binary64_2046`
2×	`associate-/l/_binary64_2048` `associate-/r/_binary64_2047` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `sum-log_binary64_2187` `frac-2neg_binary64_2110` `+-commutative_binary64_2031` `clear-num_binary64_2098` `div-inv_binary64_2096`

Counts

4 → 84

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
5.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
5.0ms	(+.f64 (.f64 a c) (.f64 b d))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series410.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
73.0ms	(+.f64 (.f64 a c) (.f64 b d))
49.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4991	2326
1	4991	2326

prune104.0ms (2.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	94	11	105

Merged error: 20.2b

Counts

105 → 11

Compiler

Compiled 3363 to 474 computations (85.9% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.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)))))
15.9b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
27.2b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite77.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2120`
76×	`times-frac_binary64_2105`
53×	`*-un-lft-identity_binary64_2099`
47×	`add-cube-cbrt_binary64_2131` `sqrt-prod_binary64_2114`
28×	`add-exp-log_binary64_2134`
24×	`associate-l_binary64_2042` `associate-r_binary64_2041`
18×	`add-cbrt-cube_binary64_2132`
15×	`unswap-sqr_binary64_2067`
10×	`sqrt-div_binary64_2115`
9×	`div-exp_binary64_2147`
8×	`pow1_binary64_2157` `prod-exp_binary64_2145`
6×	`flip3-+_binary64_2102` `associate-/r/_binary64_2047` `associate-/r*_binary64_2045` `flip-+_binary64_2073`
5×	`cbrt-undiv_binary64_2130`
4×	`add-log-exp_binary64_2135` `cbrt-unprod_binary64_2129`
3×	`associate-/l*_binary64_2046` `div-inv_binary64_2096`
2×	`1-exp_binary64_2140` `rec-exp_binary64_2146` `associate-/l/_binary64_2048` `rem-sqrt-square_binary64_2112` `pow1/2_binary64_2176` `sqrt-pow1_binary64_2116`
1×	`associate-r/_binary64_2043` `-commutative_binary64_2032` `associate-*l/_binary64_2044` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098` `frac-times_binary64_2109`

Counts

4 → 160

Calls

4 calls:

35.0ms	(.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)))))
11.0ms	(/.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)))

series594.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(.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)))))
238.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
48.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
45.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify108.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5101	5405

prune183.0ms (3.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	7	8
Picked	0	1	1
Done	0	2	2
Total	171	12	183

Merged error: 20.2b

Counts

183 → 12

Compiler

Compiled 6137 to 949 computations (84.5% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

12.0b	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
28.1b	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite37.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64_2120` `add-cube-cbrt_binary64_2131` `*-un-lft-identity_binary64_2099`
21×	`cbrt-prod_binary64_2127`
18×	`times-frac_binary64_2105`
8×	`cbrt-div_binary64_2128`
6×	`associate-/r*_binary64_2045` `add-exp-log_binary64_2134`
5×	`flip3-+_binary64_2102` `add-cbrt-cube_binary64_2132` `flip-+_binary64_2073`
4×	`pow1_binary64_2157` `add-log-exp_binary64_2135`
3×	`pow1/3_binary64_2178` `associate-/l*_binary64_2046`
2×	`associate-/l/_binary64_2048` `associate-/r/_binary64_2047`
1×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `frac-2neg_binary64_2110` `clear-num_binary64_2098` `div-inv_binary64_2096`

Counts

4 → 82

Calls

4 calls:

14.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series929.0ms (18.6%)

Counts

4 → 12

Calls

4 calls:

514.0ms	(/.f64 (+.f64 (.f64 a c) (.f64 b d)) (cbrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
143.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
138.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
134.0ms	(cbrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify81.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5194	2633

prune116.0ms (2.3%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	1	7	8
Picked	1	0	1
Done	0	3	3
Total	95	11	106

Merged error: 19.5b

Counts

106 → 11

Compiler

Compiled 4321 to 672 computations (84.4% saved)

regimes134.0ms (2.7%)

Compiler: Compiled 1259 to 797 computations (36.7% 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	39	119
1	39	119

end0.0ms (0%)

sample858.0ms (17.1%)

Algorithm

1×

intervals

Results

356.0ms	8000×	body	128	valid
20.0ms	481×	body	128	invalid

Compiler

Compiled 365 to 206 computations (43.6% saved)

Details

analyze558.0ms (11.1%)

sample21.0ms (0.4%)

simplify169.0ms (3.4%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite23.0ms (0.5%)

series302.0ms (6%)

simplify60.0ms (1.2%)

prune78.0ms (1.6%)

localize13.0ms (0.3%)

rewrite36.0ms (0.7%)

series410.0ms (8.2%)

simplify67.0ms (1.3%)

prune104.0ms (2.1%)

localize15.0ms (0.3%)

rewrite77.0ms (1.5%)

series594.0ms (11.9%)

simplify108.0ms (2.2%)

prune183.0ms (3.7%)

localize16.0ms (0.3%)

rewrite37.0ms (0.7%)

series929.0ms (18.6%)

simplify81.0ms (1.6%)

prune116.0ms (2.3%)

regimes134.0ms (2.7%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample858.0ms (17.1%)

Profiling