Details

analyze531.0ms (11.8%)

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 (0.5%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
0.0ms	11×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify204.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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: 24.5b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (.f64 b c) (.f64 a d))
24.1b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`times-frac_binary64_2149`
4×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/r_binary64_2087` `associate-/l_binary64_2088`
2×	`pow1_binary64_2204` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `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` `flip3-+_binary64_2146` `cancel-sign-sub-inv_binary64_2109` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

2 → 44

Calls

2 calls:

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

series294.0ms (6.5%)

Counts

2 → 6

Calls

2 calls:

205.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
89.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify64.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	6091	1269

prune207.0ms (4.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	43	8	51

Merged error: 23.8b

Counts

51 → 8

Compiler

Compiled 5212 to 2026 computations (61.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.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))))
29.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite34.0ms (0.8%)

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:

11.0ms	(/.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)))

series424.0ms (9.4%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
84.0ms	(-.f64 (.f64 b c) (.f64 a d))
51.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
46.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5026	2374

prune197.0ms (4.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	94	12	106

Merged error: 21.4b

Counts

106 → 12

Compiler

Compiled 5419 to 1646 computations (69.6% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.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))))
29.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
29.0b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite37.0ms (0.8%)

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:

11.0ms	(/.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))

series437.0ms (9.7%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(/.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))
48.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
43.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify71.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5026	2374

prune119.0ms (2.6%)

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: 21.4b

Counts

110 → 12

Compiler

Compiled 3861 to 845 computations (78.1% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.7b	(-.f64 (.f64 b c) (.f64 a d))
0.7b	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d))))
23.6b	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d)))

rewrite44.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_2149`
55×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
18×	`associate-/r*_binary64_2087`
16×	`add-exp-log_binary64_2181`
11×	`associate-/r/_binary64_2089`
10×	`add-cbrt-cube_binary64_2179`
8×	`div-exp_binary64_2194`
6×	`flip--_binary64_2118` `associate-/l*_binary64_2088` `div-inv_binary64_2140` `flip3--_binary64_2147`
5×	`add-log-exp_binary64_2182`
4×	`pow1_binary64_2204` `cbrt-undiv_binary64_2177`
2×	`clear-num_binary64_2142` `1-exp_binary64_2187` `rec-exp_binary64_2193` `frac-2neg_binary64_2154` `associate-/l/_binary64_2090`
1×	`diff-log_binary64_2235` `sub-neg_binary64_2136` `pow-flip_binary64_2217` `flip3-+_binary64_2146` `cancel-sign-sub-inv_binary64_2109` `flip-+_binary64_2117` `inv-pow_binary64_2228`

Counts

3 → 127

Calls

3 calls:

15.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d))))
10.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))

series488.0ms (10.8%)

Counts

3 → 9

Calls

3 calls:

279.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d))))
119.0ms	(/.f64 (+.f64 (.f64 c c) (.f64 d d)) (-.f64 (.f64 b c) (.f64 a d)))
88.0ms	(-.f64 (.f64 b c) (.f64 a d))

simplify91.0ms (2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5177	4639

prune155.0ms (3.4%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	7	8
Picked	0	1	1
Done	0	3	3
Total	136	12	148

Merged error: 21.4b

Counts

148 → 12

Compiler

Compiled 4753 to 1104 computations (76.8% saved)

regimes129.0ms (2.9%)

Compiler: Compiled 1299 to 832 computations (36% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	43	38
1	43	38

end0.0ms (0%)

sample821.0ms (18.2%)

Algorithm

1×

intervals

Results

347.0ms	8000×	body	128	valid
21.0ms	433×	body	128	invalid

Compiler

Compiled 321 to 198 computations (38.3% saved)

Details

analyze531.0ms (11.8%)

sample21.0ms (0.5%)

simplify204.0ms (4.5%)

prune2.0ms (0.1%)

localize10.0ms (0.2%)

rewrite18.0ms (0.4%)

series294.0ms (6.5%)

simplify64.0ms (1.4%)

prune207.0ms (4.6%)

localize15.0ms (0.3%)

rewrite34.0ms (0.8%)

series424.0ms (9.4%)

simplify68.0ms (1.5%)

prune197.0ms (4.4%)

localize14.0ms (0.3%)

rewrite37.0ms (0.8%)

series437.0ms (9.7%)

simplify71.0ms (1.6%)

prune119.0ms (2.6%)

localize12.0ms (0.3%)

rewrite44.0ms (1%)

series488.0ms (10.8%)

simplify91.0ms (2%)

prune155.0ms (3.4%)

regimes129.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample821.0ms (18.2%)

Profiling