Details

analyze1.6s (11.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4810	96
1	4810	96
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample89.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	169×	body	128	valid
16.0ms	30×	body	2048	valid
12.0ms	28×	body	1024	valid
11.0ms	17×	body	4096	valid
3.0ms	11×	body	512	valid
3.0ms	29×	body	128	nan
1.0ms	14×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify706.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (694.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune9.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Error

32.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite63.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2124`
15×	`add-sqr-sqrt_binary64_2146`
14×	`add-cube-cbrt_binary64_2159`
12×	`times-frac_binary64_2130`
8×	`add-log-exp_binary64_2163`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`distribute-lft-out_binary64_2075` `pow1_binary64_2185`
4×	`associate-/l*_binary64_2069`
3×	`sqrt-prod_binary64_2140` `associate-/r*_binary64_2068`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 72

Calls

4 calls:

18.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
14.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series919.0ms (6.4%)

Counts

4 → 51

Calls

4 calls:

316.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
240.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
183.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
179.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1398 to 1214 computations (13.2% saved)

simplify140.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5261	2325

prune295.0ms (2.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	115	8	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	8	124

Error

4.0b

Counts

124 → 8

Compiler

Compiled 2561 to 1369 computations (46.5% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.4b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
6.6b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite105.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_2130`
53×	`add-sqr-sqrt_binary64_2146`
40×	`*-un-lft-identity_binary64_2124`
28×	`add-cube-cbrt_binary64_2159`
27×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
13×	`associate-/l*_binary64_2069`
12×	`difference-of-squares_binary64_2093`
10×	`cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `div-exp_binary64_2175`
9×	`sqrt-prod_binary64_2140` `associate-/r*_binary64_2068`
7×	`flip--_binary64_2099` `flip3--_binary64_2128`
6×	`distribute-lft-out--_binary64_2076` `add-log-exp_binary64_2163` `prod-exp_binary64_2173` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157`
5×	`pow1_binary64_2185`
2×	`clear-num_binary64_2123` `sqrt-div_binary64_2141` `frac-2neg_binary64_2135`
1×	`cancel-sign-sub-inv_binary64_2090` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `associate-/l/_binary64_2071`

Counts

4 → 128

Calls

4 calls:

35.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
25.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.3s (9%)

Counts

4 → 55

Calls

4 calls:

421.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
344.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
305.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
223.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2130 to 1667 computations (21.7% saved)

simplify165.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4974	5197
1	4974	5197

prune434.0ms (3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	3	4	7
Picked	0	1	1
Done	0	0	0
Total	185	6	191

Error

4.0b

Counts

191 → 6

Compiler

Compiled 5230 to 2756 computations (47.3% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.2b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite66.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_2146`
28×	`*-un-lft-identity_binary64_2124`
18×	`add-cube-cbrt_binary64_2159` `times-frac_binary64_2130`
11×	`sqrt-prod_binary64_2140`
10×	`difference-of-squares_binary64_2093`
8×	`add-log-exp_binary64_2163`
7×	`cancel-sign-sub-inv_binary64_2090`
6×	`associate-/r*_binary64_2068` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
5×	`distribute-lft-out--_binary64_2076` `pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128`
3×	`associate-/l*_binary64_2069`
2×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 88

Calls

4 calls:

17.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
14.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series1.1s (7.6%)

Counts

4 → 56

Calls

4 calls:

323.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
303.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
237.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
220.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 2035 to 1768 computations (13.1% saved)

simplify146.0ms (1%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4984	3010
1	4984	3010

prune299.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	144	6	150

Error

4.0b

Counts

150 → 6

Compiler

Compiled 3604 to 2142 computations (40.6% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite83.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

102×	`times-frac_binary64_2130`
82×	`*-un-lft-identity_binary64_2124`
57×	`add-sqr-sqrt_binary64_2146`
56×	`add-cube-cbrt_binary64_2159`
18×	`associate-/r*_binary64_2068`
15×	`add-exp-log_binary64_2162`
13×	`distribute-lft-out_binary64_2075`
9×	`associate-/r/_binary64_2070` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`div-exp_binary64_2175`
6×	`pow1_binary64_2185`
5×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
3×	`cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `sqrt-div_binary64_2141` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`clear-num_binary64_2123` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `rem-sqrt-square_binary64_2137` `+-commutative_binary64_2054` `pow1/2_binary64_2204` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `inv-pow_binary64_2209` `frac-2neg_binary64_2135`

Counts

4 → 135

Calls

4 calls:

23.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series852.0ms (6%)

Counts

4 → 51

Calls

4 calls:

292.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
216.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
184.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
159.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 1532 to 1348 computations (12% saved)

simplify244.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 0 (156.0ms)

Iter	Nodes	Cost
0	4944	4811
1	4944	4811

prune384.0ms (2.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	185	1	186
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	185	7	192

Error

4.0b

Counts

192 → 7

Compiler

Compiled 4601 to 2533 computations (44.9% saved)

regimes1.1s (7.4%)

Accuracy

Total 1.5b remaining (21.6%)

Threshold costs 0b (0%)

Compiler

Compiled 3348 to 2590 computations (22.6% saved)

bsearch173.0ms (1.2%)

Steps

Iters	Range	Point
5	2.1185936279355515e+57	5.720434717612344e+57	4.492769536356283e+57
9	2.8546213422044465e-125	2.2818203321252932e-116	2.9229233280338277e-125
7	-1.7965637555557037e+135	-1.6589745466350036e+133	-8.25042444002418e+133

Iters

Range

Point

2.1185936279355515e+57

5.720434717612344e+57

4.492769536356283e+57

2.8546213422044465e-125

2.2818203321252932e-116

2.9229233280338277e-125

-1.7965637555557037e+135

-1.6589745466350036e+133

-8.25042444002418e+133

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	120	91
1	120	91

end0.0ms (0%)

sample3.9s (27.6%)

Algorithm

1×

intervals

Results

587.0ms	1146×	body	2048	valid
555.0ms	5149×	body	128	valid
298.0ms	745×	body	1024	valid
259.0ms	419×	body	4096	valid
109.0ms	367×	body	512	valid
65.0ms	661×	body	128	nan
50.0ms	373×	body	128	invalid
39.0ms	174×	body	256	valid

Compiler

Compiled 948 to 723 computations (23.7% saved)

Details

analyze1.6s (11.4%)

sample89.0ms (0.6%)

simplify706.0ms (4.9%)

prune9.0ms (0.1%)

localize26.0ms (0.2%)

rewrite63.0ms (0.4%)

series919.0ms (6.4%)

simplify140.0ms (1%)

prune295.0ms (2.1%)

localize28.0ms (0.2%)

rewrite105.0ms (0.7%)

series1.3s (9%)

simplify165.0ms (1.2%)

prune434.0ms (3%)

localize34.0ms (0.2%)

rewrite66.0ms (0.5%)

series1.1s (7.6%)

simplify146.0ms (1%)

prune299.0ms (2.1%)

localize26.0ms (0.2%)

rewrite83.0ms (0.6%)

series852.0ms (6%)

simplify244.0ms (1.7%)

prune384.0ms (2.7%)

regimes1.1s (7.4%)

bsearch173.0ms (1.2%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample3.9s (27.6%)

Profiling