Details

analyze265.0ms (3.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample32.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	242×	body	128	valid
8.0ms	280×	pre	128	true
1.0ms	14×	body	256	valid
1.0ms	24×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify413.0ms (6.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (317.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms (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

Merged error: 29.2b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
29.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `sqrt-prod_binary64_2140` `times-frac_binary64_2130`
5×	`pow1_binary64_2185`
4×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090`
3×	`distribute-lft-out--_binary64_2076`
2×	`cbrt-undiv_binary64_2158` `sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `associate-/r*_binary64_2068` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `div-sub_binary64_2129` `div-inv_binary64_2121` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series267.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
34.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune103.0ms (1.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Merged error: 0.4b

Counts

87 → 6

Compiler

Compiled 2126 to 1265 computations (40.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
22×	`times-frac_binary64_2130`
20×	`*-un-lft-identity_binary64_2124`
17×	`cbrt-undiv_binary64_2158` `div-exp_binary64_2175`
13×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
11×	`associate-/l*_binary64_2069`
10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
8×	`add-log-exp_binary64_2163`
6×	`associate-/r/_binary64_2070`
5×	`distribute-lft-out_binary64_2075` `associate-/r*_binary64_2068`
4×	`pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-inv_binary64_2121`
2×	`clear-num_binary64_2123` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-/l/_binary64_2071`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series464.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
163.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify64.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune169.0ms (2.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	107	10	117

Merged error: 0b

Counts

117 → 10

Compiler

Compiled 3365 to 2083 computations (38.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

242×	`times-frac_binary64_2130`
114×	`*-un-lft-identity_binary64_2124`
106×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
61×	`add-exp-log_binary64_2162`
47×	`add-cbrt-cube_binary64_2160`
37×	`div-exp_binary64_2175`
26×	`div-inv_binary64_2121`
25×	`cbrt-undiv_binary64_2158`
19×	`associate-/l*_binary64_2069`
18×	`associate-/r/_binary64_2070`
15×	`associate-*r/_binary64_2066`
13×	`associate-/r*_binary64_2068`
8×	`prod-exp_binary64_2173`
6×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
4×	`distribute-lft-out_binary64_2075` `pow1_binary64_2185` `1-exp_binary64_2168`
3×	`clear-num_binary64_2123` `frac-2neg_binary64_2135`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071`

Counts

4 → 226

Calls

4 calls:

18.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
11.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series558.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

194.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
172.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
156.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify136.0ms (2%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4894	8594
1	4894	8594

prune332.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	239	9	248

Merged error: 0b

Counts

248 → 9

Compiler

Compiled 7203 to 4170 computations (42.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite44.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_2124`
24×	`times-frac_binary64_2130`
21×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
18×	`associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
8×	`distribute-lft-out_binary64_2075` `add-log-exp_binary64_2163`
6×	`prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
4×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
3×	`pow-prod-down_binary64_2195` `cbrt-undiv_binary64_2158` `associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098` `div-exp_binary64_2175`
2×	`div-inv_binary64_2121`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `sum-log_binary64_2215` `-commutative_binary64_2055` `diff-log_binary64_2216` `associate-l_binary64_2065` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `associate-r/_binary64_2066` `frac-2neg_binary64_2135`

Counts

4 → 95

Calls

4 calls:

13.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
8.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series392.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

191.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
105.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify82.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune125.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	107	9	116

Merged error: 0b

Counts

116 → 9

Compiler

Compiled 2744 to 1732 computations (36.9% saved)

regimes578.0ms (8.5%)

Compiler: Compiled 7724 to 5810 computations (24.8% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.4s (36.1%)

Algorithm

1×

intervals

Results

390.0ms	7662×	body	128	valid
276.0ms	8852×	pre	128	true
40.0ms	852×	body	128	nan
34.0ms	338×	body	256	valid

Compiler

Compiled 1967 to 1481 computations (24.7% saved)

Details

analyze265.0ms (3.9%)

sample32.0ms (0.5%)

simplify413.0ms (6.1%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite39.0ms (0.6%)

series267.0ms (3.9%)

simplify87.0ms (1.3%)

prune103.0ms (1.5%)

localize14.0ms (0.2%)

rewrite49.0ms (0.7%)

series464.0ms (6.9%)

simplify64.0ms (0.9%)

prune169.0ms (2.5%)

localize14.0ms (0.2%)

rewrite71.0ms (1%)

series558.0ms (8.3%)

simplify136.0ms (2%)

prune332.0ms (4.9%)

localize12.0ms (0.2%)

rewrite44.0ms (0.7%)

series392.0ms (5.8%)

simplify82.0ms (1.2%)

prune125.0ms (1.8%)

regimes578.0ms (8.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.4s (36.1%)

Profiling