Details

analyze273.0ms (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	250×	body	128	valid
9.0ms	286×	pre	128	true
1.0ms	30×	body	128	nan
1.0ms	6×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify404.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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

28.8b

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)))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite35.0ms (0.5%)

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))
8.0ms	(-.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)))

series266.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

102.0ms	(/.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)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
38.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify100.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune104.0ms (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

Error

0.4b

Counts

87 → 6

Compiler

Compiled 2079 to 1239 computations (40.4% 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))))
0.3b	(-.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)))))

rewrite48.0ms (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 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
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))

series470.0ms (6.7%)

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))
70.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune168.0ms (2.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	103	8	111
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	109	8	117

Error

0.0b

Counts

117 → 8

Compiler

Compiled 3277 to 2023 computations (38.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.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)))))))
0.3b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite40.0ms (0.6%)

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)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series399.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

188.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
115.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune145.0ms (2.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	2	107
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	107	8	115

Error

Counts

115 → 8

Compiler

Compiled 2963 to 1893 computations (36.1% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.3b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
0.3b	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite80.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

319×	`times-frac_binary64_2130`
161×	`*-un-lft-identity_binary64_2124`
127×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
47×	`add-exp-log_binary64_2162`
45×	`associate-/r*_binary64_2068`
38×	`associate-/r/_binary64_2070`
28×	`div-exp_binary64_2175`
27×	`add-cbrt-cube_binary64_2160`
22×	`div-inv_binary64_2121`
17×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098`
14×	`cbrt-undiv_binary64_2158`
8×	`add-log-exp_binary64_2163`
6×	`associate-/l*_binary64_2069`
5×	`pow1_binary64_2185`
4×	`prod-exp_binary64_2173` `1-exp_binary64_2168` `rec-exp_binary64_2174`
2×	`clear-num_binary64_2123` `cbrt-unprod_binary64_2157` `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` `pow-flip_binary64_2198` `inv-pow_binary64_2209`

Counts

4 → 256

Calls

4 calls:

17.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
12.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.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)))

series396.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

189.0ms	(/.f64 1 (/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
110.0ms	(/.f64 2 (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify145.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4949	10473
1	4949	10473

prune503.0ms (7.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	268	8	276

Error

Counts

276 → 8

Compiler

Compiled 8575 to 5659 computations (34% saved)

regimes602.0ms (8.6%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 8060 to 6114 computations (24.1% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms (0%)

sample2.6s (36.8%)

Algorithm

1×

intervals

Results

384.0ms	7671×	body	128	valid
282.0ms	8849×	pre	128	true
42.0ms	849×	body	128	nan
33.0ms	329×	body	256	valid

Compiler

Compiled 2051 to 1557 computations (24.1% saved)

Details

analyze273.0ms (3.9%)

sample32.0ms (0.5%)

simplify404.0ms (5.8%)

prune7.0ms (0.1%)

localize11.0ms (0.2%)

rewrite35.0ms (0.5%)

series266.0ms (3.8%)

simplify100.0ms (1.4%)

prune104.0ms (1.5%)

localize14.0ms (0.2%)

rewrite48.0ms (0.7%)

series470.0ms (6.7%)

simplify69.0ms (1%)

prune168.0ms (2.4%)

localize13.0ms (0.2%)

rewrite40.0ms (0.6%)

series399.0ms (5.7%)

simplify92.0ms (1.3%)

prune145.0ms (2.1%)

localize21.0ms (0.3%)

rewrite80.0ms (1.1%)

series396.0ms (5.6%)

simplify145.0ms (2.1%)

prune503.0ms (7.2%)

regimes602.0ms (8.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.6s (36.8%)

Profiling