Details

analyze6.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample85.0ms (0.1%)

Algorithm

1×

intervals

Results

43.0ms	59×	body	1024	valid
16.0ms	139×	body	128	valid
10.0ms	42×	body	512	valid
5.0ms	16×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify437.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune15.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 20.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize27.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite288.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_2146`
118×	`times-frac_binary64_2130`
113×	`*-un-lft-identity_binary64_2124`
72×	`sqrt-prod_binary64_2140`
54×	`add-cube-cbrt_binary64_2159`
27×	`cancel-sign-sub-inv_binary64_2090`
25×	`difference-of-squares_binary64_2093`
13×	`distribute-lft-out--_binary64_2076` `associate-/r*_binary64_2068`
11×	`add-exp-log_binary64_2162`
10×	`distribute-lft-out_binary64_2075`
7×	`pow1_binary64_2185` `div-inv_binary64_2121` `add-cbrt-cube_binary64_2160`
6×	`associate-/l*_binary64_2069` `pow-flip_binary64_2198`
5×	`add-log-exp_binary64_2163`
4×	`associate-/r/_binary64_2070` `sqrt-div_binary64_2141` `div-exp_binary64_2175`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098` `1-exp_binary64_2168` `inv-pow_binary64_2209` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `diff-log_binary64_2216` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

3 → 173

Calls

3 calls:

162.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
38.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
19.0ms	(/.f64 1 (sqrt.f64 x))

series294.0ms (0.4%)

Counts

3 → 9

Calls

3 calls:

124.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
103.0ms	(/.f64 1 (sqrt.f64 x))
66.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify399.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (228.0ms)

Iter	Nodes	Cost
0	4920	3438
1	4920	3438

prune3.0s (3.6%)

Pruning

55 alts after pruning (54 fresh and 1 done)

	Pruned	Kept	Total
New	128	54	182
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	128	55	183

Merged error: 19.7b

Counts

183 → 55

Compiler

Compiled 4398 to 3343 computations (24% saved)

localize28.0ms (0%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite241.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_2146`
38×	`sqrt-prod_binary64_2140`
34×	`*-un-lft-identity_binary64_2124`
12×	`difference-of-squares_binary64_2093`
11×	`add-cube-cbrt_binary64_2159`
10×	`associate-/l*_binary64_2069` `add-exp-log_binary64_2162` `times-frac_binary64_2130` `add-cbrt-cube_binary64_2160`
9×	`distribute-lft-out--_binary64_2076`
7×	`pow1_binary64_2185` `associate-r_binary64_2064`
6×	`cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065`
5×	`add-log-exp_binary64_2163`
4×	`unswap-sqr_binary64_2092` `distribute-lft-out_binary64_2075` `sqrt-div_binary64_2141` `associate-*r/_binary64_2066`
3×	`pow-prod-down_binary64_2195`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `sqrt-pow1_binary64_2142` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071` `div-exp_binary64_2175` `cbrt-unprod_binary64_2157`
1×	`clear-num_binary64_2123` `sqrt-unprod_binary64_2144` `-commutative_binary64_2055` `associate-/r_binary64_2068` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

3 → 97

Calls

3 calls:

71.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
70.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
50.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series582.0ms (0.7%)

Counts

3 → 9

Calls

3 calls:

340.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
146.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
96.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify357.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (240.0ms)

Iter	Nodes	Cost
0	4918	2435
1	4918	2435

prune3.1s (3.7%)

Pruning

86 alts after pruning (84 fresh and 2 done)

	Pruned	Kept	Total
New	67	39	106
Fresh	8	45	53
Picked	0	1	1
Done	0	1	1
Total	75	86	161

Merged error: 0.2b

Counts

161 → 86

Compiler

Compiled 4509 to 3218 computations (28.6% saved)

localize37.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite296.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_2124`
78×	`times-frac_binary64_2130`
55×	`sqrt-prod_binary64_2140`
47×	`add-sqr-sqrt_binary64_2146`
45×	`distribute-lft-out_binary64_2075`
39×	`add-cube-cbrt_binary64_2159`
32×	`add-exp-log_binary64_2162`
27×	`associate-/l*_binary64_2069`
20×	`add-cbrt-cube_binary64_2160`
14×	`div-exp_binary64_2175`
9×	`pow1_binary64_2185`
8×	`associate-/r/_binary64_2070`
7×	`cbrt-undiv_binary64_2158` `associate-/r_binary64_2068` `associate-r*_binary64_2064`
6×	`add-log-exp_binary64_2163` `associate-l_binary64_2065` `flip3-+_binary64_2127` `flip-+_binary64_2098`
5×	`prod-exp_binary64_2173`
4×	`unswap-sqr_binary64_2092` `sqrt-div_binary64_2141` `associate-*r/_binary64_2066` `div-inv_binary64_2121`
3×	`pow-prod-down_binary64_2195` `1-exp_binary64_2168` `cbrt-unprod_binary64_2157` `rec-exp_binary64_2174`
2×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `frac-2neg_binary64_2135`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `+-commutative_binary64_2054` `pow-flip_binary64_2198` `associate-/l/_binary64_2071` `inv-pow_binary64_2209`

Counts

4 → 166

Calls

4 calls:

75.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
52.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
35.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
35.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

series634.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

307.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
172.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
119.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
35.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify431.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (266.0ms)

Iter	Nodes	Cost
0	4952	4177
1	4952	4177

prune8.0s (9.6%)

Pruning

123 alts after pruning (120 fresh and 3 done)

	Pruned	Kept	Total
New	113	65	178
Fresh	28	55	83
Picked	0	1	1
Done	0	2	2
Total	141	123	264

Merged error: 0b

Counts

264 → 123

Compiler

Compiled 7573 to 5463 computations (27.9% saved)

localize48.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite235.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_2130`
159×	`*-un-lft-identity_binary64_2124`
156×	`add-sqr-sqrt_binary64_2146`
119×	`add-cube-cbrt_binary64_2159`
87×	`sqrt-prod_binary64_2140`
49×	`distribute-lft-out_binary64_2075`
21×	`associate-/l*_binary64_2069`
20×	`associate-/r/_binary64_2070`
19×	`add-exp-log_binary64_2162`
13×	`add-cbrt-cube_binary64_2160`
12×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
11×	`associate-/r*_binary64_2068`
10×	`div-inv_binary64_2121`
9×	`pow1_binary64_2185`
8×	`div-exp_binary64_2175`
7×	`associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163` `associate-l_binary64_2065`
4×	`cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `sqrt-div_binary64_2141`
3×	`pow-prod-down_binary64_2195`
2×	`clear-num_binary64_2123` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `associate-*r/_binary64_2066` `1-exp_binary64_2168` `frac-2neg_binary64_2135` `rec-exp_binary64_2174`
1×	`sqrt-unprod_binary64_2144` `sum-log_binary64_2215` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `pow-flip_binary64_2198` `associate-/l/_binary64_2071` `inv-pow_binary64_2209` `cbrt-unprod_binary64_2157`

Counts

4 → 252

Calls

4 calls:

58.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
41.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
16.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
14.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series759.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

378.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
173.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
118.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
87.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify678.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (308.0ms)

Iter	Nodes	Cost
0	4947	9729
1	4947	9729

prune13.1s (15.8%)

Pruning

196 alts after pruning (193 fresh and 3 done)

	Pruned	Kept	Total
New	166	98	264
Fresh	24	95	119
Picked	0	1	1
Done	1	2	3
Total	191	196	387

Merged error: 0b

Counts

387 → 196

Compiler

Compiled 7549 to 5392 computations (28.6% saved)

regimes7.9s (9.6%)

Compiler: Compiled 19861 to 15630 computations (21.3% saved)

bsearch12.0s (14.5%)

simplify72.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	25
1	16	25

end0.0ms (0%)

sample30.0s (36.1%)

Algorithm

1×

intervals

Results

732.0ms	2209×	body	1024	valid
390.0ms	4271×	body	128	valid
293.0ms	1033×	body	512	valid
67.0ms	487×	body	256	valid

Compiler

Compiled 10230 to 8043 computations (21.4% saved)

Pareto

0.13803258125613885

Details

analyze6.0ms (0%)

sample85.0ms (0.1%)

simplify437.0ms (0.5%)

prune15.0ms (0%)

localize27.0ms (0%)

rewrite288.0ms (0.3%)

series294.0ms (0.4%)

simplify399.0ms (0.5%)

prune3.0s (3.6%)

localize28.0ms (0%)

rewrite241.0ms (0.3%)

series582.0ms (0.7%)

simplify357.0ms (0.4%)

prune3.1s (3.7%)

localize37.0ms (0%)

rewrite296.0ms (0.4%)

series634.0ms (0.8%)

simplify431.0ms (0.5%)

prune8.0s (9.6%)

localize48.0ms (0.1%)

rewrite235.0ms (0.3%)

series759.0ms (0.9%)

simplify678.0ms (0.8%)

prune13.1s (15.8%)

regimes7.9s (9.6%)

bsearch12.0s (14.5%)

simplify72.0ms (0.1%)

end0.0ms (0%)

sample30.0s (36.1%)

Profiling