Details

analyze2.0ms (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)

sample27.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms	83×	body	1024	valid
5.0ms	120×	body	128	valid
4.0ms	40×	body	512	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify98.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune3.0ms (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: 22.6b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.7b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite72.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_2146`
118×	`times-frac_binary64_2130`
117×	`*-un-lft-identity_binary64_2124`
76×	`sqrt-prod_binary64_2140`
56×	`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`
12×	`add-exp-log_binary64_2162`
11×	`distribute-lft-out_binary64_2075`
9×	`pow1_binary64_2185`
8×	`add-cbrt-cube_binary64_2160`
7×	`div-inv_binary64_2121`
6×	`associate-/l*_binary64_2069` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `pow-flip_binary64_2198`
4×	`associate-/r/_binary64_2070` `div-exp_binary64_2175`
3×	`sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `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` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `frac-sub_binary64_2133`

Counts

4 → 189

Calls

4 calls:

41.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
6.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

series97.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

40.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
25.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
13.0ms	(sqrt.f64 (+.f64 x 1))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4945	3696
1	4945	3696

prune238.0ms (4.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	190	11	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	191	11	202

Merged error: 22.1b

Counts

202 → 11

Compiler

Compiled 3800 to 2792 computations (26.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 x))
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)))
2.7b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_2146`
42×	`sqrt-prod_binary64_2140`
38×	`*-un-lft-identity_binary64_2124`
13×	`add-cube-cbrt_binary64_2159`
12×	`difference-of-squares_binary64_2093`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
10×	`associate-/l*_binary64_2069` `times-frac_binary64_2130`
9×	`distribute-lft-out--_binary64_2076` `pow1_binary64_2185`
7×	`associate-r_binary64_2064`
6×	`cancel-sign-sub-inv_binary64_2090` `sqrt-div_binary64_2141` `add-log-exp_binary64_2163` `associate-l_binary64_2065`
5×	`distribute-lft-out_binary64_2075`
4×	`unswap-sqr_binary64_2092` `associate-*r/_binary64_2066`
3×	`pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070` `prod-exp_binary64_2173` `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` `rem-sqrt-square_binary64_2137` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

series163.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

86.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
38.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
14.0ms	(sqrt.f64 (+.f64 1 x))

simplify74.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4956	2693
1	4956	2693

prune149.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	133	3	136

Merged error: 0.3b

Counts

136 → 3

Compiler

Compiled 2872 to 1861 computations (35.2% saved)

localize8.0ms (0.2%)

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)))

rewrite67.0ms (1.3%)

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:

20.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series161.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

82.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
33.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
21.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify88.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4952	4177
1	4952	4177

prune247.0ms (4.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	171	7	178
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	172	9	181

Merged error: 0.0b

Counts

181 → 9

Compiler

Compiled 4434 to 3033 computations (31.6% saved)

localize10.0ms (0.2%)

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)))))
0.2b	(/.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)))

rewrite65.0ms (1.3%)

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:

13.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
9.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series168.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

75.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
40.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
27.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
25.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

simplify144.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4947	9729
1	4947	9729

prune492.0ms (9.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	266	7	273

Merged error: 0b

Counts

273 → 7

Compiler

Compiled 7549 to 5392 computations (28.6% saved)

regimes277.0ms (5.4%)

Compiler: Compiled 3520 to 2796 computations (20.6% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	28
1	16	28

end0.0ms (0%)

sample2.3s (45.2%)

Algorithm

1×

intervals

Results

313.0ms	2167×	body	1024	valid
169.0ms	4381×	body	128	valid
114.0ms	984×	body	512	valid
33.0ms	468×	body	256	valid

Compiler

Compiled 1793 to 1425 computations (20.5% saved)

Details

analyze2.0ms (0%)

sample27.0ms (0.5%)

simplify98.0ms (1.9%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite72.0ms (1.4%)

series97.0ms (1.9%)

simplify97.0ms (1.9%)

prune238.0ms (4.6%)

localize8.0ms (0.2%)

rewrite48.0ms (0.9%)

series163.0ms (3.2%)

simplify74.0ms (1.4%)

prune149.0ms (2.9%)

localize8.0ms (0.2%)

rewrite67.0ms (1.3%)

series161.0ms (3.1%)

simplify88.0ms (1.7%)

prune247.0ms (4.8%)

localize10.0ms (0.2%)

rewrite65.0ms (1.3%)

series168.0ms (3.3%)

simplify144.0ms (2.8%)

prune492.0ms (9.6%)

regimes277.0ms (5.4%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.3s (45.2%)

Profiling