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)

sample26.0ms (0.5%)

Algorithm

1×

intervals

Results

10.0ms	65×	body	1024	valid
6.0ms	140×	body	128	valid
4.0ms	37×	body	512	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify174.0ms (3.2%)

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: 19.4b

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))
0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.2b	(/.f64 1 (sqrt.f64 x))
2.6b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite83.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64_2165`
118×	`times-frac_binary64_2149`
117×	`*-un-lft-identity_binary64_2143`
76×	`sqrt-prod_binary64_2159`
56×	`add-cube-cbrt_binary64_2178`
27×	`cancel-sign-sub-inv_binary64_2109`
25×	`difference-of-squares_binary64_2112`
13×	`associate-/r*_binary64_2087` `distribute-lft-out--_binary64_2095`
12×	`add-exp-log_binary64_2181`
11×	`distribute-lft-out_binary64_2094`
9×	`pow1_binary64_2204`
8×	`add-cbrt-cube_binary64_2179`
7×	`div-inv_binary64_2140`
6×	`sqrt-div_binary64_2160` `add-log-exp_binary64_2182` `associate-/l*_binary64_2088` `pow-flip_binary64_2217`
4×	`associate-/r/_binary64_2089` `div-exp_binary64_2194`
3×	`pow1/2_binary64_2223` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117`
2×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `1-exp_binary64_2187` `rec-exp_binary64_2193` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`
1×	`rem-sqrt-square_binary64_2156` `diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `flip3--_binary64_2147` `frac-sub_binary64_2152`

Counts

4 → 189

Calls

4 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series184.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
54.0ms	(/.f64 1 (sqrt.f64 x))
35.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
27.0ms	(sqrt.f64 (+.f64 x 1))

simplify84.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

201 → 201

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4913	3696
1	4913	3696

prune803.0ms (14.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	187	14	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	188	14	202

Merged error: 18.8b

Counts

202 → 14

Compiler

Compiled 13047 to 10548 computations (19.2% saved)

localize9.0ms (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)))
2.6b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite57.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64_2165`
42×	`sqrt-prod_binary64_2159`
38×	`*-un-lft-identity_binary64_2143`
13×	`add-cube-cbrt_binary64_2178`
12×	`difference-of-squares_binary64_2112`
11×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
10×	`associate-/l*_binary64_2088` `times-frac_binary64_2149`
9×	`pow1_binary64_2204` `distribute-lft-out--_binary64_2095`
7×	`associate-r_binary64_2083`
6×	`sqrt-div_binary64_2160` `add-log-exp_binary64_2182` `associate-l_binary64_2084` `cancel-sign-sub-inv_binary64_2109`
5×	`distribute-lft-out_binary64_2094`
4×	`associate-*r/_binary64_2085` `unswap-sqr_binary64_2111`
3×	`pow1/2_binary64_2223` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117`
2×	`cbrt-undiv_binary64_2177` `flip--_binary64_2118` `associate-/r/_binary64_2089` `cbrt-unprod_binary64_2176` `flip3--_binary64_2147` `prod-exp_binary64_2192` `div-exp_binary64_2194` `associate-/l/_binary64_2090`
1×	`rem-sqrt-square_binary64_2156` `diff-log_binary64_2235` `clear-num_binary64_2142` `associate-/r_binary64_2087` `sub-neg_binary64_2136` `sqrt-unprod_binary64_2163` `div-inv_binary64_2140` `-commutative_binary64_2074` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 113

Calls

4 calls:

21.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
11.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 1 x))

series312.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
66.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
53.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
25.0ms	(sqrt.f64 (+.f64 1 x))

simplify73.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5009	2693

prune222.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	12	1	13
Picked	1	0	1
Done	0	0	0
Total	135	4	139

Merged error: 0.2b

Counts

139 → 4

Compiler

Compiled 3985 to 2787 computations (30.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite82.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_2143`
78×	`times-frac_binary64_2149`
55×	`sqrt-prod_binary64_2159`
47×	`add-sqr-sqrt_binary64_2165`
45×	`distribute-lft-out_binary64_2094`
39×	`add-cube-cbrt_binary64_2178`
32×	`add-exp-log_binary64_2181`
27×	`associate-/l*_binary64_2088`
20×	`add-cbrt-cube_binary64_2179`
14×	`div-exp_binary64_2194`
9×	`pow1_binary64_2204`
8×	`associate-/r/_binary64_2089`
7×	`cbrt-undiv_binary64_2177` `associate-/r_binary64_2087` `associate-r*_binary64_2083`
6×	`add-log-exp_binary64_2182` `associate-l_binary64_2084` `flip3-+_binary64_2146` `flip-+_binary64_2117`
5×	`prod-exp_binary64_2192`
4×	`sqrt-div_binary64_2160` `div-inv_binary64_2140` `associate-*r/_binary64_2085` `unswap-sqr_binary64_2111`
3×	`1-exp_binary64_2187` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `pow-prod-down_binary64_2214`
2×	`pow1/2_binary64_2223` `clear-num_binary64_2142` `sqrt-pow1_binary64_2161` `frac-2neg_binary64_2154`
1×	`+-commutative_binary64_2073` `sqrt-unprod_binary64_2163` `sum-log_binary64_2234` `pow-flip_binary64_2217` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `associate-/l/_binary64_2090`

Counts

4 → 166

Calls

4 calls:

24.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series317.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

169.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
60.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
51.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
38.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify88.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4944	4177
1	4944	4177

prune592.0ms (10.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	168	10	178
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	171	11	182

Merged error: 0.0b

Counts

182 → 11

Compiler

Compiled 10668 to 7745 computations (27.4% saved)

localize11.0ms (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 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite74.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_2149`
159×	`*-un-lft-identity_binary64_2143`
156×	`add-sqr-sqrt_binary64_2165`
119×	`add-cube-cbrt_binary64_2178`
87×	`sqrt-prod_binary64_2159`
49×	`distribute-lft-out_binary64_2094`
21×	`associate-/l*_binary64_2088`
20×	`associate-/r/_binary64_2089`
19×	`add-exp-log_binary64_2181`
13×	`add-cbrt-cube_binary64_2179`
12×	`flip3-+_binary64_2146` `flip-+_binary64_2117`
11×	`associate-/r*_binary64_2087`
10×	`div-inv_binary64_2140`
9×	`pow1_binary64_2204`
8×	`div-exp_binary64_2194`
7×	`associate-r_binary64_2083`
6×	`add-log-exp_binary64_2182` `associate-l_binary64_2084`
4×	`sqrt-div_binary64_2160` `cbrt-undiv_binary64_2177` `unswap-sqr_binary64_2111`
3×	`pow-prod-down_binary64_2214`
2×	`pow1/2_binary64_2223` `clear-num_binary64_2142` `1-exp_binary64_2187` `rec-exp_binary64_2193` `associate-*r/_binary64_2085` `sqrt-pow1_binary64_2161` `frac-2neg_binary64_2154`
1×	`+-commutative_binary64_2073` `sqrt-unprod_binary64_2163` `cbrt-unprod_binary64_2176` `sum-log_binary64_2234` `prod-exp_binary64_2192` `pow-flip_binary64_2217` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `associate-/l/_binary64_2090`

Counts

4 → 252

Calls

4 calls:

16.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
13.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.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))))

series339.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

157.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
87.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
52.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
43.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify164.0ms (3%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4947	9756
1	4947	9756

prune715.0ms (13%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	261	3	264
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	265	10	275

Merged error: 0.0b

Counts

275 → 10

Compiler

Compiled 11644 to 8547 computations (26.6% saved)

regimes29.0ms (0.5%)

Compiler: Compiled 237 to 184 computations (22.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample1.0s (18.9%)

Algorithm

1×

intervals

Results

355.0ms	2352×	body	1024	valid
167.0ms	4192×	body	128	valid
105.0ms	955×	body	512	valid
37.0ms	501×	body	256	valid

Compiler

Compiled 278 to 218 computations (21.6% saved)

Details

analyze2.0ms (0%)

sample26.0ms (0.5%)

simplify174.0ms (3.2%)

prune3.0ms (0%)

localize7.0ms (0.1%)

rewrite83.0ms (1.5%)

series184.0ms (3.3%)

simplify84.0ms (1.5%)

prune803.0ms (14.6%)

localize9.0ms (0.2%)

rewrite57.0ms (1%)

series312.0ms (5.7%)

simplify73.0ms (1.3%)

prune222.0ms (4%)

localize9.0ms (0.2%)

rewrite82.0ms (1.5%)

series317.0ms (5.8%)

simplify88.0ms (1.6%)

prune592.0ms (10.8%)

localize11.0ms (0.2%)

rewrite74.0ms (1.3%)

series339.0ms (6.2%)

simplify164.0ms (3%)

prune715.0ms (13%)

regimes29.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (18.9%)

Profiling