Details

analyze2.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

7.0ms	67×	body	1024	valid
4.0ms	140×	body	128	valid
2.0ms	25×	body	512	valid
1.0ms	11×	body	2048	valid
1.0ms	13×	body	256	valid

Compiler

Compiled 15 to 14 computations (6.7% saved)

simplify171.0ms (4.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	11
1	71	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 29.1b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
2.8b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite16.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`sqrt-prod_binary64_2159`
14×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
6×	`cancel-sign-sub-inv_binary64_2109`
5×	`add-cube-cbrt_binary64_2178`
4×	`add-log-exp_binary64_2182` `difference-of-squares_binary64_2112`
3×	`pow1_binary64_2204` `distribute-lft-out--_binary64_2095`
2×	`sqrt-div_binary64_2160` `add-exp-log_binary64_2181` `distribute-lft-out_binary64_2094` `add-cbrt-cube_binary64_2179`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `diff-log_binary64_2235` `flip--_binary64_2118` `sub-neg_binary64_2136` `flip3--_binary64_2147` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117`

Counts

2 → 40

Calls

2 calls:

10.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series97.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
29.0ms	(sqrt.f64 (+.f64 x 1))

simplify63.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5005	794

prune71.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	43	3	46
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	3	47

Merged error: 0.1b

Counts

47 → 3

Compiler

Compiled 1029 to 725 computations (29.5% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`*-un-lft-identity_binary64_2143`
24×	`sqrt-prod_binary64_2159`
21×	`distribute-lft-out_binary64_2094`
18×	`times-frac_binary64_2149`
16×	`add-sqr-sqrt_binary64_2165`
15×	`add-cube-cbrt_binary64_2178`
7×	`add-exp-log_binary64_2181`
6×	`associate-/r*_binary64_2087`
5×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`sqrt-div_binary64_2160` `associate-/r/_binary64_2089` `div-exp_binary64_2194`
1×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `+-commutative_binary64_2073` `clear-num_binary64_2142` `1-exp_binary64_2187` `div-inv_binary64_2140` `rec-exp_binary64_2193` `sum-log_binary64_2234` `pow-flip_binary64_2217` `sqrt-pow1_binary64_2161` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`

Counts

3 → 75

Calls

3 calls:

11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
9.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
4.0ms	(sqrt.f64 (+.f64 x 1))

series128.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

61.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)))
40.0ms	(+.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4944	1516
1	4944	1516

prune189.0ms (5.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	78	6	84
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	79	8	87

Merged error: 0.0b

Counts

87 → 8

Compiler

Compiled 3028 to 2316 computations (23.5% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite69.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`sqrt-prod_binary64_2159`
70×	`add-sqr-sqrt_binary64_2165`
46×	`*-un-lft-identity_binary64_2143`
40×	`sqrt-pow1_binary64_2161`
32×	`sqrt-div_binary64_2160` `pow1_binary64_2204`
28×	`add-cube-cbrt_binary64_2178`
20×	`pow1/2_binary64_2223`
18×	`swap-sqr_binary64_2110`
12×	`rem-sqrt-square_binary64_2156`
10×	`associate-r_binary64_2083` `add-exp-log_binary64_2181` `associate-l_binary64_2084`
9×	`pow-prod-up_binary64_2213` `unswap-sqr_binary64_2111` `flip3-+_binary64_2146` `flip-+_binary64_2117` `times-frac_binary64_2149`
8×	`distribute-lft-out_binary64_2094` `add-cbrt-cube_binary64_2179`
5×	`pow-sqr_binary64_2116` `pow-prod-down_binary64_2214`
4×	`add-log-exp_binary64_2182` `frac-times_binary64_2153` `sqr-abs_binary64_2158`
3×	`associate-/r_binary64_2087` `associate-/l_binary64_2088`
2×	`associate-/r/_binary64_2089` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `div-exp_binary64_2194`
1×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `pow2_binary64_2224` `sqrt-unprod_binary64_2163` `1-exp_binary64_2187` `pow-plus_binary64_2206` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `prod-exp_binary64_2192` `pow-flip_binary64_2217` `rem-square-sqrt_binary64_2155` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`

Counts

4 → 169

Calls

4 calls:

19.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))
19.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))

series188.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 1 (+.f64 (*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
51.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
42.0ms	(sqrt.f64 (sqrt.f64 (+.f64 1 x)))
31.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 1 x))) (sqrt.f64 (sqrt.f64 (+.f64 1 x))))

simplify74.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4969	2509
1	4969	2509

prune247.0ms (7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	180	9	189

Merged error: 0.0b

Counts

189 → 9

Compiler

Compiled 4147 to 3152 computations (24% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
0.1b	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
0.2b	(cbrt.f64 (+.f64 1 x))
0.2b	(cbrt.f64 (+.f64 1 x))

rewrite37.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_2165` `*-un-lft-identity_binary64_2143`
18×	`add-cube-cbrt_binary64_2178`
13×	`cbrt-prod_binary64_2174`
10×	`associate-r_binary64_2083` `add-exp-log_binary64_2181`
9×	`sqrt-prod_binary64_2159` `times-frac_binary64_2149`
8×	`add-cbrt-cube_binary64_2179`
7×	`pow1_binary64_2204`
6×	`cbrt-div_binary64_2175`
4×	`add-log-exp_binary64_2182` `flip3-+_binary64_2146` `flip-+_binary64_2117`
3×	`associate-/r_binary64_2087` `associate-/l_binary64_2088` `associate-l_binary64_2084` `distribute-lft-out_binary64_2094` `unswap-sqr_binary64_2111`
2×	`sqrt-div_binary64_2160` `associate-/r/_binary64_2089` `associate-*r/_binary64_2085` `div-exp_binary64_2194` `pow1/3_binary64_2225`
1×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `1-exp_binary64_2187` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `rec-exp_binary64_2193` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `pow-flip_binary64_2217` `*-commutative_binary64_2074` `inv-pow_binary64_2228` `frac-2neg_binary64_2154`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
10.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

series752.0ms (21.4%)

Counts

4 → 12

Calls

4 calls:

587.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
75.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
50.0ms	(cbrt.f64 (+.f64 1 x))
40.0ms	(cbrt.f64 (+.f64 1 x))

simplify96.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4869	3063
1	4869	3063

prune247.0ms (7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	101	10	111

Merged error: 0.0b

Counts

111 → 10

Compiler

Compiled 4284 to 3375 computations (21.2% saved)

regimes52.0ms (1.5%)

Compiler: Compiled 552 to 454 computations (17.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

end0.0ms (0%)

sample869.0ms (24.7%)

Algorithm

1×

intervals

Results

208.0ms	2039×	body	1024	valid
131.0ms	4318×	body	128	valid
71.0ms	941×	body	512	valid
32.0ms	223×	body	2048	valid
27.0ms	479×	body	256	valid

Compiler

Compiled 294 to 244 computations (17% saved)

Details

analyze2.0ms (0.1%)

sample20.0ms (0.6%)

simplify171.0ms (4.9%)

prune2.0ms (0.1%)

localize5.0ms (0.1%)

rewrite16.0ms (0.5%)

series97.0ms (2.8%)

simplify63.0ms (1.8%)

prune71.0ms (2%)

localize6.0ms (0.2%)

rewrite30.0ms (0.8%)

series128.0ms (3.6%)

simplify68.0ms (1.9%)

prune189.0ms (5.4%)

localize8.0ms (0.2%)

rewrite69.0ms (2%)

series188.0ms (5.4%)

simplify74.0ms (2.1%)

prune247.0ms (7%)

localize9.0ms (0.3%)

rewrite37.0ms (1.1%)

series752.0ms (21.4%)

simplify96.0ms (2.7%)

prune247.0ms (7%)

regimes52.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample869.0ms (24.7%)

Profiling