Details

analyze48.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 17 to 17 computations (0% saved)

simplify95.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	207	12
1	207	12

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

Error

0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.3b	(*.f64 y (sqrt.f64 x))

rewrite19.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2146`
7×	`add-log-exp_binary64_2163`
6×	`add-cube-cbrt_binary64_2159` `associate-r_binary64_2064` `*-un-lft-identity_binary64_2124`
4×	`sqrt-prod_binary64_2140` `pow1_binary64_2185` `associate-+l+_binary64_2057` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-l_binary64_2065`
2×	`unswap-sqr_binary64_2092` `sum-log_binary64_2215`
1×	`pow-prod-down_binary64_2195` `associate-+l-_binary64_2059` `*-commutative_binary64_2055` `diff-log_binary64_2216` `prod-exp_binary64_2173` `+-commutative_binary64_2054` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`

Counts

2 → 39

Calls

2 calls:

9.0ms	(*.f64 y (sqrt.f64 x))
8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

series51.0ms (2%)

Counts

2 → 6

Calls

2 calls:

29.0ms	(*.f64 y (sqrt.f64 x))
22.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify67.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5033	600

prune42.0ms (1.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	39	6	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	7	46

Error

0.0b

Counts

46 → 7

Compiler

Compiled 675 to 339 computations (49.8% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite26.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_2140`
25×	`add-sqr-sqrt_binary64_2146`
18×	`associate-r_binary64_2064`
15×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`sqrt-pow1_binary64_2142`
4×	`pow-prod-down_binary64_2195` `rem-sqrt-square_binary64_2137` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `prod-exp_binary64_2173` `pow1/2_binary64_2204` `cbrt-unprod_binary64_2157`
3×	`unswap-sqr_binary64_2092`
2×	`*-commutative_binary64_2055`

Counts

4 → 88

Calls

4 calls:

9.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
7.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series178.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt.f64 (sqrt.f64 x))
51.0ms	(sqrt.f64 (sqrt.f64 x))
43.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
31.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify75.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4935	1038
1	4935	1038

prune88.0ms (3.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Error

Counts

107 → 7

Compiler

Compiled 1743 to 678 computations (61.1% saved)

localize15.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
0.4b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite30.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`sqrt-prod_binary64_2140` `pow1_binary64_2185` `associate-r_binary64_2064` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
12×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-prod_binary64_2155` `cbrt-unprod_binary64_2157`
4×	`add-log-exp_binary64_2163`
2×	`-commutative_binary64_2055` `associate-l*_binary64_2065` `pow1/3_binary64_2206`

Counts

4 → 73

Calls

4 calls:

14.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
8.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series398.0ms (15.1%)

Counts

4 → 12

Calls

4 calls:

144.0ms	(.f64 (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x)))) (sqrt.f64 (sqrt.f64 (cbrt.f64 x))))
89.0ms	(cbrt.f64 x)
83.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (fabs.f64 (cbrt.f64 x))))
83.0ms	(cbrt.f64 x)

simplify64.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4912	1616
1	4912	1616

prune84.0ms (3.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Error

Counts

92 → 7

Compiler

Compiled 2096 to 672 computations (67.9% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))
0.6b	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))
0.7b	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)

rewrite45.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`sqrt-prod_binary64_2140`
48×	`cbrt-prod_binary64_2155`
36×	`add-sqr-sqrt_binary64_2146` `associate-r_binary64_2064`
30×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
27×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
14×	`pow1_binary64_2185`
12×	`add-exp-log_binary64_2162`
10×	`add-cbrt-cube_binary64_2160`
5×	`pow-pow_binary64_2196`
4×	`pow-prod-down_binary64_2195` `sqrt-pow1_binary64_2142` `add-log-exp_binary64_2163` `associate-l_binary64_2065` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`unpow3_binary64_2190` `unswap-sqr_binary64_2092` `pow-unpow_binary64_2201` `cube-mult_binary64_2154` `sqr-pow_binary64_2096`
2×	`*-commutative_binary64_2055` `pow1/2_binary64_2204`
1×	`sqrt-pow2_binary64_2143` `rem-cbrt-cube_binary64_2148` `pow-exp_binary64_2192` `pow1/3_binary64_2206` `pow-to-exp_binary64_2193` `rem-cube-cbrt_binary64_2147`

Counts

4 → 141

Calls

4 calls:

18.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))
6.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
4.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)
4.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))

series216.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

81.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)
59.0ms	(cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3))
42.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
34.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (cbrt.f64 (pow.f64 (sqrt.f64 (sqrt.f64 x)) 3)))

simplify83.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4900	1724
1	4900	1724

prune133.0ms (5.1%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	153	7	160

Error

Counts

160 → 7

Compiler

Compiled 2873 to 1257 computations (56.2% saved)

regimes104.0ms (3.9%)

Accuracy

Total 0.1b remaining (94%)

Threshold costs 0.1b (94%)

Compiler

Compiled 902 to 676 computations (25.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample723.0ms (27.5%)

Algorithm

1×

intervals

Results

243.0ms	7996×	body	128	valid
3.0ms	119×	body	128	nan
2.0ms	72×	body	128	invalid
0.0ms	3×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 311 to 235 computations (24.4% saved)

Details

analyze48.0ms (1.8%)

sample14.0ms (0.5%)

simplify95.0ms (3.6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite19.0ms (0.7%)

series51.0ms (2%)

simplify67.0ms (2.5%)

prune42.0ms (1.6%)

localize8.0ms (0.3%)

rewrite26.0ms (1%)

series178.0ms (6.8%)

simplify75.0ms (2.8%)

prune88.0ms (3.3%)

localize15.0ms (0.6%)

rewrite30.0ms (1.1%)

series398.0ms (15.1%)

simplify64.0ms (2.4%)

prune84.0ms (3.2%)

localize11.0ms (0.4%)

rewrite45.0ms (1.7%)

series216.0ms (8.2%)

simplify83.0ms (3.2%)

prune133.0ms (5.1%)

regimes104.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample723.0ms (27.5%)

Profiling