Details

analyze206.0ms (2.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19
0	1	1
1	1	1

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	74×	body	1024	valid
4.0ms	128×	body	128	valid
4.0ms	38×	body	512	valid
1.0ms	13×	body	256	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify91.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune2.0ms (0%)

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

31.3b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(/.f64 x (+.f64 x 1))
1.9b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite339.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

30.8b

Rules

148×	`*-un-lft-identity_binary64_2124`
88×	`times-frac_binary64_2130`
85×	`add-sqr-sqrt_binary64_2146`
37×	`add-cube-cbrt_binary64_2159`
34×	`cancel-sign-sub-inv_binary64_2090`
27×	`distribute-lft-out_binary64_2075`
22×	`difference-of-squares_binary64_2093` `distribute-lft-out--_binary64_2076`
11×	`associate-/r*_binary64_2068`
9×	`difference-of-sqr-1_binary64_2094`
7×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `associate-/l*_binary64_2069`
6×	`associate-/r/_binary64_2070`
5×	`add-log-exp_binary64_2163`
3×	`pow1_binary64_2185` `flip3--_binary64_2128` `flip--_binary64_2099` `div-inv_binary64_2121`
2×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `flip3-+_binary64_2127` `flip-+_binary64_2098` `associate-/l/_binary64_2071`
1×	`diff-log_binary64_2216` `frac-sub_binary64_2133` `sub-neg_binary64_2117`

Counts

3 → 147

Calls

3 calls:

51.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
8.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 3337 to 2419 computations (27.5% saved)

series193.0ms (2.2%)

Error

0.0b

Counts

3 → 36

Calls

3 calls:

66.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
43.0ms	(/.f64 x (+.f64 x 1))
32.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 1090 to 899 computations (17.5% saved)

simplify89.0ms (1%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4960	3142
1	4960	3142

prune281.0ms (3.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	3	184

Error

0.0b

Counts

184 → 3

Compiler

Compiled 3447 to 2423 computations (29.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 3 (pow.f64 x 3))
0.1b	(/.f64 1 (*.f64 x x))
0.2b	(/.f64 1 (pow.f64 x 4))
7.4b	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))

rewrite384.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

62×	`times-frac_binary64_2130`
54×	`*-un-lft-identity_binary64_2124`
47×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
29×	`add-exp-log_binary64_2162`
24×	`unpow-prod-down_binary64_2203`
20×	`associate-/r*_binary64_2068`
13×	`add-cbrt-cube_binary64_2160` `div-exp_binary64_2175`
12×	`pow1_binary64_2185` `cube-prod_binary64_2152`
9×	`associate-/l*_binary64_2069`
8×	`sqr-pow_binary64_2096`
7×	`pow-flip_binary64_2198`
6×	`add-log-exp_binary64_2163`
5×	`1-exp_binary64_2168` `rec-exp_binary64_2174`
4×	`div-inv_binary64_2121` `pow-to-exp_binary64_2193` `pow-exp_binary64_2192` `cbrt-undiv_binary64_2158` `unpow3_binary64_2190` `cube-mult_binary64_2154`
3×	`distribute-lft-out_binary64_2075` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `prod-exp_binary64_2173`
2×	`inv-pow_binary64_2209`
1×	`sum-log_binary64_2215` `frac-add_binary64_2132` `flip3-+_binary64_2127` `flip-+_binary64_2098` `+-commutative_binary64_2054` `pow2_binary64_2205` `pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `pow-sqr_binary64_2097` `cbrt-unprod_binary64_2157`

Counts

4 → 165

Calls

4 calls:

50.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))
8.0ms	(/.f64 1 (*.f64 x x))
6.0ms	(/.f64 1 (pow.f64 x 4))
5.0ms	(/.f64 3 (pow.f64 x 3))

Compiler

Compiled 4628 to 3414 computations (26.2% saved)

series208.0ms (2.4%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

87.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))
41.0ms	(/.f64 3 (pow.f64 x 3))
30.0ms	(/.f64 1 (*.f64 x x))
27.0ms	(/.f64 1 (pow.f64 x 4))

Compiler

Compiled 864 to 686 computations (20.6% saved)

simplify83.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5123	2048

prune315.0ms (3.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	180	3	183

Error

0.0b

Counts

183 → 3

Compiler

Compiled 4546 to 3266 computations (28.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 1 x))
0.0b	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
1.9b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
1.9b	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))

rewrite1.4s (16.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

983×	`*-un-lft-identity_binary64_2124`
396×	`times-frac_binary64_2130`
262×	`distribute-lft-out_binary64_2075`
186×	`sqrt-prod_binary64_2140`
168×	`distribute-lft-out--_binary64_2076`
135×	`add-sqr-sqrt_binary64_2146`
79×	`swap-sqr_binary64_2091`
52×	`cancel-sign-sub-inv_binary64_2090`
41×	`add-cube-cbrt_binary64_2159`
24×	`difference-of-squares_binary64_2093` `sqrt-div_binary64_2141`
19×	`pow1_binary64_2185` `associate-l_binary64_2065` `associate-r_binary64_2064`
10×	`frac-sub_binary64_2133` `flip3--_binary64_2128` `flip--_binary64_2099`
9×	`frac-times_binary64_2134`
8×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `difference-of-sqr--1_binary64_2095` `pow1/2_binary64_2204` `sqrt-pow1_binary64_2142`
6×	`associate-/r/_binary64_2070`
5×	`pow-prod-up_binary64_2194`
4×	`unswap-sqr_binary64_2092` `associate-/r*_binary64_2068`
3×	`div-inv_binary64_2121` `flip3-+_binary64_2127` `flip-+_binary64_2098` `pow-prod-down_binary64_2195` `pow-sqr_binary64_2097` `associate-l/_binary64_2067` `associate-r/_binary64_2066` `associate-/l*_binary64_2069`
2×	`diff-log_binary64_2216` `sub-neg_binary64_2117` `rem-sqrt-square_binary64_2137`
1×	`pow2_binary64_2205` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `sqrt-unprod_binary64_2144` `sqr-abs_binary64_2139` `rem-square-sqrt_binary64_2136` `*-commutative_binary64_2055` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `clear-num_binary64_2123`

Counts

4 → 297

Calls

4 calls:

131.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
49.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
41.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
6.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 12499 to 9409 computations (24.7% saved)

series329.0ms (3.7%)

Error

0.0b

Counts

4 → 44

Calls

4 calls:

88.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
86.0ms	(-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))
65.0ms	(*.f64 (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))) (sqrt.f64 (-.f64 (/.f64 x (+.f64 1 x)) (/.f64 (+.f64 1 x) (+.f64 x -1)))))
34.0ms	(/.f64 x (+.f64 1 x))

Compiler

Compiled 2280 to 1825 computations (20% saved)

simplify171.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

341 → 341

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4883	7776
1	4883	7776

prune751.0ms (8.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	341	0	341
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	341	3	344

Error

0.0b

Counts

344 → 3

Compiler

Compiled 9878 to 7175 computations (27.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 x x) x)
0.0b	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))
0.0b	(*.f64 (+.f64 1 x) (+.f64 1 x))
18.9b	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))

rewrite351.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

35×	`*-un-lft-identity_binary64_2124`
32×	`frac-sub_binary64_2133`
31×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
29×	`add-sqr-sqrt_binary64_2146`
20×	`add-cube-cbrt_binary64_2159` `frac-times_binary64_2134`
19×	`flip3--_binary64_2128` `flip--_binary64_2099`
18×	`associate-/l/_binary64_2071`
16×	`times-frac_binary64_2130`
11×	`add-log-exp_binary64_2163` `pow1_binary64_2185`
10×	`associate-l/_binary64_2067` `associate-r/_binary64_2066`
8×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`difference-of-squares_binary64_2093` `cancel-sign-sub-inv_binary64_2090`
6×	`swap-sqr_binary64_2091` `distribute-lft-out_binary64_2075`
5×	`difference-of-sqr--1_binary64_2095`
4×	`diff-log_binary64_2216` `associate--l+_binary64_2061` `associate-l_binary64_2065` `associate-r_binary64_2064` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
3×	`sub-neg_binary64_2117`
2×	`distribute-rgt-in_binary64_2074` `associate--r+_binary64_2060` `distribute-lft-in_binary64_2073` `associate-/r/_binary64_2070`
1×	`associate--l-_binary64_2062` `pow2_binary64_2205` `pow-prod-down_binary64_2195` `pow-prod-up_binary64_2194` `pow-plus_binary64_2187` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `pow-sqr_binary64_2097` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `distribute-rgt-out--_binary64_2078`

Counts

4 → 150

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))
14.0ms	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))
11.0ms	(*.f64 (+.f64 1 x) (+.f64 1 x))
4.0ms	(-.f64 (*.f64 x x) x)

Compiler

Compiled 6068 to 2983 computations (50.8% saved)

series216.0ms (2.4%)

Error

Counts

4 → 33

Calls

4 calls:

53.0ms	(-.f64 (*.f64 x x) x)
47.0ms	(*.f64 (+.f64 1 x) (+.f64 1 x))
40.0ms	(-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x)))
38.0ms	(/.f64 (-.f64 (-.f64 (.f64 x x) x) (.f64 (+.f64 1 x) (+.f64 1 x))) (+.f64 (*.f64 x x) -1))

Compiler

Compiled 1120 to 798 computations (28.8% saved)

simplify110.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4951	4794
1	4951	4794

prune300.0ms (3.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	183	3	186

Error

0.0b

Counts

186 → 3

Compiler

Compiled 5659 to 2938 computations (48.1% saved)

regimes354.0ms (4%)

Accuracy

Total 0.0b remaining (82.3%)

Threshold costs 0.0b (82.3%)

Compiler

Compiled 2904 to 2280 computations (21.5% saved)

bsearch67.0ms (0.8%)

Steps

Iters	Range		Point
10	20507726279801.38	2.1367157759334464e+27	24107275353534.402
10	-7.317617846792305e+28	-246369982764684.22	-9.584030856506872e+18

Compiler

Compiled 1 to 1 computations (0% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	94	61
1	94	61

end0.0ms (0%)

sample2.5s (28.1%)

Algorithm

1×

intervals

Results

315.0ms	1998×	body	1024	valid
186.0ms	4259×	body	128	valid
123.0ms	1028×	body	512	valid
42.0ms	216×	body	2048	valid
39.0ms	499×	body	256	valid

Compiler

Compiled 1408 to 1107 computations (21.4% saved)

Details

analyze206.0ms (2.3%)

sample26.0ms (0.3%)

simplify91.0ms (1%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite339.0ms (3.8%)

series193.0ms (2.2%)

simplify89.0ms (1%)

prune281.0ms (3.2%)

localize17.0ms (0.2%)

rewrite384.0ms (4.3%)

series208.0ms (2.4%)

simplify83.0ms (0.9%)

prune315.0ms (3.6%)

localize17.0ms (0.2%)

rewrite1.4s (16.1%)

series329.0ms (3.7%)

simplify171.0ms (1.9%)

prune751.0ms (8.5%)

localize9.0ms (0.1%)

rewrite351.0ms (4%)

series216.0ms (2.4%)

simplify110.0ms (1.2%)

prune300.0ms (3.4%)

regimes354.0ms (4%)

bsearch67.0ms (0.8%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.5s (28.1%)

Profiling