Details

analyze1.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 8 to 6 computations (25% saved)

sample10.0ms (0.4%)

Algorithm

1×

intervals

Results

5.0ms

256×

body

128

valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify97.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	8	10
1	8	10

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

13.6b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.2%)

Local error

Found 4 expressions with local error:

13.6b	(/.f64 x (+.f64 (*.f64 x x) 1))
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(+.f64 (*.f64 x x) 1)
13.6b	(/.f64 x (+.f64 (*.f64 x x) 1))

rewrite14.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
9×	`times-frac_binary64_2130`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`associate-/r/_binary64_2070` `pow1_binary64_2185` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `sum-log_binary64_2215` `+-commutative_binary64_2054` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 40

Calls

4 calls:

6.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))

series89.0ms (3.3%)

Counts

2 → 18

Calls

2 calls:

56.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
33.0ms	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 179 to 153 computations (14.5% saved)

simplify82.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5702	821

prune57.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	3	59

Error

Counts

59 → 3

Compiler

Compiled 744 to 425 computations (42.9% saved)

localize8.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
0.0b	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))
13.6b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite66.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`add-sqr-sqrt_binary64_2146`
76×	`times-frac_binary64_2130`
53×	`*-un-lft-identity_binary64_2124`
47×	`sqrt-prod_binary64_2140` `add-cube-cbrt_binary64_2159`
28×	`add-exp-log_binary64_2162`
24×	`associate-l_binary64_2065` `associate-r_binary64_2064`
18×	`add-cbrt-cube_binary64_2160`
15×	`unswap-sqr_binary64_2092`
10×	`sqrt-div_binary64_2141`
9×	`div-exp_binary64_2175`
8×	`pow1_binary64_2185` `prod-exp_binary64_2173`
6×	`associate-/r/_binary64_2070` `associate-/r*_binary64_2068`
5×	`cbrt-undiv_binary64_2158` `flip3-+_binary64_2127` `flip-+_binary64_2098`
4×	`add-log-exp_binary64_2163` `cbrt-unprod_binary64_2157`
3×	`associate-/l*_binary64_2069` `div-inv_binary64_2121`
2×	`sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `1-exp_binary64_2168` `rec-exp_binary64_2174`
1×	`pow-prod-down_binary64_2195` `clear-num_binary64_2123` `-commutative_binary64_2055` `associate-l/_binary64_2067` `associate-*r/_binary64_2066` `frac-times_binary64_2134` `frac-2neg_binary64_2135`

Counts

4 → 158

Calls

8 calls:

29.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
7.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
5.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
4.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
0.0ms	(+.f64 (*.f64 x x) 1)

series216.0ms (8.1%)

Counts

4 → 44

Calls

4 calls:

65.0ms	(/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
58.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) 1))) (/.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
47.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))
46.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 876 to 728 computations (16.9% saved)

simplify100.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4988	3737
1	4988	3737

prune223.0ms (8.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	202	0	202
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	202	3	205

Error

Counts

205 → 3

Compiler

Compiled 4346 to 2670 computations (38.6% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (/.f64 1 x) 3)
0.0b	(-.f64 (/.f64 1 x) (pow.f64 (/.f64 1 x) 3))
0.0b	(-.f64 (/.f64 1 x) (pow.f64 (/.f64 1 x) 3))
0.2b	(pow.f64 (/.f64 1 x) 3)

rewrite49.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64_2146`
65×	`times-frac_binary64_2130`
52×	`*-un-lft-identity_binary64_2124`
35×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
32×	`cancel-sign-sub-inv_binary64_2090` `add-cube-cbrt_binary64_2159`
24×	`difference-of-squares_binary64_2093`
7×	`add-exp-log_binary64_2162`
6×	`div-inv_binary64_2121`
5×	`unpow3_binary64_2190` `sqr-pow_binary64_2096` `add-cbrt-cube_binary64_2160`
4×	`pow-exp_binary64_2192` `pow1_binary64_2185` `add-log-exp_binary64_2163`
3×	`pow-unpow_binary64_2201` `pow-pow_binary64_2196` `distribute-rgt-out--_binary64_2078`
2×	`cube-mult_binary64_2154` `distribute-lft-out--_binary64_2076` `cube-div_binary64_2153` `div-exp_binary64_2175` `rem-cube-cbrt_binary64_2147`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `diff-log_binary64_2216` `sub-neg_binary64_2117` `pow-flip_binary64_2198` `pow-to-exp_binary64_2193` `frac-sub_binary64_2133` `1-exp_binary64_2168` `inv-pow_binary64_2209` `rec-exp_binary64_2174`

Counts

2 → 123

Calls

4 calls:

32.0ms	(-.f64 (/.f64 1 x) (pow.f64 (/.f64 1 x) 3))
6.0ms	(pow.f64 (/.f64 1 x) 3)
0.0ms	(-.f64 (/.f64 1 x) (pow.f64 (/.f64 1 x) 3))
0.0ms	(pow.f64 (/.f64 1 x) 3)

series73.0ms (2.7%)

Counts

2 → 9

Calls

2 calls:

43.0ms	(-.f64 (/.f64 1 x) (pow.f64 (/.f64 1 x) 3))
30.0ms	(pow.f64 (/.f64 1 x) 3)

Compiler

Compiled 119 to 107 computations (10.1% saved)

simplify90.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4874	1815
1	4874	1815

prune106.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	132	3	135

Error

Counts

135 → 3

Compiler

Compiled 1758 to 1287 computations (26.8% saved)

localize9.0ms (0.3%)

Local error

Found 8 expressions with local error:

38.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))
13.6b	(/.f64 x (+.f64 (*.f64 x x) 1))
0.1b	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
0.0b	(+.f64 (*.f64 x x) 1)
0.0b	(+.f64 (*.f64 x x) 1)
0.1b	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
13.6b	(/.f64 x (+.f64 (*.f64 x x) 1))
38.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))

rewrite38.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`times-frac_binary64_2130`
42×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146` `*-un-lft-identity_binary64_2124`
36×	`cbrt-prod_binary64_2155`
30×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
10×	`associate-/r/_binary64_2070`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
6×	`add-log-exp_binary64_2163` `flip3-+_binary64_2127` `flip-+_binary64_2098`
5×	`pow1_binary64_2185` `div-inv_binary64_2121`
3×	`pow-unpow_binary64_2201` `associate-/l_binary64_2069` `associate-/r_binary64_2068`
2×	`unpow3_binary64_2190` `cbrt-undiv_binary64_2158` `cube-mult_binary64_2154` `pow-exp_binary64_2192` `sqr-pow_binary64_2096` `cube-div_binary64_2153` `div-exp_binary64_2175` `rem-cube-cbrt_binary64_2147`
1×	`cbrt-div_binary64_2156` `clear-num_binary64_2123` `pow-pow_binary64_2196` `sum-log_binary64_2215` `rem-cbrt-cube_binary64_2148` `pow1/3_binary64_2206` `+-commutative_binary64_2054` `pow-to-exp_binary64_2193` `frac-2neg_binary64_2135`

Counts

4 → 136

Calls

8 calls:

9.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))
8.0ms	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
6.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
4.0ms	(+.f64 (*.f64 x x) 1)
0.0ms	(+.f64 (*.f64 x x) 1)

series229.0ms (8.6%)

Counts

4 → 42

Calls

4 calls:

74.0ms	(pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3)
64.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 (*.f64 x x) 1)) 3))
59.0ms	(/.f64 x (+.f64 (*.f64 x x) 1))
31.0ms	(+.f64 (*.f64 x x) 1)

Compiler

Compiled 574 to 512 computations (10.8% saved)

simplify61.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5331	3126

prune143.0ms (5.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	178	3	181

Error

Counts

181 → 3

Compiler

Compiled 2726 to 1730 computations (36.5% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	89	240
1	89	240

regimes46.0ms (1.7%)

Compiler: Compiled 164 to 121 computations (26.2% saved)

bsearch26.0ms (1%)

Steps

Iters	Range		Point
7	3300.8171630890365	98334.15580277613	8059.235026241259
10	-2.6174055497552223e+163	-1.8577649206569656e+151	-1.3314234767781347e+154

Compiler

Compiled 1 to 1 computations (0% saved)

regimes38.0ms (1.4%)

Compiler: Compiled 92 to 76 computations (17.4% saved)

bsearch21.0ms (0.8%)

Steps

Iters	Range		Point
7	3300.8171630890365	98334.15580277613	10116.622441239831
9	-1.0683684742596149e+24	-3.1959860145551867e+18	-6.886016478389994e+23

Compiler

Compiled 1 to 1 computations (0% saved)

regimes25.0ms (1%)

Compiler: Compiled 25 to 24 computations (4% saved)

bsearch20.0ms (0.8%)

Steps

Iters	Range		Point
6	23020028.068672698	316186952.08936507	168600820.6981643
9	-1.0683684742596149e+24	-3.1959860145551867e+18	-6.886016478389994e+23

Compiler

Compiled 1 to 1 computations (0% saved)

regimes22.0ms (0.8%)

Compiler: Compiled 9 to 12 computations (-33.3% saved)

bsearch24.0ms (0.9%)

Steps

Iters	Range		Point
10	1.2571684454435198e-15	1.2251308373656755	1.0062406200728051
11	-3.1959860145551867e+18	-0.007102553974907408	-0.9998958798409431

Compiler

Compiled 1 to 1 computations (0% saved)

regimes8.0ms (0.3%)

Compiler: Compiled 6 to 9 computations (-50% saved)

bsearch0.0ms (0%)

regimes10.0ms (0.4%)

Accuracy

Total 0.0b remaining (93.5%)

Threshold costs 0.0b (93.5%)

Compiler

Compiled 5 to 8 computations (-60% saved)

bsearch6.0ms (0.2%)

Compiler: Compiled 107 to 80 computations (25.2% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	64	150
1	64	150

end0.0ms (0%)

sample632.0ms (23.8%)

Algorithm

1×

intervals

Results

168.0ms

8000×

body

128

valid

Compiler

Compiled 280 to 210 computations (25% saved)

Pareto

0.9675906632225816

Details

analyze1.0ms (0.1%)

sample10.0ms (0.4%)

simplify97.0ms (3.6%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

rewrite14.0ms (0.5%)

series89.0ms (3.3%)

simplify82.0ms (3.1%)

prune57.0ms (2.1%)

localize8.0ms (0.3%)

rewrite66.0ms (2.5%)

series216.0ms (8.1%)

simplify100.0ms (3.7%)

prune223.0ms (8.4%)

localize5.0ms (0.2%)

rewrite49.0ms (1.8%)

series73.0ms (2.7%)

simplify90.0ms (3.4%)

prune106.0ms (4%)

localize9.0ms (0.3%)

rewrite38.0ms (1.4%)

series229.0ms (8.6%)

simplify61.0ms (2.3%)

prune143.0ms (5.4%)

simplify5.0ms (0.2%)

regimes46.0ms (1.7%)

bsearch26.0ms (1%)

regimes38.0ms (1.4%)

bsearch21.0ms (0.8%)

regimes25.0ms (1%)

bsearch20.0ms (0.8%)

regimes22.0ms (0.8%)

bsearch24.0ms (0.9%)

regimes8.0ms (0.3%)

bsearch0.0ms (0%)

regimes10.0ms (0.4%)

bsearch6.0ms (0.2%)

simplify4.0ms (0.2%)

end0.0ms (0%)

sample632.0ms (23.8%)

Profiling