Details

analyze278.0ms (4.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample43.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	124×	body	256	valid
9.0ms	286×	pre	128	true
6.0ms	44×	body	512	valid
4.0ms	88×	body	128	valid
1.0ms	30×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify364.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (269.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 53.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.2b	(.f64 (.f64 3 a) c)
27.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
14×	`add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
9×	`pow1_binary64_2185`
8×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093` `associate-/l*_binary64_2069` `times-frac_binary64_2130`
4×	`cancel-sign-sub-inv_binary64_2090` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
3×	`flip--_binary64_2099` `pow-prod-down_binary64_2195` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `sqrt-prod_binary64_2140` `associate-r_binary64_2064`
2×	`cbrt-undiv_binary64_2158` `diff-log_binary64_2216` `sub-neg_binary64_2117` `associate-/l/_binary64_2071` `div-exp_binary64_2175`
1×	`clear-num_binary64_2123` `-commutative_binary64_2055` `associate-/r_binary64_2068` `associate-l_binary64_2065` `div-sub_binary64_2129` `div-inv_binary64_2121` `frac-2neg_binary64_2135`

Counts

4 → 77

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

series260.0ms (3.9%)

Counts

4 → 33

Calls

4 calls:

113.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
78.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
39.0ms	(.f64 (.f64 3 a) c)
30.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify50.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5232	2392

prune155.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 0.7b

Counts

111 → 10

Compiler

Compiled 2771 to 1610 computations (41.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
0.3b	(.f64 a (.f64 c c))
0.3b	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
0.3b	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

68×	`add-exp-log_binary64_2162`
32×	`add-cbrt-cube_binary64_2160`
31×	`prod-exp_binary64_2173`
24×	`times-frac_binary64_2130`
19×	`associate-l_binary64_2065` `add-sqr-sqrt_binary64_2146`
18×	`div-exp_binary64_2175`
16×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
13×	`cbrt-unprod_binary64_2157`
12×	`associate-/r*_binary64_2068`
11×	`pow1_binary64_2185`
9×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
6×	`cbrt-undiv_binary64_2158` `pow-exp_binary64_2192` `add-log-exp_binary64_2163` `pow-to-exp_binary64_2193`
4×	`pow-prod-down_binary64_2195` `associate-r_binary64_2064`
3×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `associate-*l/_binary64_2067` `sqr-pow_binary64_2096`
2×	`unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `div-inv_binary64_2121`
1×	`clear-num_binary64_2123` `sum-log_binary64_2215` `associate-/l*_binary64_2069` `+-commutative_binary64_2054` `flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-add_binary64_2132` `frac-2neg_binary64_2135`

Counts

4 → 122

Calls

4 calls:

13.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
10.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
8.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
6.0ms	(.f64 a (.f64 c c))

series473.0ms (7.1%)

Counts

4 → 33

Calls

4 calls:

186.0ms	(.f64 (/.f64 (.f64 a (*.f64 c c)) (pow.f64 b 3)) -3/8)
175.0ms	(/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3))
71.0ms	(+.f64 (.f64 (/.f64 c b) -1/2) (.f64 (/.f64 (.f64 a (.f64 c c)) (pow.f64 b 3)) -3/8))
41.0ms	(.f64 a (.f64 c c))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5158	2520

prune166.0ms (2.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	151	4	155
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	151	14	165

Merged error: 0.7b

Counts

165 → 14

Compiler

Compiled 3645 to 1902 computations (47.8% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 a c) b) -3/2)
0.3b	(.f64 (.f64 c c) (*.f64 a a))
0.3b	(/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b 3))
0.4b	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))

rewrite62.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

79×	`add-exp-log_binary64_2162`
48×	`add-cbrt-cube_binary64_2160`
37×	`prod-exp_binary64_2173`
34×	`pow1_binary64_2185`
21×	`cbrt-unprod_binary64_2157`
19×	`div-exp_binary64_2175`
18×	`times-frac_binary64_2130`
17×	`add-sqr-sqrt_binary64_2146`
15×	`pow-prod-down_binary64_2195` `add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
13×	`associate-/r*_binary64_2068`
9×	`cbrt-undiv_binary64_2158`
8×	`associate-l_binary64_2065`
6×	`unpow-prod-down_binary64_2203` `cube-prod_binary64_2152`
5×	`pow-exp_binary64_2192` `pow-to-exp_binary64_2193`
4×	`pow-prod-up_binary64_2194` `associate-/l_binary64_2069` `add-log-exp_binary64_2163` `pow-plus_binary64_2187` `associate-r*_binary64_2064`
3×	`associate-*l/_binary64_2067` `div-inv_binary64_2121` `associate-/l/_binary64_2071`
2×	`unpow3_binary64_2190` `clear-num_binary64_2123` `unswap-sqr_binary64_2092` `cube-mult_binary64_2154` `*-commutative_binary64_2055` `sqr-pow_binary64_2096` `pow2_binary64_2205` `pow-sqr_binary64_2097` `frac-2neg_binary64_2135`
1×	`flip3-+_binary64_2127` `flip-+_binary64_2098` `frac-add_binary64_2132`

Counts

4 → 135

Calls

4 calls:

14.0ms	(/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b 3))
13.0ms	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))
13.0ms	(.f64 (.f64 c c) (*.f64 a a))
8.0ms	(.f64 (/.f64 (.f64 a c) b) -3/2)

series431.0ms (6.5%)

Counts

4 → 33

Calls

4 calls:

174.0ms	(/.f64 (.f64 (.f64 c c) (*.f64 a a)) (pow.f64 b 3))
107.0ms	(/.f64 (+.f64 (.f64 (/.f64 (.f64 a c) b) -3/2) (.f64 (/.f64 (.f64 (.f64 c c) (.f64 a a)) (pow.f64 b 3)) -9/8)) (*.f64 3 a))
97.0ms	(.f64 (/.f64 (.f64 a c) b) -3/2)
53.0ms	(.f64 (.f64 c c) (*.f64 a a))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4956	3009
1	4956	3009

prune232.0ms (3.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	164	4	168
Fresh	1	11	12
Picked	1	0	1
Done	0	1	1
Total	166	16	182

Merged error: 0.7b

Counts

182 → 16

Compiler

Compiled 5298 to 2635 computations (50.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)) -9/8)
0.3b	(.f64 (/.f64 (.f64 a c) b) -3/2)
0.3b	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
0.5b	(.f64 (.f64 a c) (*.f64 a c))

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`add-exp-log_binary64_2162`
76×	`prod-exp_binary64_2173`
68×	`add-cbrt-cube_binary64_2160`
47×	`pow1_binary64_2185`
34×	`cbrt-unprod_binary64_2157`
32×	`div-exp_binary64_2175`
31×	`times-frac_binary64_2130`
29×	`add-sqr-sqrt_binary64_2146`
24×	`associate-l_binary64_2065`
19×	`pow-prod-down_binary64_2195`
18×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
12×	`cbrt-undiv_binary64_2158` `associate-/r*_binary64_2068`
10×	`unpow-prod-down_binary64_2203` `pow-exp_binary64_2192` `cube-prod_binary64_2152` `pow-to-exp_binary64_2193`
7×	`associate-r_binary64_2064`
6×	`unswap-sqr_binary64_2092`
4×	`pow-prod-up_binary64_2194` `add-log-exp_binary64_2163` `sqr-pow_binary64_2096` `pow-sqr_binary64_2097`
3×	`unpow3_binary64_2190` `cube-mult_binary64_2154` `*-commutative_binary64_2055` `div-inv_binary64_2121`
2×	`associate-*l/_binary64_2067` `pow-plus_binary64_2187`
1×	`clear-num_binary64_2123` `associate-/l*_binary64_2069` `swap-sqr_binary64_2091` `pow2_binary64_2205` `frac-2neg_binary64_2135`

Counts

4 → 172

Calls

4 calls:

18.0ms	(.f64 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)) -9/8)
12.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
7.0ms	(.f64 (/.f64 (.f64 a c) b) -3/2)
7.0ms	(.f64 (.f64 a c) (*.f64 a c))

series546.0ms (8.2%)

Counts

4 → 33

Calls

4 calls:

205.0ms	(.f64 (/.f64 (.f64 (.f64 a c) (.f64 a c)) (pow.f64 b 3)) -9/8)
192.0ms	(/.f64 (.f64 (.f64 a c) (*.f64 a c)) (pow.f64 b 3))
95.0ms	(.f64 (/.f64 (.f64 a c) b) -3/2)
53.0ms	(.f64 (.f64 a c) (*.f64 a c))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5003	2984

prune256.0ms (3.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	205	0	205
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	205	16	221

Merged error: 0.7b

Counts

221 → 16

Compiler

Compiled 5628 to 2767 computations (50.8% saved)

regimes447.0ms (6.7%)

Compiler: Compiled 6438 to 4657 computations (27.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	25
1	19	25

end0.0ms (0%)

sample2.4s (36.9%)

Algorithm

1×

intervals

Results

482.0ms	8843×	pre	128	true
393.0ms	3864×	body	256	valid
225.0ms	1457×	body	512	valid
140.0ms	2679×	body	128	valid
41.0ms	843×	body	128	nan

Compiler

Compiled 1243 to 900 computations (27.6% saved)

Details

analyze278.0ms (4.2%)

sample43.0ms (0.7%)

simplify364.0ms (5.5%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.5%)

series260.0ms (3.9%)

simplify50.0ms (0.8%)

prune155.0ms (2.3%)

localize12.0ms (0.2%)

rewrite46.0ms (0.7%)

series473.0ms (7.1%)

simplify72.0ms (1.1%)

prune166.0ms (2.5%)

localize17.0ms (0.3%)

rewrite62.0ms (0.9%)

series431.0ms (6.5%)

simplify67.0ms (1%)

prune232.0ms (3.5%)

localize15.0ms (0.2%)

rewrite63.0ms (0.9%)

series546.0ms (8.2%)

simplify77.0ms (1.2%)

prune256.0ms (3.9%)

regimes447.0ms (6.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (36.9%)

Profiling