Details

analyze687.0ms (5%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4937	96
1	4937	96
0	3	3
1	3	3

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%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample43.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	40×	body	2048	valid
8.0ms	161×	body	128	valid
5.0ms	28×	body	1024	valid
4.0ms	14×	body	4096	valid
1.0ms	9×	body	512	valid
1.0ms	17×	body	128	nan
1.0ms	16×	body	128	invalid
0.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify280.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (274.0ms)

Iter	Nodes	Cost
0	1802	24
1	1802	24

prune4.0ms (0%)

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

Error

33.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.6b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite156.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

33.3b

Rules

21×	`add-sqr-sqrt_binary64_2146`
14×	`*-un-lft-identity_binary64_2124`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163` `add-cube-cbrt_binary64_2159`
6×	`sqrt-prod_binary64_2140` `difference-of-squares_binary64_2093` `times-frac_binary64_2130` `associate-/l*_binary64_2069`
5×	`pow1_binary64_2185`
4×	`flip3--_binary64_2128` `flip--_binary64_2099` `cancel-sign-sub-inv_binary64_2090`
3×	`distribute-lft-out--_binary64_2076`
2×	`sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-/l/_binary64_2071`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `frac-2neg_binary64_2135` `div-sub_binary64_2129` `clear-num_binary64_2123` `div-inv_binary64_2121` `associate-/r*_binary64_2068`

Counts

4 → 74

Calls

4 calls:

16.0ms	(/.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)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

Compiler

Compiled 2100 to 1220 computations (41.9% saved)

series755.0ms (5.5%)

Error

5.1b

Counts

4 → 71

Calls

4 calls:

213.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
159.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
157.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
156.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)

Compiler

Compiled 3273 to 2496 computations (23.7% saved)

simplify53.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5082	2976

prune171.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	133	12	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Error

5.0b

Counts

146 → 12

Compiler

Compiled 3110 to 1711 computations (45% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 3 (.f64 a c))
0.6b	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite95.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

12×	`add-sqr-sqrt_binary64_2146`
10×	`pow1_binary64_2185`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160` `*-un-lft-identity_binary64_2124`
8×	`add-log-exp_binary64_2163`
7×	`add-cube-cbrt_binary64_2159`
4×	`sqrt-prod_binary64_2140` `cancel-sign-sub-inv_binary64_2090`
3×	`flip3--_binary64_2128` `flip--_binary64_2099` `pow-prod-down_binary64_2195` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `associate-l_binary64_2065`
2×	`sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `difference-of-squares_binary64_2093`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `distribute-lft-out--_binary64_2076` `associate-r_binary64_2064` `*-commutative_binary64_2055`

Counts

4 → 62

Calls

4 calls:

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

Compiler

Compiled 1583 to 833 computations (47.4% saved)

series577.0ms (4.2%)

Error

5.0b

Counts

4 → 60

Calls

4 calls:

160.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))) b)
159.0ms	(-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))
154.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
59.0ms	(.f64 3 (.f64 a c))

Compiler

Compiled 2764 to 2086 computations (24.5% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5040	1909

prune121.0ms (0.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	124	10	134

Error

5.0b

Counts

134 → 10

Compiler

Compiled 2479 to 1366 computations (44.9% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
4.8b	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))) 3) a)
8.9b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite545.0ms (4%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

274×	`times-frac_binary64_2130`
140×	`*-un-lft-identity_binary64_2124`
111×	`add-sqr-sqrt_binary64_2146`
110×	`add-cube-cbrt_binary64_2159`
35×	`associate-/l*_binary64_2069`
33×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
26×	`associate-/r/_binary64_2070`
18×	`div-inv_binary64_2121`
15×	`div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `distribute-lft-out_binary64_2075`
14×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
7×	`associate-/r*_binary64_2068`
6×	`add-log-exp_binary64_2163` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157`
5×	`pow1_binary64_2185`
3×	`sqrt-prod_binary64_2140`
2×	`sqrt-div_binary64_2141` `frac-2neg_binary64_2135` `clear-num_binary64_2123`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3--_binary64_2128` `flip--_binary64_2099` `rem-sqrt-square_binary64_2137` `associate-/l/_binary64_2071` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 214

Calls

4 calls:

21.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))) 3) a)
12.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 9294 to 5213 computations (43.9% saved)

series956.0ms (6.9%)

Error

5.0b

Counts

4 → 71

Calls

4 calls:

314.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
256.0ms	(/.f64 (/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))) 3) a)
163.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
157.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))

Compiler

Compiled 4410 to 3194 computations (27.6% saved)

simplify129.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

285 → 285

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4947	11422
1	4947	11422

prune518.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	284	1	285
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	286	9	295

Error

5.0b

Counts

295 → 9

Compiler

Compiled 9688 to 5410 computations (44.2% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
1.9b	(/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))) a)
7.8b	(.f64 a (/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))))) a))
21.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite792.0ms (5.8%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

409×	`times-frac_binary64_2130`
293×	`*-un-lft-identity_binary64_2124`
213×	`add-sqr-sqrt_binary64_2146`
207×	`add-cube-cbrt_binary64_2159`
126×	`distribute-rgt-neg-in_binary64_2082` `distribute-lft-neg-in_binary64_2081`
124×	`associate-r_binary64_2064`
43×	`distribute-lft-out_binary64_2075`
40×	`associate-/l*_binary64_2069`
28×	`associate-/r/_binary64_2070`
16×	`div-inv_binary64_2121`
15×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
11×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`pow1_binary64_2185` `neg-mul-1_binary64_2120`
6×	`add-log-exp_binary64_2163`
3×	`sqrt-prod_binary64_2140` `associate-l_binary64_2065` `associate-/r*_binary64_2068`
2×	`sqrt-div_binary64_2141` `div-exp_binary64_2175` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `cbrt-undiv_binary64_2158` `unswap-sqr_binary64_2092` `distribute-frac-neg_binary64_2087`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `flip3--_binary64_2128` `flip--_binary64_2099` `rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `distribute-rgt-neg-out_binary64_2084` `associate-r/_binary64_2066` `-commutative_binary64_2055` `frac-2neg_binary64_2135` `neg-sub0_binary64_2119` `div-sub_binary64_2129` `clear-num_binary64_2123` `distribute-neg-frac_binary64_2088` `associate-/l/_binary64_2071` `sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 349

Calls

4 calls:

47.0ms	(.f64 a (/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))))) a))
18.0ms	(/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 13349 to 6346 computations (52.5% saved)

series955.0ms (6.9%)

Error

5.0b

Counts

4 → 72

Calls

4 calls:

309.0ms	(/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))) a)
259.0ms	(.f64 a (/.f64 (neg.f64 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))))) a))
163.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
156.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))

Compiler

Compiled 4083 to 2835 computations (30.6% saved)

simplify137.0ms (1%)

Algorithm

1×	egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5233	14454

prune611.0ms (4.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	418	3	421
Fresh	1	6	7
Picked	1	0	1
Done	0	1	1
Total	420	10	430

Error

5.0b

Counts

430 → 10

Compiler

Compiled 13742 to 6149 computations (55.3% saved)

regimes2.3s (17.1%)

Accuracy

Total 4.7b remaining (45.7%)

Threshold costs 0b (0%)

Compiler

Compiled 15000 to 11455 computations (23.6% saved)

bsearch104.0ms (0.8%)

Steps

Iters	Range	Point
7	1.7162538938544096e+106	3.527359308077059e+107	7.728774522489216e+106
9	2.7045461500023634e-109	5.883438526044507e-104	1.3752342204584442e-108
7	-4.524584541934418e+90	-1.1382336130167342e+89	-4.439880162502227e+90

Iters

Range

Point

1.7162538938544096e+106

3.527359308077059e+107

7.728774522489216e+106

2.7045461500023634e-109

5.883438526044507e-104

1.3752342204584442e-108

-4.524584541934418e+90

-1.1382336130167342e+89

-4.439880162502227e+90

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	88
1	141	88

end0.0ms (0%)

sample3.6s (26.3%)

Algorithm

1×

intervals

Results

294.0ms	1151×	body	2048	valid
262.0ms	5150×	body	128	valid
139.0ms	718×	body	1024	valid
124.0ms	426×	body	4096	valid
52.0ms	380×	body	512	valid
33.0ms	687×	body	128	nan
23.0ms	407×	body	128	invalid
17.0ms	175×	body	256	valid

Compiler

Compiled 2881 to 2201 computations (23.6% saved)

Details

analyze687.0ms (5%)

sample43.0ms (0.3%)

simplify280.0ms (2%)

prune4.0ms (0%)

localize10.0ms (0.1%)

rewrite156.0ms (1.1%)

series755.0ms (5.5%)

simplify53.0ms (0.4%)

prune171.0ms (1.2%)

localize10.0ms (0.1%)

rewrite95.0ms (0.7%)

series577.0ms (4.2%)

simplify60.0ms (0.4%)

prune121.0ms (0.9%)

localize14.0ms (0.1%)

rewrite545.0ms (4%)

series956.0ms (6.9%)

simplify129.0ms (0.9%)

prune518.0ms (3.8%)

localize13.0ms (0.1%)

rewrite792.0ms (5.8%)

series955.0ms (6.9%)

simplify137.0ms (1%)

prune611.0ms (4.4%)

regimes2.3s (17.1%)

bsearch104.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (26.3%)

Profiling