Details

analyze901.0ms (2.4%)

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%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample86.0ms (0.2%)

Algorithm

1×

intervals

Results

20.0ms	166×	body	128	valid
19.0ms	39×	body	2048	valid
10.0ms	27×	body	1024	valid
9.0ms	15×	body	4096	valid
2.0ms	24×	body	128	nan
2.0ms	17×	body	128	invalid
1.0ms	5×	body	512	valid
1.0ms	4×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify758.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (596.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune8.0ms (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

33.4b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite284.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

33.2b

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:

25.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
23.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

Compiler

Compiled 2100 to 1220 computations (41.9% saved)

series1.3s (3.3%)

Error

6.4b

Counts

4 → 66

Calls

4 calls:

329.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
310.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
265.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
263.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2861 to 2182 computations (23.7% saved)

simplify135.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5453	2668

prune273.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	128	12	140
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	129	12	141

Error

6.2b

Counts

141 → 12

Compiler

Compiled 2965 to 1583 computations (46.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

rewrite253.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

28×	`add-sqr-sqrt_binary64_2146`
18×	`*-un-lft-identity_binary64_2124`
14×	`add-cube-cbrt_binary64_2159`
13×	`associate-r_binary64_2064`
10×	`times-frac_binary64_2130`
9×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
7×	`pow1_binary64_2185`
6×	`associate-l_binary64_2065`
5×	`flip3--_binary64_2128` `flip--_binary64_2099` `sqrt-prod_binary64_2140`
4×	`difference-of-squares_binary64_2093` `cancel-sign-sub-inv_binary64_2090`
2×	`sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117` `distribute-lft-out--_binary64_2076` `prod-exp_binary64_2173` `cbrt-unprod_binary64_2157` `frac-times_binary64_2134` `unswap-sqr_binary64_2092` `associate-*l/_binary64_2067`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow-prod-down_binary64_2195` `div-exp_binary64_2175` `cbrt-undiv_binary64_2158` `associate-r/_binary64_2066` `div-inv_binary64_2121` `-commutative_binary64_2055`

Counts

4 → 83

Calls

4 calls:

27.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 2366 to 1383 computations (41.5% saved)

series1.2s (3%)

Error

6.2b

Counts

4 → 66

Calls

4 calls:

322.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (/.f64 1/2 a))
270.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
243.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
239.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

Compiler

Compiled 2861 to 2182 computations (23.7% saved)

simplify146.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5157	2914

prune261.0ms (0.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	3	149
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	150	11	161

Error

6.2b

Counts

161 → 11

Compiler

Compiled 3092 to 1647 computations (46.7% saved)

localize25.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite2.0s (5.1%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

693×	`times-frac_binary64_2130`
439×	`add-sqr-sqrt_binary64_2146`
364×	`*-un-lft-identity_binary64_2124`
290×	`add-cube-cbrt_binary64_2159`
74×	`difference-of-squares_binary64_2093`
71×	`associate-/r*_binary64_2068`
40×	`sqrt-prod_binary64_2140`
37×	`distribute-lft-out--_binary64_2076`
25×	`add-exp-log_binary64_2162`
17×	`div-inv_binary64_2121`
15×	`div-exp_binary64_2175`
13×	`add-cbrt-cube_binary64_2160`
8×	`add-log-exp_binary64_2163`
6×	`pow1_binary64_2185` `cbrt-undiv_binary64_2158`
5×	`associate-/r/_binary64_2070`
4×	`cancel-sign-sub-inv_binary64_2090`
3×	`flip3--_binary64_2128` `flip--_binary64_2099` `1-exp_binary64_2168` `rec-exp_binary64_2174` `associate-/l*_binary64_2069`
2×	`sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `inv-pow_binary64_2209` `pow-flip_binary64_2198` `frac-2neg_binary64_2135` `clear-num_binary64_2123`

Counts

4 → 356

Calls

4 calls:

51.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 14021 to 8305 computations (40.8% saved)

series1.2s (3.1%)

Error

6.2b

Counts

4 → 66

Calls

4 calls:

330.0ms	(/.f64 1 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
273.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
248.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
237.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3119 to 2440 computations (21.8% saved)

simplify390.0ms (1%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (148.0ms)

Iter	Nodes	Cost
0	4969	16975
1	4969	16975

prune1.3s (3.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	420	2	422
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	421	12	433

Error

6.2b

Counts

433 → 12

Compiler

Compiled 13565 to 7517 computations (44.6% saved)

localize28.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite9.2s (24.2%)

Algorithm

1×	rewrite-expression-head

Error

6.2b

Rules

3251×	`times-frac_binary64_2130`
1761×	`add-sqr-sqrt_binary64_2146`
1506×	`*-un-lft-identity_binary64_2124`
1252×	`add-cube-cbrt_binary64_2159`
254×	`difference-of-squares_binary64_2093`
130×	`sqrt-prod_binary64_2140`
129×	`div-inv_binary64_2121`
127×	`distribute-lft-out--_binary64_2076`
87×	`add-exp-log_binary64_2162`
71×	`associate-/r*_binary64_2068`
70×	`div-exp_binary64_2175`
25×	`add-cbrt-cube_binary64_2160`
15×	`1-exp_binary64_2168` `rec-exp_binary64_2174` `cbrt-undiv_binary64_2158` `associate-/r/_binary64_2070`
13×	`associate-/l*_binary64_2069`
8×	`add-log-exp_binary64_2163`
5×	`pow1_binary64_2185`
4×	`cancel-sign-sub-inv_binary64_2090`
3×	`flip3--_binary64_2128` `flip--_binary64_2099`
2×	`sqrt-div_binary64_2141` `diff-log_binary64_2216` `sub-neg_binary64_2117`
1×	`pow1/2_binary64_2204` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `frac-2neg_binary64_2135` `clear-num_binary64_2123` `associate-/l/_binary64_2071`

Counts

4 → 1097

Calls

4 calls:

82.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
15.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
8.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

Compiler

Compiled 50764 to 33343 computations (34.3% saved)

series1.2s (3.1%)

Error

6.2b

Counts

4 → 66

Calls

4 calls:

319.0ms	(/.f64 (/.f64 1 a) (/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b) 2)))
275.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
253.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
248.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Compiler

Compiled 3377 to 2698 computations (20.1% saved)

simplify1.0s (2.7%)

Algorithm

1×	egg-herbie

Counts

1163 → 1163

Iterations

Useful iterations: 0 (141.0ms)

Iter	Nodes	Cost
0	4991	63984
1	4991	63984

prune7.2s (18.9%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	1163	0	1163
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	1163	12	1175

Error

6.2b

Counts

1175 → 12

Compiler

Compiled 44301 to 26638 computations (39.9% saved)

regimes3.0s (7.8%)

Accuracy

Total 4.7b remaining (44.7%)

Threshold costs 0b (0%)

Compiler

Compiled 8120 to 6350 computations (21.8% saved)

bsearch127.0ms (0.3%)

Steps

Iters	Range		Point
8	1.1174011683600933e-45	3.090616621213472e-41	6.612192249716975e-43
10	-9.566101091422452e+29	-3.705054009934488e+18	-9.448798679205101e+29

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample5.9s (15.4%)

Algorithm

1×

intervals

Results

549.0ms	1145×	body	2048	valid
509.0ms	5165×	body	128	valid
294.0ms	766×	body	1024	valid
246.0ms	406×	body	4096	valid
96.0ms	330×	body	512	valid
63.0ms	683×	body	128	nan
44.0ms	361×	body	128	invalid
35.0ms	188×	body	256	valid

Compiler

Compiled 2119 to 1648 computations (22.2% saved)

Details

analyze901.0ms (2.4%)

sample86.0ms (0.2%)

simplify758.0ms (2%)

prune8.0ms (0%)

localize24.0ms (0.1%)

rewrite284.0ms (0.7%)

series1.3s (3.3%)

simplify135.0ms (0.4%)

prune273.0ms (0.7%)

localize22.0ms (0.1%)

rewrite253.0ms (0.7%)

series1.2s (3%)

simplify146.0ms (0.4%)

prune261.0ms (0.7%)

localize25.0ms (0.1%)

rewrite2.0s (5.1%)

series1.2s (3.1%)

simplify390.0ms (1%)

prune1.3s (3.5%)

localize28.0ms (0.1%)

rewrite9.2s (24.2%)

series1.2s (3.1%)

simplify1.0s (2.7%)

prune7.2s (18.9%)

regimes3.0s (7.8%)

bsearch127.0ms (0.3%)

simplify7.0ms (0%)

end0.0ms (0%)

sample5.9s (15.4%)

Profiling