Details

analyze696.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify278.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	5230	22

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

27.9b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
27.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite16.0ms (0.1%)

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×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `pow1_binary64_2185` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `div-sub_binary64_2129` `flip-+_binary64_2098` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 44

Calls

4 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series588.0ms (5.1%)

Counts

2 → 48

Calls

2 calls:

417.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))
171.0ms	(-.f64 (.f64 b c) (.f64 a d))

Compiler

Compiled 1068 to 882 computations (17.4% saved)

simplify120.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4930	1785
1	4930	1785

prune183.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	9	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Error

3.5b

Counts

93 → 9

Compiler

Compiled 1890 to 265 computations (86% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
18.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
0.0b	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
18.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite60.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2146`
21×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
18×	`sqrt-prod_binary64_2140` `times-frac_binary64_2130`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 86

Calls

8 calls:

19.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(/.f64 (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

series1.0s (9%)

Counts

4 → 94

Calls

4 calls:

546.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
180.0ms	(-.f64 (.f64 b c) (.f64 a d))
159.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
140.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3558 to 2514 computations (29.3% saved)

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5182	3736

prune232.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	177	3	180
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	179	10	189

Error

3.5b

Counts

189 → 10

Compiler

Compiled 5476 to 796 computations (85.5% saved)

localize14.0ms (0.1%)

Local error

Found 8 expressions with local error:

30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
18.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
0.9b	(-.f64 (.f64 b c) (.f64 a d))
18.0b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_2146`
21×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
18×	`sqrt-prod_binary64_2140` `times-frac_binary64_2130`
6×	`sqrt-div_binary64_2141` `pow1_binary64_2185` `associate-/r*_binary64_2068` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`associate-/l*_binary64_2069` `flip3-+_binary64_2127` `flip-+_binary64_2098`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `associate-/r/_binary64_2070` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `cancel-sign-sub-inv_binary64_2090` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 86

Calls

8 calls:

9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
6.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
0.0ms	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))

series1.1s (9.3%)

Counts

4 → 94

Calls

4 calls:

531.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
203.0ms	(-.f64 (.f64 b c) (.f64 a d))
174.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
150.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 3810 to 2766 computations (27.4% saved)

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5182	3736

prune196.0ms (1.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	180	0	180
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	180	10	190

Error

3.5b

Counts

190 → 10

Compiler

Compiled 5809 to 1182 computations (79.7% saved)

localize19.0ms (0.2%)

Local error

Found 8 expressions with local error:

9.7b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
8.4b	(/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
0.9b	(-.f64 (.f64 c b) (.f64 d a))
0.0b	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
9.7b	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.3b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite137.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

585×	`sqrt-prod_binary64_2140`
567×	`times-frac_binary64_2130`
302×	`add-sqr-sqrt_binary64_2146`
299×	`add-cube-cbrt_binary64_2159` `*-un-lft-identity_binary64_2124`
50×	`sqrt-div_binary64_2141`
33×	`associate-/l*_binary64_2069`
22×	`associate-/r/_binary64_2070`
14×	`flip3-+_binary64_2127` `flip-+_binary64_2098`
11×	`div-inv_binary64_2121`
9×	`associate-/r*_binary64_2068` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
7×	`pow1_binary64_2185`
4×	`add-log-exp_binary64_2163`
3×	`cbrt-undiv_binary64_2158` `sqrt-pow1_binary64_2142` `rem-sqrt-square_binary64_2137` `pow1/2_binary64_2204` `div-exp_binary64_2175`
2×	`div-sub_binary64_2129`
1×	`clear-num_binary64_2123` `associate-/l/_binary64_2071` `frac-2neg_binary64_2135`

Counts

4 → 402

Calls

8 calls:

26.0ms	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
0.0ms	(/.f64 (/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))

series1.0s (8.9%)

Counts

4 → 88

Calls

4 calls:

529.0ms	(/.f64 (/.f64 (-.f64 (.f64 c b) (.f64 d a)) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))) (sqrt.f64 (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))))
166.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
161.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
158.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

Compiler

Compiled 4248 to 2820 computations (33.6% saved)

simplify309.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5170	26501

prune640.0ms (5.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	490	0	490
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	490	10	500

Error

3.5b

Counts

500 → 10

Compiler

Compiled 24577 to 2216 computations (91% saved)

simplify19.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	261	1254
1	261	1254

regimes805.0ms (7%)

Accuracy

Total 9.8b remaining (65.9%)

Threshold costs 0b (0%)

Compiler

Compiled 4342 to 2433 computations (44% saved)

bsearch118.0ms (1%)

Steps

Iters	Range		Point
9	1.585010678955201e+40	6.464176775332817e+45	5.943546987088161e+45
10	1.5317612403127707e-115	3.142734090316026e-99	4.0526762739374186e-107
8	-2.271203142594088e-161	-4.727330348033218e-164	-2.178304667980649e-161
8	-6.401469326770505e+102	-6.659753031856651e+99	-2.623594142603243e+102

Compiler

Compiled 1 to 4 computations (-300% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	138
1	80	138

end0.0ms (0%)

sample3.6s (31.6%)

Algorithm

1×

intervals

Results

433.0ms	8000×	body	128	valid
26.0ms	494×	body	128	invalid

Compiler

Compiled 2730 to 1477 computations (45.9% saved)

Pareto

0.19977401600125344

Details

analyze696.0ms (6.1%)

sample22.0ms (0.2%)

simplify278.0ms (2.4%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite16.0ms (0.1%)

series588.0ms (5.1%)

simplify120.0ms (1.1%)

prune183.0ms (1.6%)

localize25.0ms (0.2%)

rewrite60.0ms (0.5%)

series1.0s (9%)

simplify83.0ms (0.7%)

prune232.0ms (2%)

localize14.0ms (0.1%)

rewrite33.0ms (0.3%)

series1.1s (9.3%)

simplify111.0ms (1%)

prune196.0ms (1.7%)

localize19.0ms (0.2%)

rewrite137.0ms (1.2%)

series1.0s (8.9%)

simplify309.0ms (2.7%)

prune640.0ms (5.6%)

simplify19.0ms (0.2%)

regimes805.0ms (7%)

bsearch118.0ms (1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (31.6%)

Profiling