Details

analyze691.0ms (5.6%)

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

Symmetry

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample47.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	40×	body	2048	valid
8.0ms	159×	body	128	valid
5.0ms	18×	body	4096	valid
5.0ms	14×	body	512	valid
4.0ms	20×	body	1024	valid
1.0ms	21×	body	128	nan
0.0ms	5×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify286.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (281.0ms)

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

34.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite109.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Error

34.1b

Rules

12×	`add-sqr-sqrt_binary64_2487`
10×	`pow1_binary64_2526`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `*-un-lft-identity_binary64_2465`
8×	`add-log-exp_binary64_2504`
7×	`add-cube-cbrt_binary64_2500`
4×	`sqrt-prod_binary64_2481` `cancel-sign-sub-inv_binary64_2431`
3×	`flip3--_binary64_2469` `flip--_binary64_2440` `pow-prod-down_binary64_2536` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498` `associate-r_binary64_2405`
2×	`sqrt-div_binary64_2482` `diff-log_binary64_2557` `sub-neg_binary64_2458` `difference-of-squares_binary64_2434`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `rem-sqrt-square_binary64_2478` `distribute-lft-out--_binary64_2417` `associate-l_binary64_2406` `*-commutative_binary64_2396`

Counts

4 → 62

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(.f64 (.f64 3 a) c)
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 1583 to 924 computations (41.6% saved)

series542.0ms (4.4%)

Error

13.1b

Counts

4 → 55

Calls

4 calls:

166.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
158.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
55.0ms	(.f64 (.f64 3 a) c)

Compiler

Compiled 2403 to 1824 computations (24.1% saved)

simplify54.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4946	1702
1	4946	1702

prune122.0ms (1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	106	11	117
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	106	12	118

Error

13.1b

Counts

118 → 12

Compiler

Compiled 2431 to 1353 computations (44.3% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
5.2b	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
11.1b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite223.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Error

8.3b

Rules

45×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
22×	`times-frac_binary64_2471`
21×	`*-un-lft-identity_binary64_2465`
17×	`div-exp_binary64_2516` `cbrt-undiv_binary64_2499`
13×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
12×	`add-sqr-sqrt_binary64_2487`
11×	`add-cube-cbrt_binary64_2500` `associate-/l*_binary64_2410`
6×	`add-log-exp_binary64_2504` `associate-/r/_binary64_2411`
5×	`pow1_binary64_2526` `distribute-lft-out_binary64_2416` `associate-/r*_binary64_2409`
4×	`div-inv_binary64_2462` `flip3-+_binary64_2468` `flip-+_binary64_2439`
3×	`sqrt-prod_binary64_2481`
2×	`sqrt-div_binary64_2482` `frac-2neg_binary64_2476` `clear-num_binary64_2464`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3--_binary64_2469` `flip--_binary64_2440` `rem-sqrt-square_binary64_2478` `associate-/l/_binary64_2412` `sum-log_binary64_2556` `+-commutative_binary64_2395`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 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)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 3893 to 2136 computations (45.1% saved)

series955.0ms (7.8%)

Error

5.8b

Counts

4 → 68

Calls

4 calls:

319.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
255.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (.f64 3 a))
169.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
145.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 4188 to 3037 computations (27.5% saved)

simplify113.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4928	4308
1	4928	4308

prune208.0ms (1.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	164	6	170
Fresh	6	4	10
Picked	0	1	1
Done	0	1	1
Total	170	12	182

Error

5.7b

Counts

182 → 12

Compiler

Compiled 4507 to 2433 computations (46% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 c))
0.5b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 c)))
2.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite175.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

30×	`add-exp-log_binary64_2503`
21×	`add-sqr-sqrt_binary64_2487`
19×	`*-un-lft-identity_binary64_2465`
18×	`add-cbrt-cube_binary64_2501`
15×	`add-cube-cbrt_binary64_2500`
13×	`times-frac_binary64_2471` `associate-r_binary64_2405`
10×	`pow1_binary64_2526` `div-exp_binary64_2516`
8×	`prod-exp_binary64_2514`
6×	`add-log-exp_binary64_2504`
5×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cbrt-undiv_binary64_2499` `associate-/r/_binary64_2411`
4×	`cbrt-unprod_binary64_2498` `frac-times_binary64_2475` `associate-l/_binary64_2408` `associate-l*_binary64_2406`
3×	`sqrt-prod_binary64_2481` `1-exp_binary64_2509` `rec-exp_binary64_2515` `associate-/l*_binary64_2410`
2×	`sqrt-div_binary64_2482` `distribute-lft-out_binary64_2416` `pow-prod-down_binary64_2536` `pow-flip_binary64_2539` `div-inv_binary64_2462` `associate-*r/_binary64_2407` `unswap-sqr_binary64_2433`
1×	`pow1/2_binary64_2545` `sqrt-pow1_binary64_2483` `flip3--_binary64_2469` `flip--_binary64_2440` `rem-sqrt-square_binary64_2478` `sum-log_binary64_2556` `+-commutative_binary64_2395` `inv-pow_binary64_2550` `frac-2neg_binary64_2476` `clear-num_binary64_2464` `associate-/r_binary64_2409` `-commutative_binary64_2396`

Counts

4 → 101

Calls

4 calls:

17.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 c))
12.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 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 3073 to 1740 computations (43.4% saved)

series837.0ms (6.8%)

Error

5.7b

Counts

4 → 70

Calls

4 calls:

261.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 c)))
214.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c))))) (/.f64 -1 c))
156.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c)))))
145.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 3578 to 2729 computations (23.7% saved)

simplify63.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5089	3669

prune174.0ms (1.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	168	3	171
Fresh	2	7	9
Picked	0	1	1
Done	1	1	2
Total	171	12	183

Error

5.7b

Counts

183 → 12

Compiler

Compiled 3730 to 2047 computations (45.1% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

9.3b	(sqrt.f64 (.f64 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (*.f64 c -3)))
11.1b	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
22.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

rewrite183.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

5.7b

Rules

13×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
12×	`pow1_binary64_2526` `*-un-lft-identity_binary64_2465`
10×	`add-sqr-sqrt_binary64_2487`
8×	`add-cube-cbrt_binary64_2500`
7×	`sqrt-prod_binary64_2481`
5×	`sqrt-pow1_binary64_2483` `sqrt-div_binary64_2482`
4×	`add-log-exp_binary64_2504` `times-frac_binary64_2471` `associate-/r*_binary64_2409`
3×	`pow1/2_binary64_2545` `prod-exp_binary64_2514` `div-exp_binary64_2516` `cbrt-undiv_binary64_2499` `cbrt-unprod_binary64_2498` `pow-prod-down_binary64_2536`
2×	`flip3--_binary64_2469` `flip--_binary64_2440` `rem-sqrt-square_binary64_2478` `distribute-lft-out_binary64_2416` `associate-/r/_binary64_2411`
1×	`frac-2neg_binary64_2476` `clear-num_binary64_2464` `div-inv_binary64_2462` `flip3-+_binary64_2468` `flip-+_binary64_2439` `associate-/l_binary64_2410` `associate-l/_binary64_2408`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
11.0ms	(sqrt.f64 (.f64 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (*.f64 c -3)))
4.0ms	(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 3885 to 2175 computations (44% saved)

series1.0s (8.3%)

Error

5.7b

Counts

4 → 62

Calls

4 calls:

329.0ms	(/.f64 (.f64 a (.f64 c -3)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))))
274.0ms	(sqrt.f64 (.f64 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (.f64 a c)))))) (*.f64 c -3)))
167.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))
158.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 3 (*.f64 a c))))

Compiler

Compiled 7634 to 5076 computations (33.5% saved)

simplify59.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5297	2804

prune249.0ms (2%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	132	12	144

Error

5.7b

Counts

144 → 12

Compiler

Compiled 6084 to 3386 computations (44.3% saved)

regimes2.4s (19.3%)

Accuracy

Total 1.6b remaining (22.4%)

Threshold costs 0b (0%)

Compiler

Compiled 15799 to 11869 computations (24.9% saved)

bsearch95.0ms (0.8%)

Steps

Iters	Range	Point
6	1.6321693647229805e+62	8.2218560581562955e+62	7.524306741962282e+62
8	-3.284834576918865e-217	-1.4831442676984904e-221	-2.2723855696978872e-219
9	-6.948808739696305e+156	-1.0565256005736422e+149	-4.632381428632677e+153

Iters

Range

Point

1.6321693647229805e+62

8.2218560581562955e+62

7.524306741962282e+62

-3.284834576918865e-217

-1.4831442676984904e-221

-2.2723855696978872e-219

-6.948808739696305e+156

-1.0565256005736422e+149

-4.632381428632677e+153

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	127	85
1	127	85

Removed

()

end0.0ms (0%)

sample3.6s (29.5%)

Algorithm

1×

intervals

Results

289.0ms	1122×	body	2048	valid
271.0ms	5163×	body	128	valid
155.0ms	786×	body	1024	valid
125.0ms	391×	body	4096	valid
51.0ms	360×	body	512	valid
39.0ms	686×	body	128	nan
18.0ms	355×	body	128	invalid
17.0ms	178×	body	256	valid

Compiler

Compiled 3085 to 2314 computations (25% saved)

Details

analyze691.0ms (5.6%)

sample47.0ms (0.4%)

simplify286.0ms (2.3%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite109.0ms (0.9%)

series542.0ms (4.4%)

simplify54.0ms (0.4%)

prune122.0ms (1%)

localize17.0ms (0.1%)

rewrite223.0ms (1.8%)

series955.0ms (7.8%)

simplify113.0ms (0.9%)

prune208.0ms (1.7%)

localize12.0ms (0.1%)

rewrite175.0ms (1.4%)

series837.0ms (6.8%)

simplify63.0ms (0.5%)

prune174.0ms (1.4%)

localize24.0ms (0.2%)

rewrite183.0ms (1.5%)

series1.0s (8.3%)

simplify59.0ms (0.5%)

prune249.0ms (2%)

regimes2.4s (19.3%)

bsearch95.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.6s (29.5%)

Profiling