Details

analyze273.0ms (4.3%)

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)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

10.0ms	102×	body	256	valid
9.0ms	294×	pre	128	true
8.0ms	154×	body	128	valid
2.0ms	38×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify414.0ms (6.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (312.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	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: 43.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
38.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_2487`
14×	`*-un-lft-identity_binary64_2465`
9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
8×	`add-log-exp_binary64_2504` `add-cube-cbrt_binary64_2500`
6×	`difference-of-squares_binary64_2434` `times-frac_binary64_2471` `sqrt-prod_binary64_2481` `associate-/l*_binary64_2410`
5×	`pow1_binary64_2526`
4×	`flip--_binary64_2440` `cancel-sign-sub-inv_binary64_2431` `flip3--_binary64_2469`
3×	`distribute-lft-out--_binary64_2417`
2×	`associate-/l/_binary64_2412` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `div-exp_binary64_2516` `diff-log_binary64_2557` `sqrt-div_binary64_2482`
1×	`associate-/r*_binary64_2409` `pow1/2_binary64_2545` `clear-num_binary64_2464` `div-sub_binary64_2470` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `prod-exp_binary64_2514` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483` `cbrt-unprod_binary64_2498`

Counts

4 → 74

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series277.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
71.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune100.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 0.2b

Counts

87 → 4

Compiler

Compiled 2044 to 1208 computations (40.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
22×	`times-frac_binary64_2471`
20×	`*-un-lft-identity_binary64_2465`
17×	`cbrt-undiv_binary64_2499` `div-exp_binary64_2516`
13×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
11×	`associate-/l*_binary64_2410`
10×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
8×	`add-log-exp_binary64_2504`
6×	`associate-/r/_binary64_2411`
5×	`associate-/r*_binary64_2409` `distribute-lft-out_binary64_2416`
4×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `div-inv_binary64_2462` `pow1_binary64_2526`
2×	`clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-/l/_binary64_2412` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

4 → 99

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series471.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
162.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
36.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify64.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune159.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	2	0	2
Picked	0	1	1
Done	1	0	1
Total	107	8	115

Merged error: 0b

Counts

115 → 8

Compiler

Compiled 3198 to 1973 computations (38.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
0.3b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))

rewrite77.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

242×	`times-frac_binary64_2471`
114×	`*-un-lft-identity_binary64_2465`
106×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
61×	`add-exp-log_binary64_2503`
47×	`add-cbrt-cube_binary64_2501`
37×	`div-exp_binary64_2516`
26×	`div-inv_binary64_2462`
25×	`cbrt-undiv_binary64_2499`
19×	`associate-/l*_binary64_2410`
18×	`associate-/r/_binary64_2411`
15×	`associate-*r/_binary64_2407`
13×	`associate-/r*_binary64_2409`
8×	`prod-exp_binary64_2514`
6×	`add-log-exp_binary64_2504` `cbrt-unprod_binary64_2498`
4×	`pow1_binary64_2526` `distribute-lft-out_binary64_2416` `1-exp_binary64_2509`
3×	`clear-num_binary64_2464` `frac-2neg_binary64_2476`
1×	`flip3-+_binary64_2468` `flip--_binary64_2440` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `flip3--_binary64_2469`

Counts

4 → 226

Calls

4 calls:

20.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
12.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series584.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
183.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
166.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
36.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify135.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4894	8594
1	4894	8594

prune350.0ms (5.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	238	8	246

Merged error: 0b

Counts

246 → 8

Compiler

Compiled 7098 to 4103 computations (42.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.1b	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite46.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_2465`
24×	`times-frac_binary64_2471`
21×	`add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
18×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `associate-r_binary64_2405`
9×	`pow1_binary64_2526`
8×	`add-log-exp_binary64_2504` `distribute-lft-out_binary64_2416`
6×	`prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`
4×	`associate-/r*_binary64_2409` `associate-/r/_binary64_2411`
3×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `pow-prod-down_binary64_2536` `associate-/l*_binary64_2410`
2×	`div-inv_binary64_2462`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `flip--_binary64_2440` `sum-log_binary64_2556` `associate-r/_binary64_2407` `clear-num_binary64_2464` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `flip3--_binary64_2469` `associate-l_binary64_2406`

Counts

4 → 95

Calls

4 calls:

14.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
9.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

series438.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
116.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
77.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
42.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune130.0ms (2.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	107	8	115

Merged error: 0b

Counts

115 → 8

Compiler

Compiled 2744 to 1732 computations (36.9% saved)

regimes365.0ms (5.8%)

Compiler: Compiled 4964 to 3710 computations (25.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.1s (32.9%)

Algorithm

1×

intervals

Results

296.0ms	2975×	body	256	valid
291.0ms	8918×	pre	128	true
265.0ms	5023×	body	128	valid
43.0ms	918×	body	128	nan
0.0ms	2×	body	512	valid

Compiler

Compiled 1277 to 956 computations (25.1% saved)

Details

analyze273.0ms (4.3%)

sample39.0ms (0.6%)

simplify414.0ms (6.5%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite36.0ms (0.6%)

series277.0ms (4.4%)

simplify88.0ms (1.4%)

prune100.0ms (1.6%)

localize14.0ms (0.2%)

rewrite51.0ms (0.8%)

series471.0ms (7.5%)

simplify64.0ms (1%)

prune159.0ms (2.5%)

localize16.0ms (0.3%)

rewrite77.0ms (1.2%)

series584.0ms (9.2%)

simplify135.0ms (2.1%)

prune350.0ms (5.5%)

localize13.0ms (0.2%)

rewrite46.0ms (0.7%)

series438.0ms (6.9%)

simplify82.0ms (1.3%)

prune130.0ms (2.1%)

regimes365.0ms (5.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (32.9%)

Profiling