Details

analyze497.0ms (8%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5132	96
0	3	3
1	3	3

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	287×	pre	128	true
9.0ms	169×	body	128	valid
8.0ms	87×	body	256	valid
1.0ms	31×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify323.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (317.0ms)

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)))
0.2b	(-.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))
37.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite39.0ms (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:

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

series270.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
65.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
36.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune98.0ms (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 2020 to 1194 computations (40.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(+.f64 b (sqrt.f64 (-.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)))))

rewrite52.0ms (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))
14.0ms	(/.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))

series455.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
159.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune159.0ms (2.6%)

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: 0.0b

Counts

115 → 8

Compiler

Compiled 3240 to 1997 computations (38.4% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_2465`
15×	`add-sqr-sqrt_binary64_2487`
14×	`add-cube-cbrt_binary64_2500`
12×	`times-frac_binary64_2471`
8×	`add-log-exp_binary64_2504`
6×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
5×	`pow1_binary64_2526` `distribute-lft-out_binary64_2416`
4×	`associate-/r*_binary64_2409`
3×	`sqrt-prod_binary64_2481` `associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `flip-+_binary64_2439` `associate-/r/_binary64_2411` `sqrt-div_binary64_2482` `flip3--_binary64_2469`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556` `pow1/2_binary64_2545` `clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `sub-neg_binary64_2458` `cancel-sign-sub-inv_binary64_2431` `div-exp_binary64_2516` `div-inv_binary64_2462` `rem-sqrt-square_binary64_2478` `diff-log_binary64_2557` `frac-2neg_binary64_2476` `sqrt-pow1_binary64_2483`

Counts

4 → 72

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series323.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify77.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune111.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	83	9	92

Merged error: 0b

Counts

92 → 9

Compiler

Compiled 2358 to 1472 computations (37.6% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))) a)
0.3b	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) a))

rewrite61.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-exp-log_binary64_2503`
47×	`add-cbrt-cube_binary64_2501`
41×	`prod-exp_binary64_2514`
31×	`*-un-lft-identity_binary64_2465`
23×	`cbrt-unprod_binary64_2498`
21×	`times-frac_binary64_2471` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
18×	`pow1_binary64_2526`
14×	`div-exp_binary64_2516` `associate-l_binary64_2406`
9×	`pow-prod-down_binary64_2536`
8×	`cbrt-undiv_binary64_2499`
6×	`add-log-exp_binary64_2504`
5×	`distribute-lft-out_binary64_2416`
4×	`associate-l/_binary64_2408` `associate-/r_binary64_2409` `associate-r/_binary64_2407` `rec-exp_binary64_2515` `associate-r*_binary64_2405` `1-exp_binary64_2509`
3×	`associate-/l*_binary64_2410`
2×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `flip-+_binary64_2439` `div-inv_binary64_2462` `associate-/r/_binary64_2411`
1×	`+-commutative_binary64_2395` `frac-times_binary64_2475` `sum-log_binary64_2556` `clear-num_binary64_2464` `frac-2neg_binary64_2476`

Counts

4 → 118

Calls

4 calls:

20.0ms	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) a))
13.0ms	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))) a)
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

series608.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

218.0ms	(.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))) a)
165.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
164.0ms	(.f64 (/.f64 1 a) (.f64 (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) a))
61.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

simplify96.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5055	3427

prune149.0ms (2.4%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	129	1	130
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	130	9	139

Merged error: 0b

Counts

139 → 9

Compiler

Compiled 3312 to 1991 computations (39.9% saved)

regimes401.0ms (6.5%)

Compiler: Compiled 5416 to 4070 computations (24.9% 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%)

sample2.2s (35.5%)

Algorithm

1×

intervals

Results

297.0ms	2975×	body	256	valid
295.0ms	8939×	pre	128	true
268.0ms	5024×	body	128	valid
46.0ms	939×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 1390 to 1046 computations (24.7% saved)

Details

analyze497.0ms (8%)

sample38.0ms (0.6%)

simplify323.0ms (5.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite39.0ms (0.6%)

series270.0ms (4.4%)

simplify91.0ms (1.5%)

prune98.0ms (1.6%)

localize14.0ms (0.2%)

rewrite52.0ms (0.8%)

series455.0ms (7.3%)

simplify65.0ms (1%)

prune159.0ms (2.6%)

localize12.0ms (0.2%)

rewrite30.0ms (0.5%)

series323.0ms (5.2%)

simplify77.0ms (1.2%)

prune111.0ms (1.8%)

localize14.0ms (0.2%)

rewrite61.0ms (1%)

series608.0ms (9.8%)

simplify96.0ms (1.5%)

prune149.0ms (2.4%)

regimes401.0ms (6.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.2s (35.5%)

Profiling