Details

analyze260.0ms (4.5%)

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)

sample33.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	246×	body	128	valid
9.0ms	290×	pre	128	true
2.0ms	34×	body	128	nan
1.0ms	10×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify222.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	927	24
1	927	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: 28.1b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
28.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_98`
13×	`*-un-lft-identity_binary64_77`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113`
7×	`add-cube-cbrt_binary64_109`
6×	`sqrt-prod_binary64_92` `times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
5×	`pow1_binary64_135`
4×	`flip--_binary64_52` `flip3--_binary64_81`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `sub-neg_binary64_70` `div-exp_binary64_125` `diff-log_binary64_166` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `prod-exp_binary64_123` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 70

Calls

4 calls:

13.0ms	(/.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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series530.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
135.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
131.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune106.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 0.4b

Counts

83 → 6

Compiler

Compiled 2068 to 1237 computations (40.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
22×	`times-frac_binary64_83`
20×	`*-un-lft-identity_binary64_77`
17×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
13×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
8×	`add-log-exp_binary64_113`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135` `div-inv_binary64_74`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `flip3--_binary64_81` `diff-log_binary64_166` `associate-/l/_binary64_26` `sum-log_binary64_165`

Counts

4 → 98

Calls

4 calls:

16.0ms	(/.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))

series907.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

399.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
314.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
131.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune176.0ms (3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	10	110
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Merged error: 0b

Counts

116 → 10

Compiler

Compiled 3339 to 2068 computations (38.1% 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 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 b b) (.f64 c (*.f64 a 4)))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_77`
15×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`times-frac_binary64_83`
8×	`add-log-exp_binary64_113`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
5×	`pow1_binary64_135` `distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_92` `associate-/l*_binary64_24`
2×	`flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `flip--_binary64_52` `associate-/r/_binary64_25` `flip3--_binary64_81`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sub-neg_binary64_70` `+-commutative_binary64_9` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 71

Calls

4 calls:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
9.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series636.0ms (11%)

Counts

4 → 12

Calls

4 calls:

338.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
67.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune125.0ms (2.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 0b

Counts

93 → 9

Compiler

Compiled 2424 to 1519 computations (37.3% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 c (.f64 (*.f64 c a) 16))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite65.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `*-un-lft-identity_binary64_77`
27×	`pow1_binary64_135`
23×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
21×	`times-frac_binary64_83`
16×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
7×	`associate-/r*_binary64_23`
6×	`associate-l_binary64_20` `associate-/l*_binary64_24`
4×	`add-log-exp_binary64_113` `associate-/r/_binary64_25` `distribute-lft-out_binary64_30`
2×	`flip-+_binary64_51` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `div-exp_binary64_125` `-commutative_binary64_10` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88` `associate-r*_binary64_19` `div-inv_binary64_74`
1×	`div-sub_binary64_82` `flip--_binary64_52` `flip3--_binary64_81`

Counts

4 → 110

Calls

4 calls:

17.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
14.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
11.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
8.0ms	(.f64 c (.f64 (*.f64 c a) 16))

series672.0ms (11.6%)

Counts

4 → 12

Calls

4 calls:

440.0ms	(/.f64 c (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
142.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
53.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
36.0ms	(.f64 c (.f64 (*.f64 c a) 16))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4973	4088
1	4973	4088

prune219.0ms (3.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	122	9	131

Merged error: 0b

Counts

131 → 9

Compiler

Compiled 5083 to 2965 computations (41.7% saved)

regimes83.0ms (1.4%)

Compiler: Compiled 927 to 678 computations (26.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	45
1	96	45

end0.0ms (0%)

sample1.2s (21.5%)

Algorithm

1×

intervals

Results

380.0ms	7688×	body	128	valid
260.0ms	8852×	pre	128	true
39.0ms	852×	body	128	nan
31.0ms	312×	body	256	valid

Compiler

Compiled 367 to 269 computations (26.7% saved)

Details

analyze260.0ms (4.5%)

sample33.0ms (0.6%)

simplify222.0ms (3.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite37.0ms (0.6%)

series530.0ms (9.1%)

simplify98.0ms (1.7%)

prune106.0ms (1.8%)

localize14.0ms (0.2%)

rewrite51.0ms (0.9%)

series907.0ms (15.6%)

simplify75.0ms (1.3%)

prune176.0ms (3%)

localize12.0ms (0.2%)

rewrite34.0ms (0.6%)

series636.0ms (11%)

simplify85.0ms (1.5%)

prune125.0ms (2.2%)

localize21.0ms (0.4%)

rewrite65.0ms (1.1%)

series672.0ms (11.6%)

simplify80.0ms (1.4%)

prune219.0ms (3.8%)

regimes83.0ms (1.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (21.5%)

Profiling