Details

analyze582.0ms (0.7%)

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)

sample86.0ms (0.1%)

Algorithm

1×

intervals

Results

23.0ms	115×	body	256	valid
17.0ms	281×	pre	128	true
15.0ms	49×	body	512	valid
9.0ms	92×	body	128	valid
2.0ms	25×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify832.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (652.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune10.0ms (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

Merged error: 52.7b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize25.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
25.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

rewrite86.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64_78`
10×	`add-log-exp_binary64_117`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
8×	`add-sqr-sqrt_binary64_100`
7×	`add-cube-cbrt_binary64_113`
6×	`distribute-lft-out_binary64_29`
5×	`times-frac_binary64_84` `associate-/l*_binary64_23` `pow1_binary64_139`
3×	`sqrt-prod_binary64_94` `distribute-rgt-neg-in_binary64_36`
2×	`associate-+l-_binary64_13` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `neg-sub0_binary64_73` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `sum-log_binary64_169` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `div-sub_binary64_83` `pow1/2_binary64_158` `sub-neg_binary64_71` `neg-log_binary64_171`

Counts

4 → 70

Calls

4 calls:

24.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
17.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series511.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
161.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
108.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify128.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5668	1826

prune832.0ms (1%)

Pruning

42 alts after pruning (41 fresh and 1 done)

	Pruned	Kept	Total
New	41	41	82
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	42	42	84

Merged error: 0.1b

Counts

84 → 42

Compiler

Compiled 2962 to 1892 computations (36.1% saved)

localize83.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (neg.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 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
0.3b	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite291.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
34×	`times-frac_binary64_84`
32×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
14×	`associate-/l*_binary64_23`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
12×	`add-cube-cbrt_binary64_113`
10×	`add-log-exp_binary64_117` `distribute-lft-out--_binary64_30` `difference-of-squares_binary64_47`
8×	`sqrt-prod_binary64_94` `associate-/r*_binary64_22`
7×	`cancel-sign-sub-inv_binary64_44`
6×	`associate-/r/_binary64_24`
5×	`flip3--_binary64_82` `flip--_binary64_53` `distribute-rgt-neg-in_binary64_36`
4×	`div-inv_binary64_75` `pow1_binary64_139`
3×	`diff-log_binary64_170`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77` `sub-neg_binary64_71`
1×	`neg-sub0_binary64_73` `associate-/l/_binary64_25` `associate--l-_binary64_16` `neg-log_binary64_171`

Counts

4 → 122

Calls

4 calls:

96.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
56.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
50.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
23.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.2s (1.4%)

Counts

4 → 12

Calls

4 calls:

526.0ms	(/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
310.0ms	(/.f64 (/.f64 (.f64 (.f64 4 a) c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 2 a))
198.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
166.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

simplify457.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (281.0ms)

Iter	Nodes	Cost
0	4957	4144
1	4957	4144

prune2.1s (2.5%)

Pruning

74 alts after pruning (73 fresh and 1 done)

	Pruned	Kept	Total
New	91	43	134
Fresh	10	30	40
Picked	1	0	1
Done	0	1	1
Total	102	74	176

Merged error: 0b

Counts

176 → 74

Compiler

Compiled 6276 to 3918 computations (37.6% saved)

localize28.0ms (0%)

Local error

Found 4 expressions with local error:

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

rewrite147.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

59×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
55×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
43×	`times-frac_binary64_84`
27×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18`
23×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
14×	`distribute-lft-out--_binary64_30` `difference-of-squares_binary64_47`
9×	`pow1_binary64_139`
8×	`associate-/r*_binary64_22`
7×	`sqrt-prod_binary64_94` `distribute-rgt-neg-in_binary64_36`
6×	`add-log-exp_binary64_117`
4×	`associate-/l*_binary64_23` `associate-/r/_binary64_24`
3×	`flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `pow-prod-down_binary64_149`
2×	`frac-2neg_binary64_89` `associate-*r/_binary64_20` `clear-num_binary64_77`
1×	`-commutative_binary64_9` `associate-l*_binary64_19` `diff-log_binary64_170` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71`

Counts

4 → 138

Calls

4 calls:

34.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (.f64 2 a))
32.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
20.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
10.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

series2.1s (2.4%)

Counts

4 → 12

Calls

4 calls:

938.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
596.0ms	(/.f64 (.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))))) (.f64 2 a))
459.0ms	(/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify224.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (145.0ms)

Iter	Nodes	Cost
0	4907	4229
1	4907	4229

prune4.7s (5.4%)

Pruning

101 alts after pruning (99 fresh and 2 done)

	Pruned	Kept	Total
New	110	40	150
Fresh	13	59	72
Picked	0	1	1
Done	0	1	1
Total	123	101	224

Merged error: 0b

Counts

224 → 101

Compiler

Compiled 7931 to 4961 computations (37.4% saved)

localize103.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))))))
0.3b	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.4b	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
0.7b	(pow.f64 (.f64 (.f64 4 a) c) 3)

rewrite454.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64_100`
57×	`times-frac_binary64_84`
53×	`*-un-lft-identity_binary64_78`
33×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `difference-of-squares_binary64_47`
29×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
21×	`sqr-pow_binary64_50`
20×	`pow1_binary64_139`
12×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
10×	`distribute-lft-out--_binary64_30` `associate-/l*_binary64_23`
9×	`unpow-prod-down_binary64_157` `pow-prod-down_binary64_149`
6×	`sqrt-prod_binary64_94`
4×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
3×	`rem-cube-cbrt_binary64_101` `pow-exp_binary64_146` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `pow-pow_binary64_150` `associate-/r_binary64_22` `pow-unpow_binary64_155` `associate-r/_binary64_20` `distribute-rgt-neg-in_binary64_36`
2×	`-commutative_binary64_9` `associate-l*_binary64_19` `flip-+_binary64_52` `flip3--_binary64_82` `div-inv_binary64_75` `flip--_binary64_53` `associate-/l/_binary64_25` `flip3-+_binary64_81`
1×	`cube-mult_binary64_108` `distribute-lft-in_binary64_27` `pow-to-exp_binary64_147` `distribute-rgt-in_binary64_28` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-sub_binary64_83` `unpow3_binary64_144` `cube-prod_binary64_106`

Counts

4 → 157

Calls

4 calls:

230.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))))))
42.0ms	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
36.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
12.0ms	(pow.f64 (.f64 (.f64 4 a) c) 3)

series1.1s (1.3%)

Counts

4 → 12

Calls

4 calls:

603.0ms	(.f64 (.f64 4 a) (/.f64 c (-.f64 (neg.f64 b) (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))))))
221.0ms	(/.f64 (-.f64 (pow.f64 b 6) (pow.f64 (.f64 (.f64 4 a) c) 3)) (+.f64 (pow.f64 b 4) (.f64 4 (.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
130.0ms	(pow.f64 (.f64 (.f64 4 a) c) 3)
124.0ms	(.f64 (.f64 a c) (+.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify262.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (129.0ms)

Iter	Nodes	Cost
0	4979	8094
1	4979	8094

prune6.5s (7.5%)

Pruning

157 alts after pruning (154 fresh and 3 done)

	Pruned	Kept	Total
New	107	62	169
Fresh	6	92	98
Picked	0	1	1
Done	0	2	2
Total	113	157	270

Merged error: 0b

Counts

270 → 157

Compiler

Compiled 10443 to 6565 computations (37.1% saved)

regimes13.7s (15.9%)

Compiler: Compiled 52526 to 38140 computations (27.4% saved)

bsearch12.9s (15%)

simplify26.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	72	68
1	72	68

end0.0ms (0%)

sample36.5s (42.5%)

Algorithm

1×

intervals

Results

1.1s	3735×	body	256	valid
759.0ms	8787×	pre	128	true
690.0ms	1512×	body	512	valid
387.0ms	2753×	body	128	valid
104.0ms	787×	body	128	nan

Compiler

Compiled 13419 to 9741 computations (27.4% saved)

Pareto

0.0

Details

analyze582.0ms (0.7%)

sample86.0ms (0.1%)

simplify832.0ms (1%)

prune10.0ms (0%)

localize25.0ms (0%)

rewrite86.0ms (0.1%)

series511.0ms (0.6%)

simplify128.0ms (0.1%)

prune832.0ms (1%)

localize83.0ms (0.1%)

rewrite291.0ms (0.3%)

series1.2s (1.4%)

simplify457.0ms (0.5%)

prune2.1s (2.5%)

localize28.0ms (0%)

rewrite147.0ms (0.2%)

series2.1s (2.4%)

simplify224.0ms (0.3%)

prune4.7s (5.4%)

localize103.0ms (0.1%)

rewrite454.0ms (0.5%)

series1.1s (1.3%)

simplify262.0ms (0.3%)

prune6.5s (7.5%)

regimes13.7s (15.9%)

bsearch12.9s (15%)

simplify26.0ms (0%)

end0.0ms (0%)

sample36.5s (42.5%)

Profiling