Details

analyze464.0ms (7.1%)

Algorithm

1×

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample39.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	172×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	27×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	14×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	18×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify229.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune5.0ms (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: 35.0b

Counts

2 → 1

Compiler

Compiled 65 to 53 computations (18.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite40.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_789`
14×	`*-un-lft-identity_binary64_767`
9×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806` `add-cube-cbrt_binary64_802`
6×	`times-frac_binary64_773` `associate-/l*_binary64_712` `sqrt-prod_binary64_783` `difference-of-squares_binary64_736`
5×	`pow1_binary64_828`
4×	`cancel-sign-sub-inv_binary64_733` `flip--_binary64_742` `flip3--_binary64_771`
3×	`distribute-lft-out--_binary64_719`
2×	`associate-/l/_binary64_714` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `diff-log_binary64_859` `div-exp_binary64_818` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r*_binary64_711` `cbrt-unprod_binary64_800` `prod-exp_binary64_816` `pow1/2_binary64_847` `sqrt-pow1_binary64_785` `div-sub_binary64_772` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series507.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
122.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
119.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4895	1979
1	4895	1979

prune439.0ms (6.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	78	8	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	78	9	87

Merged error: 7.0b

Counts

87 → 9

Compiler

Compiled 8858 to 5870 computations (33.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
3.5b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
9.7b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
22×	`times-frac_binary64_773`
21×	`*-un-lft-identity_binary64_767`
17×	`cbrt-undiv_binary64_801` `div-exp_binary64_818`
13×	`cbrt-unprod_binary64_800` `prod-exp_binary64_816`
12×	`add-sqr-sqrt_binary64_789`
11×	`associate-/l*_binary64_712` `add-cube-cbrt_binary64_802`
6×	`associate-/r/_binary64_713` `add-log-exp_binary64_806`
5×	`distribute-lft-out_binary64_718` `associate-/r*_binary64_711` `pow1_binary64_828`
4×	`flip-+_binary64_741` `flip3-+_binary64_770` `div-inv_binary64_764`
3×	`sqrt-prod_binary64_783`
2×	`frac-2neg_binary64_778` `clear-num_binary64_766` `sqrt-div_binary64_784`
1×	`rem-sqrt-square_binary64_780` `associate-/l/_binary64_714` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `flip--_binary64_742` `sqrt-pow1_binary64_785` `flip3--_binary64_771`

Counts

4 → 102

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series932.0ms (14.2%)

Counts

4 → 12

Calls

4 calls:

376.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
305.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))))) (.f64 a 2))
129.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4977	3121
1	4977	3121

prune262.0ms (4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	115	8	123

Merged error: 6.9b

Counts

123 → 8

Compiler

Compiled 5639 to 3507 computations (37.8% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_767`
15×	`add-sqr-sqrt_binary64_789`
14×	`add-cube-cbrt_binary64_802`
12×	`times-frac_binary64_773`
8×	`add-log-exp_binary64_806`
6×	`add-exp-log_binary64_805` `add-cbrt-cube_binary64_803`
5×	`distribute-lft-out_binary64_718` `pow1_binary64_828`
4×	`associate-/r*_binary64_711`
3×	`associate-/l*_binary64_712` `sqrt-prod_binary64_783`
2×	`associate-/r/_binary64_713` `flip-+_binary64_741` `flip3-+_binary64_770` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `cbrt-undiv_binary64_801` `sub-neg_binary64_760` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `div-exp_binary64_818` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `div-inv_binary64_764`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series624.0ms (9.5%)

Counts

4 → 12

Calls

4 calls:

315.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
120.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify69.0ms (1%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5091	1969

prune107.0ms (1.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Merged error: 6.9b

Counts

92 → 7

Compiler

Compiled 2405 to 1406 computations (41.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
0.6b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.8b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
24.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64_773`
80×	`*-un-lft-identity_binary64_767`
55×	`add-sqr-sqrt_binary64_789`
54×	`add-cube-cbrt_binary64_802`
16×	`associate-/r*_binary64_711`
15×	`add-exp-log_binary64_805`
13×	`distribute-lft-out_binary64_718`
9×	`add-cbrt-cube_binary64_803`
8×	`add-log-exp_binary64_806`
7×	`div-exp_binary64_818`
6×	`pow1_binary64_828`
5×	`div-inv_binary64_764`
3×	`cbrt-undiv_binary64_801` `associate-/l*_binary64_712` `sqrt-prod_binary64_783`
2×	`1-exp_binary64_811` `rec-exp_binary64_817` `flip--_binary64_742` `flip3--_binary64_771` `sqrt-div_binary64_784`
1×	`frac-2neg_binary64_778` `rem-sqrt-square_binary64_780` `associate-/r/_binary64_713` `sub-neg_binary64_760` `pow-flip_binary64_841` `flip-+_binary64_741` `cancel-sign-sub-inv_binary64_733` `diff-log_binary64_859` `+-commutative_binary64_697` `sum-log_binary64_858` `pow1/2_binary64_847` `flip3-+_binary64_770` `sqrt-pow1_binary64_785` `clear-num_binary64_766` `inv-pow_binary64_852`

Counts

4 → 127

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series560.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

261.0ms	(/.f64 1 (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) c))
125.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4957	4182
1	4957	4182

prune183.0ms (2.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	139	7	146

Merged error: 6.9b

Counts

146 → 7

Compiler

Compiled 4095 to 2377 computations (42% saved)

regimes138.0ms (2.1%)

Compiler: Compiled 372 to 309 computations (16.9% saved)

bsearch111.0ms (1.7%)

Steps

Iters	Range	Point
8	5.047843856159705e+79	3.275486995190224e+82	1.7935647805371114e+82
11	-3.290852731649204e-307	2.1876641165742222e-285	-1.4618690896455906e-308
8	-1.6249009059312762e+154	-3.534796202621665e+151	-2.598568989113781e+152

Iters

Range

Point

5.047843856159705e+79

3.275486995190224e+82

1.7935647805371114e+82

-3.290852731649204e-307

2.1876641165742222e-285

-1.4618690896455906e-308

-1.6249009059312762e+154

-3.534796202621665e+151

-2.598568989113781e+152

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	105	82
1	105	82

end0.0ms (0%)

sample1.4s (21.5%)

Algorithm

1×

intervals

Results

295.0ms	1134×	body	2048	valid
273.0ms	5060×	body	128	valid
155.0ms	792×	body	1024	valid
132.0ms	417×	body	4096	valid
59.0ms	403×	body	512	valid
33.0ms	666×	body	128	nan
21.0ms	194×	body	256	valid
20.0ms	380×	body	128	invalid

Compiler

Compiled 237 to 176 computations (25.7% saved)

Details

analyze464.0ms (7.1%)

sample39.0ms (0.6%)

simplify229.0ms (3.5%)

prune5.0ms (0.1%)

localize11.0ms (0.2%)

rewrite40.0ms (0.6%)

series507.0ms (7.7%)

simplify73.0ms (1.1%)

prune439.0ms (6.7%)

localize14.0ms (0.2%)

rewrite53.0ms (0.8%)

series932.0ms (14.2%)

simplify78.0ms (1.2%)

prune262.0ms (4%)

localize12.0ms (0.2%)

rewrite30.0ms (0.5%)

series624.0ms (9.5%)

simplify69.0ms (1%)

prune107.0ms (1.6%)

localize15.0ms (0.2%)

rewrite43.0ms (0.7%)

series560.0ms (8.6%)

simplify100.0ms (1.5%)

prune183.0ms (2.8%)

regimes138.0ms (2.1%)

bsearch111.0ms (1.7%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.5%)

Profiling