Details

analyze351.0ms (3.6%)

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)

sample32.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	245×	body	128	valid
9.0ms	284×	pre	128	true
1.0ms	28×	body	128	nan
1.0ms	11×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify571.0ms (5.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (472.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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

Error

27.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

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))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
26.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64_782`
14×	`*-un-lft-identity_binary64_760`
9×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
8×	`add-cube-cbrt_binary64_795` `add-log-exp_binary64_799`
6×	`sqrt-prod_binary64_776` `difference-of-squares_binary64_729` `associate-/l*_binary64_705` `times-frac_binary64_766`
5×	`pow1_binary64_821`
4×	`cancel-sign-sub-inv_binary64_726` `flip--_binary64_735` `flip3--_binary64_764`
3×	`distribute-lft-out--_binary64_712`
2×	`diff-log_binary64_852` `cbrt-undiv_binary64_794` `associate-/l/_binary64_707` `sqrt-div_binary64_777` `div-exp_binary64_811` `sub-neg_binary64_753`
1×	`rem-sqrt-square_binary64_773` `frac-2neg_binary64_771` `prod-exp_binary64_809` `sqrt-pow1_binary64_778` `associate-/r*_binary64_704` `div-inv_binary64_757` `div-sub_binary64_765` `cbrt-unprod_binary64_793` `pow1/2_binary64_840` `clear-num_binary64_759`

Counts

4 → 74

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
14.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series372.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
111.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
85.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
46.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify147.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (119.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune139.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	6	87

Error

0.3b

Counts

87 → 6

Compiler

Compiled 2121 to 1268 computations (40.2% saved)

localize14.0ms (0.1%)

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 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.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)))))

rewrite64.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
22×	`times-frac_binary64_766`
20×	`*-un-lft-identity_binary64_760`
17×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
13×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
11×	`associate-/l*_binary64_705`
10×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
8×	`add-log-exp_binary64_799`
6×	`associate-/r/_binary64_706`
5×	`distribute-lft-out_binary64_711` `associate-/r*_binary64_704`
4×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734` `pow1_binary64_821`
2×	`frac-2neg_binary64_771` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `associate-/l/_binary64_707` `cancel-sign-sub-inv_binary64_726` `+-commutative_binary64_690` `sum-log_binary64_851` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 99

Calls

4 calls:

16.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
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))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series638.0ms (6.5%)

Counts

4 → 12

Calls

4 calls:

283.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
222.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
90.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
44.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify78.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune246.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	102	9	111
Fresh	5	0	5
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

Counts

117 → 9

Compiler

Compiled 3297 to 2039 computations (38.2% saved)

localize23.0ms (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 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(-.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)))))))

rewrite57.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_760`
24×	`times-frac_binary64_766`
21×	`add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
18×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-r_binary64_700`
9×	`pow1_binary64_821`
8×	`distribute-lft-out_binary64_711` `add-log-exp_binary64_799`
6×	`prod-exp_binary64_809` `cbrt-unprod_binary64_793`
4×	`associate-/r/_binary64_706` `associate-/r*_binary64_704`
3×	`cbrt-undiv_binary64_794` `flip3-+_binary64_763` `flip-+_binary64_734` `associate-/l*_binary64_705` `div-exp_binary64_811` `pow-prod-down_binary64_831`
2×	`div-inv_binary64_757`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cancel-sign-sub-inv_binary64_726` `+-commutative_binary64_690` `sum-log_binary64_851` `associate-l_binary64_701` `associate-r/_binary64_702` `clear-num_binary64_759` `sub-neg_binary64_753` `-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

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)))))))
11.0ms	(+.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))))))
4.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series581.0ms (6%)

Counts

4 → 12

Calls

4 calls:

271.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
179.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
80.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
51.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify99.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4961	2612
1	4961	2612

prune217.0ms (2.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	107	9	116

Error

Counts

116 → 9

Compiler

Compiled 3001 to 1918 computations (36.1% saved)

localize50.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
0.3b	(.f64 c (.f64 (*.f64 a a) 16))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.4b	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

rewrite158.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796`
31×	`times-frac_binary64_766`
27×	`*-un-lft-identity_binary64_760`
19×	`prod-exp_binary64_809` `add-cube-cbrt_binary64_795` `cbrt-unprod_binary64_793` `add-sqr-sqrt_binary64_782`
18×	`cbrt-undiv_binary64_794` `div-exp_binary64_811`
14×	`associate-/l*_binary64_705`
13×	`pow1_binary64_821`
8×	`associate-/r/_binary64_706` `associate-/r*_binary64_704`
6×	`pow-prod-down_binary64_831`
5×	`div-inv_binary64_757`
4×	`distribute-lft-out_binary64_711` `flip3-+_binary64_763` `add-log-exp_binary64_799` `flip-+_binary64_734`
3×	`frac-2neg_binary64_771` `associate-/l/_binary64_707` `associate-l_binary64_701` `clear-num_binary64_759`
1×	`associate-r_binary64_700` `div-sub_binary64_765` `*-commutative_binary64_691` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 128

Calls

4 calls:

42.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
35.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
21.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
15.0ms	(.f64 c (.f64 (*.f64 a a) 16))

series1.0s (10.3%)

Counts

4 → 12

Calls

4 calls:

568.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
283.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
118.0ms	(/.f64 (-.f64 (pow.f64 b 4) (.f64 c (.f64 c (.f64 (.f64 a a) 16)))) (+.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
34.0ms	(.f64 c (.f64 (*.f64 a a) 16))

simplify182.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4948	6159
1	4948	6159

prune305.0ms (3.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	140	9	149

Error

Counts

149 → 9

Compiler

Compiled 6437 to 3820 computations (40.7% saved)

regimes701.0ms (7.2%)

Accuracy

Total 0.3b remaining (99.9%)

Threshold costs 0.3b (99.9%)

Compiler

Compiled 6996 to 5230 computations (25.2% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample3.7s (37.4%)

Algorithm

1×

intervals

Results

613.0ms	7673×	body	128	valid
427.0ms	8805×	pre	128	true
65.0ms	805×	body	128	nan
50.0ms	327×	body	256	valid

Compiler

Compiled 1785 to 1336 computations (25.2% saved)

Details

analyze351.0ms (3.6%)

sample32.0ms (0.3%)

simplify571.0ms (5.9%)

prune7.0ms (0.1%)

localize11.0ms (0.1%)

rewrite51.0ms (0.5%)

series372.0ms (3.8%)

simplify147.0ms (1.5%)

prune139.0ms (1.4%)

localize14.0ms (0.1%)

rewrite64.0ms (0.7%)

series638.0ms (6.5%)

simplify78.0ms (0.8%)

prune246.0ms (2.5%)

localize23.0ms (0.2%)

rewrite57.0ms (0.6%)

series581.0ms (6%)

simplify99.0ms (1%)

prune217.0ms (2.2%)

localize50.0ms (0.5%)

rewrite158.0ms (1.6%)

series1.0s (10.3%)

simplify182.0ms (1.9%)

prune305.0ms (3.1%)

regimes701.0ms (7.2%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.7s (37.4%)

Profiling