Details

analyze1.3s (16.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0.6%	99.1%	0.3%	11
1.8%	98%	0.3%	12
2.6%	97.1%	0.3%	13
4%	95.7%	0.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample26.0ms (0.3%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 35 to 35 computations (0% saved)

simplify181.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4854	25
1	4854	25

prune2.0ms (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

Error

22.3b

Counts

2 → 1

Compiler

Compiled 34 to 28 computations (17.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 b y))
0.0b	(*.f64 z (-.f64 t a))
1.1b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
21.5b	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

rewrite39.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_20901`
26×	`*-un-lft-identity_binary64_20879`
22×	`add-cube-cbrt_binary64_20914`
18×	`cancel-sign-sub-inv_binary64_20845`
12×	`distribute-rgt-in_binary64_20829` `distribute-lft-in_binary64_20828`
10×	`add-cbrt-cube_binary64_20915` `add-exp-log_binary64_20917` `associate-r_binary64_20819`
9×	`times-frac_binary64_20885`
8×	`associate-+r+_binary64_20811` `pow1_binary64_20940`
6×	`associate-l_binary64_20820` `sub-neg_binary64_20872` `add-log-exp_binary64_20918`
4×	`associate-*r/_binary64_20821`
3×	`associate-/l_binary64_20824` `associate-/r_binary64_20823` `flip3-+_binary64_20882` `flip-+_binary64_20853`
2×	`flip3--_binary64_20883` `flip--_binary64_20854` `pow-prod-down_binary64_20950` `associate-/l/_binary64_20826` `associate-/r/_binary64_20825` `distribute-lft-out--_binary64_20831` `unswap-sqr_binary64_20847` `*-commutative_binary64_20810` `difference-of-squares_binary64_20848` `prod-exp_binary64_20928` `cbrt-unprod_binary64_20912`
1×	`div-exp_binary64_20930` `cbrt-undiv_binary64_20913` `frac-2neg_binary64_20890` `+-commutative_binary64_20809` `sum-log_binary64_20970` `div-inv_binary64_20876` `clear-num_binary64_20878`

Counts

4 → 110

Calls

4 calls:

8.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
8.0ms	(*.f64 z (-.f64 b y))
7.0ms	(*.f64 z (-.f64 t a))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))

series529.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

418.0ms	(/.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))
50.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
31.0ms	(*.f64 z (-.f64 t a))
30.0ms	(*.f64 z (-.f64 b y))

simplify51.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5665	2127

prune139.0ms (1.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	111	11	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	11	123

Error

21.7b

Counts

123 → 11

Compiler

Compiled 3200 to 573 computations (82.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 t a))
0.9b	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
1.1b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
21.5b	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))

rewrite41.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_20901`
29×	`*-un-lft-identity_binary64_20879`
26×	`add-cube-cbrt_binary64_20914`
20×	`times-frac_binary64_20885` `associate-r_binary64_20819`
19×	`add-exp-log_binary64_20917`
13×	`add-cbrt-cube_binary64_20915`
12×	`cancel-sign-sub-inv_binary64_20845`
9×	`pow1_binary64_20940`
8×	`distribute-rgt-in_binary64_20829` `distribute-lft-in_binary64_20828` `associate-+r+_binary64_20811`
6×	`associate-l_binary64_20820` `add-log-exp_binary64_20918`
5×	`flip3-+_binary64_20882` `flip-+_binary64_20853` `prod-exp_binary64_20928`
4×	`div-exp_binary64_20930` `associate-/r/_binary64_20825` `sub-neg_binary64_20872` `unswap-sqr_binary64_20847`
3×	`associate-/l_binary64_20824` `associate-/r_binary64_20823` `cbrt-unprod_binary64_20912` `associate-*r/_binary64_20821`
2×	`pow-prod-down_binary64_20950` `rec-exp_binary64_20929` `cbrt-undiv_binary64_20913` `1-exp_binary64_20923` `div-inv_binary64_20876` `-commutative_binary64_20810` `associate-l/_binary64_20822` `frac-times_binary64_20889`
1×	`flip3--_binary64_20883` `inv-pow_binary64_20964` `flip--_binary64_20854` `un-div-inv_binary64_20877` `frac-2neg_binary64_20890` `+-commutative_binary64_20809` `sum-log_binary64_20970` `distribute-lft-out--_binary64_20831` `pow-flip_binary64_20953` `clear-num_binary64_20878` `difference-of-squares_binary64_20848`

Counts

4 → 124

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))
7.0ms	(*.f64 z (-.f64 t a))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
5.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))

series576.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

420.0ms	(.f64 (+.f64 (.f64 x y) (.f64 z (-.f64 t a))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))
73.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
47.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
36.0ms	(*.f64 z (-.f64 t a))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5005	2604

prune120.0ms (1.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	134	2	136
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	136	11	147

Error

21.7b

Counts

147 → 11

Compiler

Compiled 3741 to 843 computations (77.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 z (-.f64 t a))
0.7b	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
1.1b	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
21.3b	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_20885`
66×	`add-sqr-sqrt_binary64_20901`
64×	`*-un-lft-identity_binary64_20879`
62×	`add-cube-cbrt_binary64_20914`
19×	`add-exp-log_binary64_20917`
18×	`associate-/r*_binary64_20823`
13×	`add-cbrt-cube_binary64_20915`
12×	`cancel-sign-sub-inv_binary64_20845`
11×	`associate-/r/_binary64_20825`
8×	`div-exp_binary64_20930` `distribute-rgt-in_binary64_20829` `distribute-lft-in_binary64_20828` `associate-+r+_binary64_20811`
7×	`flip3-+_binary64_20882` `flip-+_binary64_20853` `pow1_binary64_20940`
6×	`associate-/l*_binary64_20824` `div-inv_binary64_20876` `add-log-exp_binary64_20918`
5×	`associate-r_binary64_20819`
4×	`cbrt-undiv_binary64_20913` `sub-neg_binary64_20872`
3×	`associate-l_binary64_20820`
2×	`associate-/l/_binary64_20826` `rec-exp_binary64_20929` `frac-2neg_binary64_20890` `1-exp_binary64_20923` `clear-num_binary64_20878` `associate-*r/_binary64_20821`
1×	`flip3--_binary64_20883` `inv-pow_binary64_20964` `flip--_binary64_20854` `pow-prod-down_binary64_20950` `+-commutative_binary64_20809` `sum-log_binary64_20970` `distribute-lft-out--_binary64_20831` `unswap-sqr_binary64_20847` `*-commutative_binary64_20810` `pow-flip_binary64_20953` `difference-of-squares_binary64_20848` `prod-exp_binary64_20928` `cbrt-unprod_binary64_20912`

Counts

4 → 164

Calls

4 calls:

10.0ms	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
8.0ms	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))
8.0ms	(*.f64 z (-.f64 t a))
5.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))

series1.3s (16.1%)

Counts

4 → 12

Calls

4 calls:

905.0ms	(/.f64 1 (/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a)))))
304.0ms	(/.f64 (+.f64 y (.f64 z (-.f64 b y))) (+.f64 (.f64 x y) (*.f64 z (-.f64 t a))))
47.0ms	(+.f64 (.f64 x y) (.f64 z (-.f64 t a)))
33.0ms	(*.f64 z (-.f64 t a))

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5079	5593

prune160.0ms (2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	174	2	176
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	175	12	187

Error

21.7b

Counts

187 → 12

Compiler

Compiled 5612 to 989 computations (82.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))
0.9b	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
1.1b	(+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a))))
21.5b	(.f64 (+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a)))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64_20901`
43×	`*-un-lft-identity_binary64_20879`
28×	`add-cube-cbrt_binary64_20914` `cbrt-prod_binary64_20910`
23×	`associate-r_binary64_20819`
20×	`times-frac_binary64_20885`
19×	`add-exp-log_binary64_20917`
14×	`pow1_binary64_20940`
12×	`cbrt-div_binary64_20911`
11×	`associate-l_binary64_20820` `add-cbrt-cube_binary64_20915`
10×	`swap-sqr_binary64_20846`
7×	`unswap-sqr_binary64_20847`
6×	`flip3--_binary64_20883` `flip--_binary64_20854` `distribute-lft-out--_binary64_20831` `pow1/3_binary64_20961` `add-log-exp_binary64_20918` `frac-times_binary64_20889`
5×	`flip3-+_binary64_20882` `flip-+_binary64_20853` `prod-exp_binary64_20928`
4×	`div-exp_binary64_20930` `associate-/r/_binary64_20825` `difference-of-squares_binary64_20848` `associate-*l/_binary64_20822`
3×	`associate-/l_binary64_20824` `associate-/r_binary64_20823` `pow-prod-down_binary64_20950` `cbrt-unprod_binary64_20912` `associate-*r/_binary64_20821`
2×	`rec-exp_binary64_20929` `cbrt-undiv_binary64_20913` `1-exp_binary64_20923` `pow-sqr_binary64_20852` `pow-prod-up_binary64_20949` `div-inv_binary64_20876` `*-commutative_binary64_20810`
1×	`inv-pow_binary64_20964` `un-div-inv_binary64_20877` `frac-2neg_binary64_20890` `+-commutative_binary64_20809` `sum-log_binary64_20970` `pow2_binary64_20960` `pow-flip_binary64_20953` `clear-num_binary64_20878` `pow-plus_binary64_20942`

Counts

4 → 142

Calls

4 calls:

13.0ms	(.f64 (+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a)))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))
12.0ms	(*.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))
5.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
4.0ms	(+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a))))

series667.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

417.0ms	(.f64 (+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a)))) (/.f64 1 (+.f64 y (.f64 z (-.f64 b y)))))
118.0ms	(*.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))
76.0ms	(/.f64 1 (+.f64 y (*.f64 z (-.f64 b y))))
55.0ms	(+.f64 (.f64 x y) (.f64 (.f64 z (.f64 (cbrt.f64 (-.f64 t a)) (cbrt.f64 (-.f64 t a)))) (cbrt.f64 (-.f64 t a))))

simplify99.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4962	3247
1	4962	3247

prune147.0ms (1.8%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	152	2	154
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	152	14	166

Error

21.7b

Counts

166 → 14

Compiler

Compiled 5171 to 1061 computations (79.5% saved)

regimes724.0ms (9%)

Accuracy

Total 0.7b remaining (3%)

Threshold costs 0.7b (3%)

Compiler

Compiled 10956 to 6546 computations (40.3% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	25
1	38	25

end0.0ms (0%)

sample1.6s (19.5%)

Algorithm

1×

intervals

Results

420.0ms	8000×	body	128	valid
24.0ms	424×	body	128	invalid

Compiler

Compiled 1423 to 856 computations (39.8% saved)

Details

analyze1.3s (16.6%)

sample26.0ms (0.3%)

simplify181.0ms (2.3%)

prune2.0ms (0%)

localize12.0ms (0.2%)

rewrite39.0ms (0.5%)

series529.0ms (6.6%)

simplify51.0ms (0.6%)

prune139.0ms (1.7%)

localize14.0ms (0.2%)

rewrite41.0ms (0.5%)

series576.0ms (7.2%)

simplify82.0ms (1%)

prune120.0ms (1.5%)

localize13.0ms (0.2%)

rewrite48.0ms (0.6%)

series1.3s (16.1%)

simplify92.0ms (1.1%)

prune160.0ms (2%)

localize17.0ms (0.2%)

rewrite55.0ms (0.7%)

series667.0ms (8.3%)

simplify99.0ms (1.2%)

prune147.0ms (1.8%)

regimes724.0ms (9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.6s (19.5%)

Profiling