Details

analyze1.1s (12.9%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

Compiler

Compiled 30 to 25 computations (16.7% saved)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
11.0ms	160×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify230.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4993	37
1	4993	37

prune11.0ms (0.1%)

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: 9.3b

Counts

2 → 2

Compiler

Compiled 133 to 108 computations (18.8% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
4.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
6.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
9.7b	(.f64 r (.f64 w w))

rewrite93.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
18×	`difference-of-squares_binary64`
17×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`div-inv_binary64`
9×	`associate-/l*_binary64` `distribute-lft-out--_binary64`
6×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `associate-*r/_binary64` `div-sub_binary64` `flip--_binary64`

Counts

4 → 177

Calls

4 calls:

33.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
14.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
11.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
9.0ms	(.f64 r (.f64 w w))

series358.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
103.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
83.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
57.0ms	(.f64 r (.f64 w w))

simplify73.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5468	4089

prune845.0ms (9.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	181	8	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	183	8	191

Merged error: 3.1b

Counts

191 → 8

Compiler

Compiled 16811 to 11624 computations (30.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (*.f64 r r))
1.1b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
6.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite80.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`add-cube-cbrt_binary64`
35×	`associate-r_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`difference-of-squares_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 179

Calls

4 calls:

25.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
16.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
10.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))

series345.0ms (4%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
101.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
84.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
42.0ms	(/.f64 2 (*.f64 r r))

simplify88.0ms (1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5248	4160

prune1.0s (12.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	186	13	199

Merged error: 0.0b

Counts

199 → 13

Compiler

Compiled 21302 to 15112 computations (29.1% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
0.7b	(/.f64 2 (*.f64 r r))
2.6b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite113.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64`
143×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
100×	`add-exp-log_binary64`
82×	`add-cbrt-cube_binary64`
78×	`cbrt-prod_binary64`
44×	`cbrt-unprod_binary64` `prod-exp_binary64`
32×	`associate-/r*_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
26×	`difference-of-squares_binary64`
13×	`distribute-lft-out--_binary64`
9×	`pow1_binary64` `frac-times_binary64`
6×	`associate-r/_binary64` `associate-/l_binary64` `div-inv_binary64`
5×	`associate-*l/_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64`
3×	`pow-prod-down_binary64` `associate-l_binary64`
2×	`cbrt-div_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3--_binary64` `associate-r_binary64` `pow1/3_binary64` `associate-/r/_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 236

Calls

4 calls:

40.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
13.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
4.0ms	(cbrt.f64 (-.f64 1 v))

series398.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
141.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
52.0ms	(cbrt.f64 (-.f64 1 v))
33.0ms	(/.f64 2 (*.f64 r r))

simplify137.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

248 → 248

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4995	6289
1	4995	6289

prune695.0ms (8.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	248	13	261

Merged error: 0.0b

Counts

261 → 13

Compiler

Compiled 10977 to 7049 computations (35.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w)))
0.7b	(/.f64 2 (*.f64 r r))
3.1b	(/.f64 r (/.f64 (-.f64 1 v) w))
4.6b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w))))

rewrite116.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

261×	`times-frac_binary64`
186×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
123×	`add-cube-cbrt_binary64`
72×	`associate-r_binary64`
64×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
42×	`difference-of-squares_binary64`
26×	`cbrt-unprod_binary64` `prod-exp_binary64`
23×	`associate-/r*_binary64`
21×	`distribute-lft-out--_binary64`
18×	`pow1_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
10×	`div-inv_binary64`
9×	`pow-prod-down_binary64`
6×	`associate-/l*_binary64`
5×	`associate-*r/_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 256

Calls

4 calls:

27.0ms	(.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w)))
24.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w))))
11.0ms	(/.f64 r (/.f64 (-.f64 1 v) w))
5.0ms	(/.f64 2 (*.f64 r r))

series324.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

110.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w))))
101.0ms	(.f64 (.f64 r w) (/.f64 r (/.f64 (-.f64 1 v) w)))
80.0ms	(/.f64 r (/.f64 (-.f64 1 v) w))
33.0ms	(/.f64 2 (*.f64 r r))

simplify109.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

268 → 268

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5046	5606

prune498.0ms (5.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	268	0	268
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	268	13	281

Merged error: 0.0b

Counts

281 → 13

Compiler

Compiled 8992 to 5191 computations (42.3% saved)

regimes142.0ms (1.7%)

Compiler: Compiled 1699 to 1341 computations (21.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	55
1	130	55

end0.0ms (0%)

sample1.6s (18.7%)

Algorithm

1×

intervals

Results

553.0ms	8000×	body	128	valid
350.0ms	5007×	body	128	invalid

Compiler

Compiled 464 to 368 computations (20.7% saved)

Details

analyze1.1s (12.9%)

sample46.0ms (0.5%)

simplify230.0ms (2.7%)

prune11.0ms (0.1%)

localize18.0ms (0.2%)

rewrite93.0ms (1.1%)

series358.0ms (4.2%)

simplify73.0ms (0.9%)

prune845.0ms (9.9%)

localize17.0ms (0.2%)

rewrite80.0ms (0.9%)

series345.0ms (4%)

simplify88.0ms (1%)

prune1.0s (12.3%)

localize21.0ms (0.2%)

rewrite113.0ms (1.3%)

series398.0ms (4.7%)

simplify137.0ms (1.6%)

prune695.0ms (8.1%)

localize17.0ms (0.2%)

rewrite116.0ms (1.4%)

series324.0ms (3.8%)

simplify109.0ms (1.3%)

prune498.0ms (5.8%)

regimes142.0ms (1.7%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.6s (18.7%)

Profiling