Details

analyze1.2s (18.2%)

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 (0.7%)

Algorithm

1×

intervals

Results

20.0ms	256×	body	128	valid
11.0ms	150×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify215.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4971	37
1	4971	37

prune9.0ms (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: 9.6b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
7.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.8b	(.f64 r (.f64 w w))

rewrite80.0ms (1.2%)

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:

24.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
13.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
8.0ms	(.f64 r (.f64 w w))

series359.0ms (5.5%)

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)))))
96.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
87.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
62.0ms	(.f64 r (.f64 w w))

simplify72.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5464	4089

prune341.0ms (5.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	8	189
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Merged error: 4.5b

Counts

191 → 9

Compiler

Compiled 6347 to 3682 computations (42% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (*.f64 r r))
0.5b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
7.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite71.0ms (1.1%)

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:

22.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
12.0ms	(/.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))

series349.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
107.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
88.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
35.0ms	(/.f64 2 (*.f64 r r))

simplify84.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5244	4160

prune400.0ms (6.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	187	13	200

Merged error: 0.0b

Counts

200 → 13

Compiler

Compiled 6459 to 3820 computations (40.9% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
0.4b	(/.f64 2 (*.f64 r r))
0.4b	(/.f64 1 (.f64 (.f64 r w) w))
5.0b	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))

rewrite43.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
39×	`times-frac_binary64`
37×	`add-cbrt-cube_binary64`
25×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
24×	`div-exp_binary64`
22×	`prod-exp_binary64`
15×	`pow1_binary64`
12×	`cbrt-undiv_binary64`
10×	`cbrt-unprod_binary64`
9×	`associate-/r_binary64` `associate-/l_binary64`
7×	`div-inv_binary64`
6×	`pow-prod-down_binary64` `1-exp_binary64` `rec-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-flip_binary64`
1×	`associate-/r/_binary64` `associate-l_binary64` `inv-pow_binary64` `*-commutative_binary64`

Counts

4 → 128

Calls

4 calls:

13.0ms	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))
7.0ms	(/.f64 1 (.f64 (.f64 r w) w))
5.0ms	(.f64 (.f64 r w) w)
5.0ms	(/.f64 2 (*.f64 r r))

series167.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

49.0ms	(/.f64 r (/.f64 1 (.f64 (.f64 r w) w)))
48.0ms	(.f64 (.f64 r w) w)
36.0ms	(/.f64 1 (.f64 (.f64 r w) w))
34.0ms	(/.f64 2 (*.f64 r r))

simplify98.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5410	1609

prune236.0ms (3.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	140	13	153

Merged error: 0.0b

Counts

153 → 13

Compiler

Compiled 4499 to 2833 computations (37% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w)))))
0.4b	(/.f64 2 (*.f64 r r))
5.0b	(.f64 r (.f64 w (*.f64 r w)))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w))))))

rewrite81.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

135×	`add-exp-log_binary64`
107×	`times-frac_binary64`
72×	`add-sqr-sqrt_binary64`
66×	`*-un-lft-identity_binary64`
65×	`add-cbrt-cube_binary64`
59×	`prod-exp_binary64`
46×	`div-exp_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
25×	`cbrt-unprod_binary64`
20×	`cbrt-undiv_binary64`
16×	`pow1_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
10×	`1-exp_binary64` `rec-exp_binary64` `div-inv_binary64`
7×	`pow-prod-down_binary64` `distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64` `inv-pow_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 196

Calls

4 calls:

28.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w))))))
14.0ms	(/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w)))))
7.0ms	(.f64 r (.f64 w (*.f64 r w)))
5.0ms	(/.f64 2 (*.f64 r r))

series299.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w))))))
94.0ms	(/.f64 1 (/.f64 (-.f64 1 v) (.f64 r (.f64 w (*.f64 r w)))))
46.0ms	(.f64 r (.f64 w (*.f64 r w)))
32.0ms	(/.f64 2 (*.f64 r r))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5277	4283

prune377.0ms (5.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	207	1	208
Fresh	2	9	11
Picked	1	0	1
Done	0	1	1
Total	210	11	221

Merged error: 0.0b

Counts

221 → 11

Compiler

Compiled 6619 to 3935 computations (40.5% saved)

regimes137.0ms (2.1%)

Compiler: Compiled 918 to 741 computations (19.3% saved)

bsearch62.0ms (1%)

Steps

Iters	Range		Point
8	5.040825715378987e-05	0.01923498271855242	8.580410111110405e-05
5	-1.864326081068736e+60	-6.7016757651596725e+59	-9.302112022616566e+59

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	206	126
1	206	126

end0.0ms (0%)

sample1.6s (25.3%)

Algorithm

1×

intervals

Results

597.0ms	8000×	body	128	valid
351.0ms	4686×	body	128	invalid

Compiler

Compiled 419 to 326 computations (22.2% saved)

Details

analyze1.2s (18.2%)

sample46.0ms (0.7%)

simplify215.0ms (3.3%)

prune9.0ms (0.1%)

localize25.0ms (0.4%)

rewrite80.0ms (1.2%)

series359.0ms (5.5%)

simplify72.0ms (1.1%)

prune341.0ms (5.2%)

localize20.0ms (0.3%)

rewrite71.0ms (1.1%)

series349.0ms (5.3%)

simplify84.0ms (1.3%)

prune400.0ms (6.1%)

localize18.0ms (0.3%)

rewrite43.0ms (0.7%)

series167.0ms (2.6%)

simplify98.0ms (1.5%)

prune236.0ms (3.6%)

localize19.0ms (0.3%)

rewrite81.0ms (1.2%)

series299.0ms (4.6%)

simplify76.0ms (1.2%)

prune377.0ms (5.8%)

regimes137.0ms (2.1%)

bsearch62.0ms (1%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.6s (25.3%)

Profiling