Details

analyze1.1s (15.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0.4%	99.4%	0.2%	10
5.6%	94.2%	0.2%	11
7.1%	92.7%	0.2%	12
8.8%	91%	0.2%	13
15.6%	84.2%	0.2%	14

Compiler

Compiled 14 to 13 computations (7.1% saved)

sample23.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 27 to 30 computations (-11.1% saved)

simplify320.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (149.0ms)

Iter	Nodes	Cost
0	4963	19
1	4963	19

prune3.0ms (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

Merged error: 2.5b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
8.2b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

236×	`*-un-lft-identity_binary64_15579`
200×	`times-frac_binary64_15585`
126×	`add-sqr-sqrt_binary64_15600`
86×	`add-cube-cbrt_binary64_15611`
44×	`distribute-lft-out_binary64_15532`
42×	`distribute-lft-out--_binary64_15533`
22×	`associate-/r*_binary64_15525`
20×	`difference-of-squares_binary64_15548`
10×	`associate-/l*_binary64_15526`
9×	`add-exp-log_binary64_15614` `add-cbrt-cube_binary64_15612`
8×	`div-inv_binary64_15576`
4×	`cbrt-undiv_binary64_15610` `div-exp_binary64_15627` `associate-/l/_binary64_15528`
2×	`clear-num_binary64_15578` `pow1_binary64_15637` `add-log-exp_binary64_15615` `div-sub_binary64_15584` `frac-2neg_binary64_15590`
1×	`flip--_binary64_15554` `flip3--_binary64_15583` `associate-/r/_binary64_15527` `flip3-+_binary64_15582` `associate-+l-_binary64_15516` `flip-+_binary64_15553`

Counts

2 → 175

Calls

2 calls:

16.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
9.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

series358.0ms (5.2%)

Counts

2 → 6

Calls

2 calls:

307.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
50.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	6100	4859

prune210.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	176	5	181
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	177	5	182

Merged error: 0b

Counts

182 → 5

Compiler

Compiled 4255 to 1700 computations (60% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite43.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

103×	`*-un-lft-identity_binary64_15579`
53×	`add-sqr-sqrt_binary64_15600`
51×	`times-frac_binary64_15585`
31×	`associate-l_binary64_15522`
26×	`add-cube-cbrt_binary64_15611`
22×	`distribute-lft-out_binary64_15532` `distribute-lft-out--_binary64_15533`
11×	`difference-of-squares_binary64_15548`
9×	`add-exp-log_binary64_15614` `add-cbrt-cube_binary64_15612`
5×	`associate-/r_binary64_15525` `associate-/l_binary64_15526`
4×	`pow1_binary64_15637` `associate-/r/_binary64_15527`
3×	`associate-r_binary64_15521`
2×	`div-inv_binary64_15576` `cbrt-undiv_binary64_15610` `div-exp_binary64_15627` `add-log-exp_binary64_15615` `associate-/l/_binary64_15528` `flip3-+_binary64_15582` `prod-exp_binary64_15625` `cbrt-unprod_binary64_15609` `flip-+_binary64_15553` `unswap-sqr_binary64_15547`
1×	`pow-prod-down_binary64_15647` `clear-num_binary64_15578` `flip--_binary64_15554` `flip3--_binary64_15583` `associate-l/_binary64_15524` `div-sub_binary64_15584` `frac-2neg_binary64_15590` `-commutative_binary64_15512`

Counts

2 → 102

Calls

2 calls:

17.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
14.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

series408.0ms (6%)

Counts

2 → 6

Calls

2 calls:

307.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
101.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5399	2064

prune101.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	108	5	113

Merged error: 0b

Counts

113 → 5

Compiler

Compiled 2339 to 1033 computations (55.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite121.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

186×	`*-un-lft-identity_binary64_15579`
82×	`times-frac_binary64_15585`
56×	`add-sqr-sqrt_binary64_15600`
44×	`distribute-lft-out--_binary64_15533`
40×	`distribute-lft-out_binary64_15532`
30×	`add-cube-cbrt_binary64_15611`
22×	`associate-l_binary64_15522`
12×	`associate-/r/_binary64_15527`
10×	`associate-/r*_binary64_15525` `add-exp-log_binary64_15614` `add-cbrt-cube_binary64_15612`
8×	`difference-of-squares_binary64_15548`
6×	`distribute-rgt-out--_binary64_15535` `pow1_binary64_15637` `div-inv_binary64_15576` `add-log-exp_binary64_15615` `flip3-+_binary64_15582` `associate-/l*_binary64_15526` `flip-+_binary64_15553`
4×	`associate-*l/_binary64_15524`
3×	`associate-r_binary64_15521`
2×	`clear-num_binary64_15578` `flip--_binary64_15554` `cbrt-undiv_binary64_15610` `flip3--_binary64_15583` `sub-div_binary64_15586` `div-exp_binary64_15627` `frac-2neg_binary64_15590` `frac-sub_binary64_15588`
1×	`pow-prod-down_binary64_15647` `diff-log_binary64_15668` `sub-neg_binary64_15572` `prod-exp_binary64_15625` `cbrt-unprod_binary64_15609` `*-commutative_binary64_15512` `unswap-sqr_binary64_15547`

Counts

4 → 147

Calls

4 calls:

43.0ms	(*.f64 (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1))) a)
42.0ms	(-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))
9.0ms	(/.f64 y (+.f64 (-.f64 t z) 1))
8.0ms	(/.f64 z (+.f64 (-.f64 t z) 1))

series584.0ms (8.6%)

Counts

4 → 12

Calls

4 calls:

284.0ms	(*.f64 (-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1))) a)
167.0ms	(-.f64 (/.f64 y (+.f64 (-.f64 t z) 1)) (/.f64 z (+.f64 (-.f64 t z) 1)))
74.0ms	(/.f64 y (+.f64 (-.f64 t z) 1))
60.0ms	(/.f64 z (+.f64 (-.f64 t z) 1))

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5335	3428

prune179.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	159	5	164

Merged error: 0b

Counts

164 → 5

Compiler

Compiled 4306 to 2183 computations (49.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 y z))
0.6b	(cbrt.f64 (-.f64 y z))
0.6b	(cbrt.f64 (-.f64 y z))
3.3b	(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (+.f64 (-.f64 t z) 1)) a))

rewrite105.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

440×	`times-frac_binary64_15585`
399×	`*-un-lft-identity_binary64_15579`
295×	`cbrt-prod_binary64_15607`
264×	`add-sqr-sqrt_binary64_15600`
200×	`add-cube-cbrt_binary64_15611`
59×	`distribute-lft-out--_binary64_15533`
54×	`distribute-lft-out_binary64_15532`
32×	`difference-of-squares_binary64_15548`
28×	`associate-/r*_binary64_15525`
10×	`div-inv_binary64_15576`
9×	`add-exp-log_binary64_15614`
8×	`cbrt-div_binary64_15608` `associate-/l*_binary64_15526`
6×	`add-cbrt-cube_binary64_15612`
4×	`flip--_binary64_15554` `pow1_binary64_15637` `flip3--_binary64_15583` `add-log-exp_binary64_15615`
3×	`cbrt-undiv_binary64_15610` `div-exp_binary64_15627` `pow1/3_binary64_15658`
2×	`associate-/l/_binary64_15528`
1×	`clear-num_binary64_15578` `associate-/r/_binary64_15527` `frac-2neg_binary64_15590`

Counts

4 → 322

Calls

4 calls:

21.0ms	(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (+.f64 (-.f64 t z) 1)) a))
7.0ms	(cbrt.f64 (-.f64 y z))
4.0ms	(cbrt.f64 (-.f64 y z))
3.0ms	(cbrt.f64 (-.f64 y z))

series1.2s (17.2%)

Counts

4 → 12

Calls

4 calls:

561.0ms	(/.f64 (cbrt.f64 (-.f64 y z)) (/.f64 (cbrt.f64 (+.f64 (-.f64 t z) 1)) a))
205.0ms	(cbrt.f64 (-.f64 y z))
204.0ms	(cbrt.f64 (-.f64 y z))
203.0ms	(cbrt.f64 (-.f64 y z))

simplify173.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

334 → 334

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4901	12464
1	4901	12464

prune715.0ms (10.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	334	0	334
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	334	5	339

Merged error: 0b

Counts

339 → 5

Compiler

Compiled 17660 to 6953 computations (60.6% saved)

regimes70.0ms (1%)

Compiler: Compiled 505 to 435 computations (13.9% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	155	28
1	155	28

end0.0ms (0%)

sample789.0ms (11.6%)

Algorithm

1×

intervals

Results

338.0ms	8000×	body	128	valid
23.0ms	466×	body	128	invalid

Compiler

Compiled 145 to 122 computations (15.9% saved)

Details

analyze1.1s (15.9%)

sample23.0ms (0.3%)

simplify320.0ms (4.7%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite48.0ms (0.7%)

series358.0ms (5.2%)

simplify90.0ms (1.3%)

prune210.0ms (3.1%)

localize10.0ms (0.1%)

rewrite43.0ms (0.6%)

series408.0ms (6%)

simplify73.0ms (1.1%)

prune101.0ms (1.5%)

localize14.0ms (0.2%)

rewrite121.0ms (1.8%)

series584.0ms (8.6%)

simplify89.0ms (1.3%)

prune179.0ms (2.6%)

localize18.0ms (0.3%)

rewrite105.0ms (1.5%)

series1.2s (17.2%)

simplify173.0ms (2.5%)

prune715.0ms (10.5%)

regimes70.0ms (1%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample789.0ms (11.6%)

Profiling