Details

analyze538.0ms (9.1%)

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
3.1%	96.7%	0.2%	8
19.9%	79.9%	0.2%	9
22.8%	77%	0.2%	10
35.1%	64.7%	0.2%	11
45%	54.8%	0.2%	12
53.8%	45.1%	1.2%	13
56.2%	42.4%	1.5%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample18.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 19 to 21 computations (-10.5% saved)

simplify306.0ms (5.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (133.0ms)

Iter	Nodes	Cost
0	5598	13

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

Merged error: 2.8b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (-.f64 z y))
2.7b	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_13173`
70×	`*-un-lft-identity_binary64_13151`
51×	`times-frac_binary64_13157`
31×	`associate-l_binary64_13092`
26×	`add-cube-cbrt_binary64_13186`
22×	`distribute-lft-out--_binary64_13103` `difference-of-squares_binary64_13120`
9×	`add-exp-log_binary64_13189` `add-cbrt-cube_binary64_13187`
5×	`associate-/r_binary64_13095` `associate-/l_binary64_13096`
4×	`pow1_binary64_13212` `associate-/r/_binary64_13097`
3×	`flip--_binary64_13126` `flip3--_binary64_13155` `associate-r_binary64_13091`
2×	`associate-/l/_binary64_13098` `prod-exp_binary64_13200` `cbrt-undiv_binary64_13185` `cbrt-unprod_binary64_13184` `div-inv_binary64_13148` `add-log-exp_binary64_13190` `unswap-sqr_binary64_13119` `div-exp_binary64_13202`
1×	`frac-2neg_binary64_13162` `pow-prod-down_binary64_13222` `div-sub_binary64_13156` `-commutative_binary64_13082` `associate-l/_binary64_13094` `clear-num_binary64_13150`

Counts

2 → 102

Calls

2 calls:

15.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
9.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

series352.0ms (5.9%)

Counts

2 → 6

Calls

2 calls:

261.0ms	(*.f64 (/.f64 (-.f64 x y) (-.f64 z y)) t)
91.0ms	(/.f64 (-.f64 x y) (-.f64 z y))

simplify66.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4999	1792
1	4999	1792

prune231.0ms (3.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	6	109

Merged error: 0.0b

Counts

109 → 6

Compiler

Compiled 4685 to 2057 computations (56.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 x y))
0.5b	(cbrt.f64 (-.f64 x y))
0.5b	(cbrt.f64 (-.f64 x y))
0.5b	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod_binary64_13182`
37×	`add-sqr-sqrt_binary64_13173`
35×	`*-un-lft-identity_binary64_13151`
18×	`cbrt-div_binary64_13183`
15×	`add-cube-cbrt_binary64_13186`
11×	`pow1_binary64_13212`
10×	`swap-sqr_binary64_13118`
9×	`pow1/3_binary64_13233` `flip--_binary64_13126` `flip3--_binary64_13155` `distribute-lft-out--_binary64_13103`
8×	`associate-r_binary64_13091` `associate-l_binary64_13092`
7×	`difference-of-squares_binary64_13120`
6×	`add-exp-log_binary64_13189`
4×	`add-cbrt-cube_binary64_13187` `add-log-exp_binary64_13190` `frac-times_binary64_13161` `unswap-sqr_binary64_13119`
2×	`pow-prod-down_binary64_13222` `pow-sqr_binary64_13124` `associate-r/_binary64_13093` `associate-l/_binary64_13094` `pow-prod-up_binary64_13221`
1×	`pow2_binary64_13232` `prod-exp_binary64_13200` `cbrt-unprod_binary64_13184` `*-commutative_binary64_13082` `pow-plus_binary64_13214`

Counts

4 → 101

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
4.0ms	(cbrt.f64 (-.f64 x y))
4.0ms	(cbrt.f64 (-.f64 x y))
3.0ms	(cbrt.f64 (-.f64 x y))

series913.0ms (15.4%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(*.f64 (cbrt.f64 (-.f64 x y)) (cbrt.f64 (-.f64 x y)))
224.0ms	(cbrt.f64 (-.f64 x y))
221.0ms	(cbrt.f64 (-.f64 x y))
217.0ms	(cbrt.f64 (-.f64 x y))

simplify64.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5254	1620

prune124.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	113	6	119

Merged error: 0.0b

Counts

119 → 6

Compiler

Compiled 4167 to 715 computations (82.8% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (-.f64 z y))
0.0b	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
0.0b	(/.f64 x (-.f64 z y))
2.7b	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`*-un-lft-identity_binary64_13151`
95×	`add-sqr-sqrt_binary64_13173`
81×	`times-frac_binary64_13157`
39×	`add-cube-cbrt_binary64_13186`
35×	`distribute-lft-out--_binary64_13103`
23×	`difference-of-squares_binary64_13120`
21×	`cancel-sign-sub-inv_binary64_13117`
18×	`associate-l_binary64_13092`
14×	`associate-/r/_binary64_13097`
10×	`add-exp-log_binary64_13189` `add-cbrt-cube_binary64_13187` `associate-/r*_binary64_13095`
9×	`flip--_binary64_13126` `flip3--_binary64_13155`
7×	`div-inv_binary64_13148`
6×	`distribute-rgt-out--_binary64_13105` `add-log-exp_binary64_13190` `pow1_binary64_13212` `associate-/l*_binary64_13096`
4×	`associate-*l/_binary64_13094`
3×	`associate-r_binary64_13091`
2×	`frac-2neg_binary64_13162` `cbrt-undiv_binary64_13185` `sub-div_binary64_13158` `clear-num_binary64_13150` `frac-sub_binary64_13160` `div-exp_binary64_13202`
1×	`prod-exp_binary64_13200` `pow-prod-down_binary64_13222` `cbrt-unprod_binary64_13184` `*-commutative_binary64_13082` `unswap-sqr_binary64_13119` `sub-neg_binary64_13144` `diff-log_binary64_13243`

Counts

4 → 160

Calls

4 calls:

39.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
33.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
9.0ms	(/.f64 y (-.f64 z y))
6.0ms	(/.f64 x (-.f64 z y))

series639.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

366.0ms	(*.f64 (-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y))) t)
141.0ms	(-.f64 (/.f64 x (-.f64 z y)) (/.f64 y (-.f64 z y)))
77.0ms	(/.f64 x (-.f64 z y))
56.0ms	(/.f64 y (-.f64 z y))

simplify77.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5341	2845

prune382.0ms (6.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	170	2	172
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	171	7	178

Merged error: 0b

Counts

178 → 7

Compiler

Compiled 4589 to 1321 computations (71.2% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y)))
0.0b	(/.f64 (-.f64 z y) x)
0.8b	(/.f64 1 (/.f64 (-.f64 z y) x))
2.7b	(*.f64 (-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y))) t)

rewrite203.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`times-frac_binary64_13157`
187×	`add-sqr-sqrt_binary64_13173`
151×	`*-un-lft-identity_binary64_13151`
81×	`add-cube-cbrt_binary64_13186`
39×	`difference-of-squares_binary64_13120`
29×	`distribute-lft-out--_binary64_13103`
22×	`associate-/r*_binary64_13095`
21×	`cancel-sign-sub-inv_binary64_13117`
19×	`add-exp-log_binary64_13189`
17×	`associate-l_binary64_13092`
13×	`add-cbrt-cube_binary64_13187`
9×	`div-inv_binary64_13148`
8×	`associate-/l*_binary64_13096` `div-exp_binary64_13202`
7×	`pow1_binary64_13212`
6×	`add-log-exp_binary64_13190`
4×	`flip--_binary64_13126` `cbrt-undiv_binary64_13185` `flip3--_binary64_13155`
3×	`associate-r_binary64_13091` `associate-*l/_binary64_13094` `associate-/r/_binary64_13097`
2×	`frac-2neg_binary64_13162` `associate-/l/_binary64_13098` `rec-exp_binary64_13201` `1-exp_binary64_13195` `clear-num_binary64_13150` `frac-sub_binary64_13160`
1×	`inv-pow_binary64_13236` `prod-exp_binary64_13200` `pow-prod-down_binary64_13222` `pow-flip_binary64_13225` `div-sub_binary64_13156` `cbrt-unprod_binary64_13184` `*-commutative_binary64_13082` `unswap-sqr_binary64_13119` `sub-neg_binary64_13144` `diff-log_binary64_13243`

Counts

4 → 220

Calls

4 calls:

79.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y))) t)
76.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y)))
10.0ms	(/.f64 1 (/.f64 (-.f64 z y) x))
7.0ms	(/.f64 (-.f64 z y) x)

series798.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(*.f64 (-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y))) t)
245.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 z y) x)) (/.f64 y (-.f64 z y)))
121.0ms	(/.f64 1 (/.f64 (-.f64 z y) x))
57.0ms	(/.f64 (-.f64 z y) x)

simplify92.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4963	4326
1	4963	4326

prune203.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	231	1	232
Fresh	2	2	4
Picked	0	1	1
Done	0	2	2
Total	233	6	239

Merged error: 0b

Counts

239 → 6

Compiler

Compiled 5359 to 1508 computations (71.9% saved)

regimes56.0ms (0.9%)

Compiler: Compiled 408 to 276 computations (32.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	49
1	29	49

end0.0ms (0%)

sample656.0ms (11%)

Algorithm

1×

intervals

Results

259.0ms	8000×	body	128	valid
22.0ms	614×	body	128	invalid

Compiler

Compiled 150 to 96 computations (36% saved)

Details

analyze538.0ms (9.1%)

sample18.0ms (0.3%)

simplify306.0ms (5.2%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite35.0ms (0.6%)

series352.0ms (5.9%)

simplify66.0ms (1.1%)

prune231.0ms (3.9%)

localize16.0ms (0.3%)

rewrite37.0ms (0.6%)

series913.0ms (15.4%)

simplify64.0ms (1.1%)

prune124.0ms (2.1%)

localize8.0ms (0.1%)

rewrite104.0ms (1.8%)

series639.0ms (10.8%)

simplify77.0ms (1.3%)

prune382.0ms (6.4%)

localize9.0ms (0.1%)

rewrite203.0ms (3.4%)

series798.0ms (13.4%)

simplify92.0ms (1.5%)

prune203.0ms (3.4%)

regimes56.0ms (0.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample656.0ms (11%)

Profiling