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)

simplify189.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4869	19
1	4869	19

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

1.9b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
9.1b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

rewrite111.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`*-un-lft-identity_binary64_16105`
373×	`times-frac_binary64_16111`
239×	`add-sqr-sqrt_binary64_16127`
152×	`add-cube-cbrt_binary64_16140`
100×	`cancel-sign-sub-inv_binary64_16071`
77×	`distribute-lft-out--_binary64_16057`
74×	`distribute-lft-out_binary64_16056`
42×	`difference-of-squares_binary64_16074`
22×	`associate-/r*_binary64_16049`
14×	`div-inv_binary64_16102`
10×	`add-exp-log_binary64_16143` `associate-/l*_binary64_16050` `add-cbrt-cube_binary64_16141`
5×	`add-log-exp_binary64_16144`
4×	`div-exp_binary64_16156` `cbrt-undiv_binary64_16139` `associate-/l/_binary64_16052`
3×	`pow1_binary64_16166` `div-sub_binary64_16110`
2×	`flip--_binary64_16080` `flip3--_binary64_16109` `associate-/r/_binary64_16051` `frac-2neg_binary64_16116` `clear-num_binary64_16104`
1×	`flip-+_binary64_16079` `associate--r-_binary64_16044` `diff-log_binary64_16197` `sub-neg_binary64_16098` `flip3-+_binary64_16108` `associate-+l-_binary64_16040`

Counts

3 → 291

Calls

3 calls:

44.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
16.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
9.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

series300.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

145.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
131.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
23.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify121.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5471	8521

prune321.0ms (4.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	295	5	300
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	295	6	301

Error

0.0b

Counts

301 → 6

Compiler

Compiled 6875 to 2735 computations (60.2% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
0.0b	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
0.5b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64_16105`
54×	`add-sqr-sqrt_binary64_16127`
51×	`times-frac_binary64_16111`
31×	`associate-l_binary64_16046`
27×	`add-cube-cbrt_binary64_16140`
22×	`distribute-lft-out--_binary64_16057` `distribute-lft-out_binary64_16056`
11×	`difference-of-squares_binary64_16074`
10×	`add-exp-log_binary64_16143` `add-cbrt-cube_binary64_16141`
5×	`add-log-exp_binary64_16144` `pow1_binary64_16166` `associate-/r_binary64_16049` `associate-/l_binary64_16050`
4×	`associate-/r/_binary64_16051`
3×	`associate-r_binary64_16045`
2×	`flip-+_binary64_16079` `cbrt-unprod_binary64_16138` `div-exp_binary64_16156` `flip--_binary64_16080` `flip3--_binary64_16109` `cbrt-undiv_binary64_16139` `div-inv_binary64_16102` `associate-/l/_binary64_16052` `unswap-sqr_binary64_16073` `flip3-+_binary64_16108` `prod-exp_binary64_16154`
1×	`diff-log_binary64_16197` `sub-neg_binary64_16098` `pow-prod-down_binary64_16176` `cancel-sign-sub-inv_binary64_16071` `associate-l/_binary64_16048` `-commutative_binary64_16036` `frac-2neg_binary64_16116` `div-sub_binary64_16110` `clear-num_binary64_16104`

Counts

3 → 114

Calls

3 calls:

16.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
11.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
3.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

series325.0ms (4.9%)

Counts

3 → 9

Calls

3 calls:

140.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
139.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
46.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5839	2442

prune116.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	123	6	129

Error

Counts

129 → 6

Compiler

Compiled 2684 to 1189 computations (55.7% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) a)
2.2b	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
2.2b	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
2.2b	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))

rewrite104.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

143×	`*-un-lft-identity_binary64_16105`
93×	`cbrt-prod_binary64_16136`
75×	`times-frac_binary64_16111`
68×	`add-sqr-sqrt_binary64_16127`
38×	`add-cube-cbrt_binary64_16140`
30×	`distribute-lft-out--_binary64_16057` `distribute-lft-out_binary64_16056`
15×	`difference-of-squares_binary64_16074` `cbrt-div_binary64_16137`
13×	`add-exp-log_binary64_16143` `pow1_binary64_16166`
12×	`associate-*l/_binary64_16048`
9×	`add-cbrt-cube_binary64_16141`
6×	`cbrt-unprod_binary64_16138` `pow-prod-down_binary64_16176` `associate-/r/_binary64_16051` `prod-exp_binary64_16154`
5×	`frac-times_binary64_16115`
4×	`add-log-exp_binary64_16144`
3×	`flip-+_binary64_16079` `associate-r/_binary64_16047` `pow1/3_binary64_16187` `div-inv_binary64_16102` `flip3-+_binary64_16108` `associate-r*_binary64_16045`
1×	`-commutative_binary64_16036` `associate-l*_binary64_16046`

Counts

4 → 148

Calls

4 calls:

43.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) a)
12.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
11.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
10.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))

series593.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
151.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
149.0ms	(cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))
141.0ms	(.f64 (.f64 (*.f64 (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) (cbrt.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)))) a)

simplify143.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4965	4372
1	4965	4372

prune250.0ms (3.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	160	0	160
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	160	6	166

Error

Counts

166 → 6

Compiler

Compiled 6787 to 3083 computations (54.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))))
0.0b	(/.f64 1 (+.f64 (-.f64 t z) 1))
0.2b	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
8.5b	(.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64_16105`
34×	`add-sqr-sqrt_binary64_16127`
32×	`add-exp-log_binary64_16143` `times-frac_binary64_16111`
25×	`add-cube-cbrt_binary64_16140`
22×	`associate-r_binary64_16045`
20×	`add-cbrt-cube_binary64_16141`
14×	`distribute-lft-out_binary64_16056`
13×	`prod-exp_binary64_16154`
12×	`pow1_binary64_16166`
8×	`distribute-lft-out--_binary64_16057` `associate-l_binary64_16046`
7×	`cbrt-unprod_binary64_16138`
6×	`associate-*r/_binary64_16047` `div-exp_binary64_16156` `add-log-exp_binary64_16144`
5×	`associate-/r*_binary64_16049`
4×	`flip--_binary64_16080` `flip3--_binary64_16109` `frac-times_binary64_16115` `un-div-inv_binary64_16103` `pow-prod-down_binary64_16176` `associate-/r/_binary64_16051`
3×	`rec-exp_binary64_16155` `cbrt-undiv_binary64_16139` `unswap-sqr_binary64_16073` `1-exp_binary64_16149` `associate-/l*_binary64_16050`
2×	`flip-+_binary64_16079` `div-inv_binary64_16102` `flip3-+_binary64_16108` `associate-l/_binary64_16048` `-commutative_binary64_16036`
1×	`difference-of-squares_binary64_16074` `inv-pow_binary64_16190` `diff-log_binary64_16197` `sub-neg_binary64_16098` `cancel-sign-sub-inv_binary64_16071` `pow-flip_binary64_16179` `frac-2neg_binary64_16116` `clear-num_binary64_16104`

Counts

4 → 129

Calls

4 calls:

19.0ms	(.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))))
14.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
8.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))
4.0ms	(-.f64 x (.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))))

series263.0ms (4%)

Counts

4 → 12

Calls

4 calls:

131.0ms	(-.f64 x (.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))))
73.0ms	(.f64 (-.f64 y z) (.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1))))
40.0ms	(*.f64 a (/.f64 1 (+.f64 (-.f64 t z) 1)))
20.0ms	(/.f64 1 (+.f64 (-.f64 t z) 1))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5092	2155

prune125.0ms (1.9%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	141	0	141
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	141	6	147

Error

Counts

147 → 6

Compiler

Compiled 2718 to 1347 computations (50.4% saved)

regimes696.0ms (10.5%)

Accuracy

Total 0.3b remaining (100%)

Threshold costs 0.3b (100%)

Compiler

Compiled 9387 to 6707 computations (28.6% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	164	19
1	164	19

end0.0ms (0%)

sample1.6s (24.2%)

Algorithm

1×

intervals

Results

343.0ms	7999×	body	128	valid
21.0ms	511×	body	128	invalid
0.0ms	1×	body	256	valid

Compiler

Compiled 1345 to 965 computations (28.3% saved)

Details

analyze1.1s (15.9%)

sample23.0ms (0.3%)

simplify189.0ms (2.8%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite111.0ms (1.7%)

series300.0ms (4.5%)

simplify121.0ms (1.8%)

prune321.0ms (4.8%)

localize12.0ms (0.2%)

rewrite41.0ms (0.6%)

series325.0ms (4.9%)

simplify70.0ms (1%)

prune116.0ms (1.8%)

localize14.0ms (0.2%)

rewrite104.0ms (1.6%)

series593.0ms (8.9%)

simplify143.0ms (2.2%)

prune250.0ms (3.8%)

localize11.0ms (0.2%)

rewrite56.0ms (0.8%)

series263.0ms (4%)

simplify67.0ms (1%)

prune125.0ms (1.9%)

regimes696.0ms (10.5%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.6s (24.2%)

Profiling