Details

analyze1.0s (13.2%)

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	18×	body	128	invalid

Compiler

Compiled 27 to 30 computations (-11.1% saved)

simplify168.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (162.0ms)

Iter	Nodes	Cost
0	4920	19
1	4920	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

Merged error: 2.2b

Counts

2 → 1

Compiler

Compiled 26 to 24 computations (7.7% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (+.f64 (-.f64 t z) 1) a)
0.0b	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
10.8b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))

rewrite124.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

417×	`*-un-lft-identity_binary64`
373×	`times-frac_binary64`
239×	`add-sqr-sqrt_binary64`
152×	`add-cube-cbrt_binary64`
100×	`cancel-sign-sub-inv_binary64`
77×	`distribute-lft-out--_binary64`
74×	`distribute-lft-out_binary64`
42×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
14×	`div-inv_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate--r-_binary64` `associate-+l-_binary64` `flip-+_binary64`

Counts

3 → 291

Calls

3 calls:

47.0ms	(-.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))
10.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

series641.0ms (8%)

Counts

3 → 9

Calls

3 calls:

306.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a))
281.0ms	(-.f64 x (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) a)))
53.0ms	(/.f64 (+.f64 (-.f64 t z) 1) a)

simplify113.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

300 → 300

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5472	8521

prune766.0ms (9.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	296	4	300
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	296	5	301

Merged error: 0b

Counts

301 → 5

Compiler

Compiled 16896 to 9450 computations (44.1% saved)

localize10.0ms (0.1%)

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))
1.3b	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64`
54×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
27×	`add-cube-cbrt_binary64`
22×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64`
11×	`difference-of-squares_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
4×	`associate-/r/_binary64`
3×	`associate-r_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

3 → 114

Calls

3 calls:

19.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
15.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))
4.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))

series683.0ms (8.6%)

Counts

3 → 9

Calls

3 calls:

306.0ms	(*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a)
276.0ms	(-.f64 x (*.f64 (/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1)) a))
101.0ms	(/.f64 (-.f64 y z) (+.f64 (-.f64 t z) 1))

simplify66.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5944	2442

prune136.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	2	1	3
Picked	0	1	1
Done	1	0	1
Total	124	4	128

Merged error: 0b

Counts

128 → 4

Compiler

Compiled 2984 to 1471 computations (50.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
0.0b	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))
0.1b	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
1.3b	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)

rewrite127.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

447×	`*-un-lft-identity_binary64`
392×	`times-frac_binary64`
254×	`add-sqr-sqrt_binary64`
158×	`add-cube-cbrt_binary64`
98×	`associate-l_binary64`
82×	`distribute-lft-out_binary64` `distribute-lft-out--_binary64`
41×	`difference-of-squares_binary64`
36×	`associate-/r*_binary64`
28×	`add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`associate-/r/_binary64`
10×	`div-inv_binary64`
9×	`flip3--_binary64` `div-exp_binary64` `flip--_binary64`
8×	`associate-/l*_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64`
6×	`add-log-exp_binary64`
5×	`unswap-sqr_binary64` `prod-exp_binary64`
4×	`rec-exp_binary64`
3×	`cbrt-unprod_binary64` `associate-r_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `div-sub_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 334

Calls

4 calls:

34.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)
18.0ms	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
13.0ms	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))
4.0ms	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))

series780.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

309.0ms	(-.f64 x (*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a))
230.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))) a)
143.0ms	(/.f64 1 (/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z)))
97.0ms	(/.f64 (+.f64 (-.f64 t z) 1) (-.f64 y z))

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5704	7839

prune402.0ms (5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	346	0	346
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	346	4	350

Merged error: 0b

Counts

350 → 4

Compiler

Compiled 8620 to 4144 computations (51.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 a)
0.5b	(cbrt.f64 a)
0.7b	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
4.9b	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))

rewrite191.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

731×	`*-un-lft-identity_binary64`
675×	`times-frac_binary64`
410×	`add-sqr-sqrt_binary64`
263×	`add-cube-cbrt_binary64`
175×	`associate-r_binary64`
172×	`cbrt-prod_binary64`
135×	`distribute-lft-out--_binary64`
132×	`distribute-lft-out_binary64`
69×	`difference-of-squares_binary64`
34×	`associate-/r*_binary64`
30×	`add-exp-log_binary64`
21×	`add-cbrt-cube_binary64`
13×	`div-inv_binary64`
9×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`pow-prod-down_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64` `associate-/r/_binary64`
1×	`flip3--_binary64` `associate-r/_binary64` `associate-l_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 452

Calls

4 calls:

70.0ms	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
22.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)

series870.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

316.0ms	(/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a)))
243.0ms	(.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (/.f64 (-.f64 y z) (/.f64 (+.f64 (-.f64 t z) 1) (cbrt.f64 a))))
157.0ms	(cbrt.f64 a)
154.0ms	(cbrt.f64 a)

simplify134.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

464 → 464

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5010	12991

prune642.0ms (8.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	464	0	464
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	464	4	468

Merged error: 0b

Counts

468 → 4

Compiler

Compiled 14318 to 5239 computations (63.4% saved)

regimes64.0ms (0.8%)

Compiler: Compiled 315 to 315 computations (0% saved)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	134	19
1	134	19

end0.0ms (0%)

sample764.0ms (9.6%)

Algorithm

1×

intervals

Results

348.0ms	7997×	body	128	valid
19.0ms	460×	body	128	invalid
0.0ms	3×	body	1024	valid

Compiler

Compiled 101 to 95 computations (5.9% saved)

Details

analyze1.0s (13.2%)

sample23.0ms (0.3%)

simplify168.0ms (2.1%)

prune2.0ms (0%)

localize15.0ms (0.2%)

rewrite124.0ms (1.6%)

series641.0ms (8%)

simplify113.0ms (1.4%)

prune766.0ms (9.6%)

localize10.0ms (0.1%)

rewrite50.0ms (0.6%)

series683.0ms (8.6%)

simplify66.0ms (0.8%)

prune136.0ms (1.7%)

localize13.0ms (0.2%)

rewrite127.0ms (1.6%)

series780.0ms (9.8%)

simplify120.0ms (1.5%)

prune402.0ms (5%)

localize14.0ms (0.2%)

rewrite191.0ms (2.4%)

series870.0ms (10.9%)

simplify134.0ms (1.7%)

prune642.0ms (8.1%)

regimes64.0ms (0.8%)

bsearch0.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample764.0ms (9.6%)

Profiling