Details

analyze222.0ms (4.8%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample17.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	16×	body	128	invalid

Compiler

Compiled 23 to 24 computations (-4.3% saved)

simplify97.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	111	16
1	111	16

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

5.3b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize144.0ms (3.1%)

Local error

Found 2 expressions with local error:

1.2b	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
5.0b	(.f64 y (+.f64 1 (.f64 z z)))

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64_9973`
26×	`add-exp-log_binary64_10005`
20×	`add-sqr-sqrt_binary64_9989`
18×	`add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
16×	`add-cbrt-cube_binary64_10003`
13×	`associate-/l*_binary64_9912`
12×	`div-exp_binary64_10018`
6×	`cbrt-undiv_binary64_10001`
5×	`prod-exp_binary64_10016`
4×	`associate-*r/_binary64_9909` `pow1_binary64_10028`
3×	`cbrt-unprod_binary64_10000` `associate-l_binary64_9908` `associate-r_binary64_9907` `div-inv_binary64_9964`
2×	`flip3-+_binary64_9970` `1-exp_binary64_10011` `rec-exp_binary64_10017` `flip-+_binary64_9941` `add-log-exp_binary64_10006` `associate-/r/_binary64_9913`
1×	`associate-/l/_binary64_9914` `distribute-lft-in_binary64_9916` `pow-prod-down_binary64_10038` `distribute-rgt-in_binary64_9917` `unswap-sqr_binary64_9935` `associate-/r_binary64_9911` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `-commutative_binary64_9898`

Counts

2 → 74

Calls

2 calls:

10.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
6.0ms	(.f64 y (+.f64 1 (.f64 z z)))

series88.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

50.0ms	(/.f64 (/.f64 1 x) (.f64 y (+.f64 1 (.f64 z z))))
37.0ms	(.f64 y (+.f64 1 (.f64 z z)))

simplify68.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5190	1317

prune96.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	71	9	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	9	81

Error

4.4b

Counts

81 → 9

Compiler

Compiled 1427 to 870 computations (39% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
1.2b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite47.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`add-exp-log_binary64_10005`
31×	`times-frac_binary64_9973`
30×	`add-cbrt-cube_binary64_10003`
28×	`sqrt-div_binary64_9984`
24×	`add-sqr-sqrt_binary64_9989`
22×	`add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
18×	`div-exp_binary64_10018`
16×	`associate-*r/_binary64_9909`
15×	`prod-exp_binary64_10016`
14×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
13×	`associate-/l*_binary64_9912`
11×	`pow1_binary64_10028`
9×	`cbrt-undiv_binary64_10001` `cbrt-unprod_binary64_10000` `sqrt-prod_binary64_9983`
8×	`frac-times_binary64_9977` `associate-/r/_binary64_9913`
6×	`associate-r_binary64_9907`
4×	`associate-*l/_binary64_9910` `add-log-exp_binary64_10006`
3×	`1-exp_binary64_10011` `rec-exp_binary64_10017` `pow-prod-down_binary64_10038` `div-inv_binary64_9964`
2×	`pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`
1×	`associate-l_binary64_9908` `associate-/l/_binary64_9914` `associate-/r_binary64_9911` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `-commutative_binary64_9898`

Counts

4 → 123

Calls

4 calls:

16.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
12.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series128.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z)))))
42.0ms	(.f64 (.f64 y (sqrt.f64 (+.f64 1 (.f64 z z)))) (sqrt.f64 (+.f64 1 (.f64 z z))))
17.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
16.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify96.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4955	2530
1	4955	2530

prune151.0ms (3.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	134	10	144

Error

4.4b

Counts

144 → 10

Compiler

Compiled 3033 to 1886 computations (37.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
1.0b	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))))
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite88.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`times-frac_binary64_9973`
145×	`add-exp-log_binary64_10005`
103×	`add-sqr-sqrt_binary64_9989`
84×	`associate-r_binary64_9907`
81×	`*-un-lft-identity_binary64_9967`
79×	`add-cube-cbrt_binary64_10002`
66×	`div-exp_binary64_10018`
53×	`prod-exp_binary64_10016`
48×	`sqrt-prod_binary64_9983`
45×	`add-cbrt-cube_binary64_10003`
19×	`1-exp_binary64_10011` `rec-exp_binary64_10017`
17×	`cbrt-undiv_binary64_10001`
13×	`cbrt-unprod_binary64_10000`
11×	`pow1_binary64_10028`
10×	`sqrt-div_binary64_9984`
9×	`associate-l_binary64_9908` `div-inv_binary64_9964`
7×	`unswap-sqr_binary64_9935`
6×	`associate-/r/_binary64_9913`
5×	`flip3-+_binary64_9970` `associate-*l/_binary64_9910` `flip-+_binary64_9941`
4×	`add-log-exp_binary64_10006`
3×	`associate-/l*_binary64_9912`
2×	`pow1/2_binary64_10047` `pow-prod-down_binary64_10038` `pow-flip_binary64_10041` `sqrt-pow1_binary64_9985` `rem-sqrt-square_binary64_9980`
1×	`frac-times_binary64_9977` `inv-pow_binary64_10052` `associate-/r_binary64_9911` `associate-r/_binary64_9909` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `*-commutative_binary64_9898`

Counts

4 → 216

Calls

4 calls:

43.0ms	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))))
7.0ms	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series120.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

44.0ms	(/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y))
40.0ms	(.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) (/.f64 (/.f64 1 x) (sqrt.f64 (+.f64 1 (.f64 z z)))))
18.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
17.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify111.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4935	5475
1	4935	5475

prune354.0ms (7.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	231	7	238

Error

4.4b

Counts

238 → 7

Compiler

Compiled 6076 to 3837 computations (36.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
2.9b	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))
18.5b	(sqrt.f64 (+.f64 1 (*.f64 z z)))

rewrite93.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

477×	`times-frac_binary64_9973`
202×	`add-sqr-sqrt_binary64_9989`
200×	`add-cube-cbrt_binary64_10002` `*-un-lft-identity_binary64_9967`
102×	`sqrt-prod_binary64_9983`
56×	`sqrt-div_binary64_9984`
52×	`associate-/r/_binary64_9913`
51×	`add-exp-log_binary64_10005`
50×	`associate-*l/_binary64_9910`
40×	`associate-/l*_binary64_9912`
34×	`div-inv_binary64_9964`
30×	`div-exp_binary64_10018`
28×	`flip3-+_binary64_9970` `flip-+_binary64_9941`
27×	`add-cbrt-cube_binary64_10003`
14×	`cbrt-undiv_binary64_10001`
9×	`associate-/r*_binary64_9911`
6×	`prod-exp_binary64_10016` `pow1_binary64_10028`
4×	`1-exp_binary64_10011` `rec-exp_binary64_10017` `add-log-exp_binary64_10006`
2×	`cbrt-unprod_binary64_10000` `associate-/l/_binary64_9914` `pow1/2_binary64_10047` `sqrt-pow1_binary64_9985` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `rem-sqrt-square_binary64_9980`

Counts

4 → 338

Calls

4 calls:

23.0ms	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
11.0ms	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
3.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

series122.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(/.f64 (/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x) (sqrt.f64 (+.f64 1 (*.f64 z z))))
41.0ms	(/.f64 (/.f64 1 (.f64 (sqrt.f64 (+.f64 1 (.f64 z z))) y)) x)
18.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))
17.0ms	(sqrt.f64 (+.f64 1 (*.f64 z z)))

simplify171.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

350 → 350

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4955	14073
1	4955	14073

prune629.0ms (13.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	349	1	350
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	350	7	357

Error

4.4b

Counts

357 → 7

Compiler

Compiled 11024 to 6461 computations (41.4% saved)

regimes529.0ms (11.4%)

Accuracy

Total 1.0b remaining (16.6%)

Threshold costs 0b (0%)

Compiler

Compiled 6411 to 5237 computations (18.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	29
1	15	29

end0.0ms (0%)

sample1.2s (26%)

Algorithm

1×

intervals

Results

291.0ms	8000×	body	128	valid
16.0ms	451×	body	128	invalid

Compiler

Compiled 833 to 672 computations (19.3% saved)

Details

analyze222.0ms (4.8%)

sample17.0ms (0.4%)

simplify97.0ms (2.1%)

prune2.0ms (0%)

localize144.0ms (3.1%)

rewrite22.0ms (0.5%)

series88.0ms (1.9%)

simplify68.0ms (1.5%)

prune96.0ms (2.1%)

localize11.0ms (0.2%)

rewrite47.0ms (1%)

series128.0ms (2.8%)

simplify96.0ms (2.1%)

prune151.0ms (3.3%)

localize10.0ms (0.2%)

rewrite88.0ms (1.9%)

series120.0ms (2.6%)

simplify111.0ms (2.4%)

prune354.0ms (7.6%)

localize9.0ms (0.2%)

rewrite93.0ms (2%)

series122.0ms (2.6%)

simplify171.0ms (3.7%)

prune629.0ms (13.6%)

regimes529.0ms (11.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (26%)

Profiling