Details

sample38.0ms

Algorithm

intervals

Results

10.0ms	253×	body	80	valid
3.0ms	21×	body	640	valid
2.0ms	11×	body	1280	valid
1.0ms	8×	body	320	valid
1.0ms	7×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	111	6
3	288	6
4	714	6
5	1498	6
6	3410	6
7	5001	6

prune5.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 23.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.8b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.8b	(/ (* (- y z) (- t x)) (- a z))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`flip3--` `flip--`
10×	`add-exp-log` `add-cbrt-cube`
8×	`frac-times` `associate-/l/`
7×	`add-cube-cbrt`
5×	`pow1` `times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
4×	`associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `flip3-+` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+` `div-inv` `distribute-lft-out` `associate-/l` `unswap-sqr`

Counts

3 → 81

Calls

3 calls:

8.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
11.0ms	(/ (* (- y z) (- t x)) (- a z))

series94.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
49.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
36.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify52.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	466	583
1	2158	534
2	5001	534

prune456.0ms

Filtered

90 candidates to 67 candidates (25.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	10	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 4.0b

Counts

91 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(cbrt (- a z))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

75×	`add-sqr-sqrt`
59×	`*-un-lft-identity`
52×	`times-frac`
46×	`associate-r`
37×	`cbrt-prod`
27×	`add-cube-cbrt`
25×	`add-exp-log`
18×	`cbrt-div` `add-cbrt-cube`
17×	`associate-l`
16×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`flip3--` `flip--`
8×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `add-log-exp` `unswap-sqr`
5×	`frac-times`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 134

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
36.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series153.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
52.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
50.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify85.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	752	1839
1	3320	1671
2	5001	1580

prune1.0s

Filtered

146 candidates to 104 candidates (28.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	143	13	156

Merged error: 4.0b

Counts

156 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.6b	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
1.7b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
4.2b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

174×	`add-sqr-sqrt`
134×	`times-frac`
132×	`cbrt-prod`
122×	`*-un-lft-identity`
85×	`add-exp-log`
84×	`associate-l`
60×	`add-cube-cbrt`
47×	`associate-r`
41×	`add-cbrt-cube`
36×	`prod-exp` `cbrt-unprod`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-undiv` `div-exp`
15×	`unswap-sqr`
11×	`pow1`
8×	`cbrt-div`
6×	`frac-times` `associate-*r/` `associate-/r/` `add-log-exp`
4×	`flip3--` `pow-prod-down` `associate-*l/` `flip--`
3×	`div-inv`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+`

Counts

4 → 239

Calls

4 calls:

3.0ms	(cbrt (- y z))
59.0ms	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
32.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
5.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series499.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- y z))
367.0ms	(* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))
55.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
52.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

251 → 251

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1220	3991
1	4970	3474
2	5001	3474

prune3.6s

Filtered

251 candidates to 177 candidates (29.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	251	0	251
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	251	13	264

Merged error: 4.0b

Counts

264 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
2.5b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
8.6b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

182×	`times-frac`
167×	`add-sqr-sqrt`
123×	`cbrt-prod`
104×	`*-un-lft-identity`
80×	`associate-l`
78×	`cbrt-div`
61×	`associate-r`
60×	`add-cube-cbrt`
42×	`associate-/r/`
36×	`add-exp-log`
33×	`flip3--` `flip--`
22×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
21×	`frac-times`
20×	`unswap-sqr`
14×	`cbrt-undiv` `div-exp`
11×	`associate-r/` `associate-l/`
10×	`prod-exp` `cbrt-unprod`
6×	`pow1` `div-inv` `add-log-exp`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 233

Calls

4 calls:

3.0ms	(cbrt (- a z))
4.0ms	(cbrt (cbrt (- a z)))
87.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
3.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
27.0ms	(cbrt (cbrt (- a z)))
53.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
53.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1414	5022
1	5001	4781

prune4.0s

Filtered

245 candidates to 204 candidates (16.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	245	0	245
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	245	13	258

Merged error: 4.0b

Counts

258 → 13

regimes599.0ms

Accuracy

18.5% (6.7b remaining)

Error of 11.0b against oracle of 4.2b and baseline of 12.5b

bsearch119.0ms

Steps

Iters	Range		Point
7	4.1145120506979136e-106	1.220063346597708e-104	4.155912687798854e-106
8	-3.38764186627733e-237	-5.512570556209431e-240	-6.469423575567743e-238

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	47
1	45	47

end0.0ms

sample971.0ms

Algorithm

intervals

Results

307.0ms	7808×	body	80	valid
73.0ms	495×	body	640	valid
53.0ms	276×	body	1280	valid
47.0ms	423×	body	320	valid
19.0ms	255×	body	160	valid
3.0ms	15×	body	2560	valid

Details

sample38.0ms

simplify67.0ms

prune5.0ms

localize9.0ms

rewrite29.0ms

series94.0ms

simplify52.0ms

prune456.0ms

localize13.0ms

rewrite51.0ms

series153.0ms

simplify85.0ms

prune1.0s

localize16.0ms

rewrite112.0ms

series499.0ms

simplify128.0ms

prune3.6s

localize17.0ms

rewrite111.0ms

series159.0ms

simplify64.0ms

prune4.0s

regimes599.0ms

bsearch119.0ms

simplify2.0ms

end0.0ms

sample971.0ms

Profiling