Details

sample48.0ms

Algorithm

intervals

Results

9.0ms	234×	body	80	valid
2.0ms	13×	body	1280	valid
1.0ms	10×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	13×	body	160	valid

simplify62.0ms

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

prune4.0ms

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: 23.6b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.7b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.3b	(/ (* (- y z) (- t x)) (- a z))

rewrite32.0ms

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))

series96.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
51.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify51.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune141.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 2.9b

Counts

91 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.2b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.6b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite52.0ms

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)))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- a z))
25.0ms	(cbrt (- a z))
57.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
54.0ms	(+ 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 (68.0ms)

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

prune184.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	143	3	146
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	144	11	155

Merged error: 2.9b

Counts

155 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

2.6b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
2.6b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
2.6b	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
9.3b	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-div`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cbrt-prod` `frac-times` `pow1/3` `associate-r/` `associate-l/`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 47

Calls

4 calls:

24.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
20.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
20.0ms	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

series6.1s

Counts

4 → 12

Calls

4 calls:

2.0s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
2.1s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
2.0s	(cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))
53.0ms	(+ x (* (* (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))) (cbrt (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))))

simplify82.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 3 (71.0ms)

Iter	Nodes	Cost
0	225	1417
1	644	1158
2	2826	963
3	5002	921

prune129.0ms

Filtered

57 candidates to 59 candidates (-3.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	58	12	70

Merged error: 2.8b

Counts

70 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.8b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.1b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
98×	`times-frac`
84×	`cbrt-prod`
74×	`*-un-lft-identity`
69×	`add-exp-log`
61×	`associate-r`
44×	`cbrt-div`
42×	`add-cbrt-cube`
36×	`add-cube-cbrt`
29×	`associate-l`
27×	`cbrt-undiv` `div-exp`
24×	`prod-exp` `cbrt-unprod`
19×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-/r/`
15×	`flip3--` `flip--`
12×	`unswap-sqr`
9×	`frac-times`
6×	`pow1` `add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`div-inv`
2×	`pow1/3`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 183

Calls

4 calls:

3.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
64.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (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 (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

series169.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
27.0ms	(cbrt (- a z))
59.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
57.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1139	4158
1	5001	3690

prune206.0ms

Filtered

147 candidates to 195 candidates (-32.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	195	12	207

Merged error: 2.8b

Counts

207 → 12

regimes561.0ms

Accuracy

26.4% (7.1b remaining)

Error of 10.6b against oracle of 3.4b and baseline of 13.1b

bsearch59.0ms

Steps

Iters	Range		Point
10	1.4775817241464269e+144	3.135577897946779e+162	7.70695134579329e+159
8	-1.9625633189006593e+193	-1.8182700245817008e+189	-5.122786243344427e+190

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	47
1	36	47

end0.0ms

sample906.0ms

Algorithm

intervals

Results

310.0ms	7759×	body	80	valid
73.0ms	517×	body	640	valid
48.0ms	421×	body	320	valid
46.0ms	254×	body	1280	valid
26.0ms	288×	body	160	valid
4.0ms	17×	body	2560	valid

Details

sample48.0ms

simplify62.0ms

prune4.0ms

localize9.0ms

rewrite32.0ms

series96.0ms

simplify51.0ms

prune141.0ms

localize13.0ms

rewrite52.0ms

series163.0ms

simplify85.0ms

prune184.0ms

localize22.0ms

rewrite67.0ms

series6.1s

simplify82.0ms

prune129.0ms

localize17.0ms

rewrite86.0ms

series169.0ms

simplify62.0ms

prune206.0ms

regimes561.0ms

bsearch59.0ms

simplify2.0ms

end0.0ms

sample906.0ms

Profiling