Details

sample891.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 87.5%

Results

10.0ms	247×	body	80	valid
3.0ms	21×	body	640	valid
2.0ms	13×	body	1280	valid
1.0ms	13×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	1×	body	2560	valid

simplify63.0ms

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: 26.2b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.4b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.3b	(/ (* (- y z) (- t x)) (- a z))

rewrite33.0ms

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:

11.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series96.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(* (- y z) (- t x))
52.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
35.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify53.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

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

prune154.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	79	11	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	11	91

Merged error: 5.4b

Counts

91 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.0b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
9.9b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite54.0ms

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))
37.0ms	(* (/ (- 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)))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
26.0ms	(cbrt (- a z))
56.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
53.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify90.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (73.0ms)

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

prune201.0ms

Filtered

104 candidates to 146 candidates (-40.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	139	7	146
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	143	14	157

Merged error: 5.4b

Counts

157 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (cbrt (- a z)))
1.7b	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
9.7b	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

rewrite120.0ms

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))
3.0ms	(cbrt (cbrt (- a z)))
94.0ms	(* (/ (/ (- 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))))))

series162.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- a z))
26.0ms	(cbrt (cbrt (- a z)))
56.0ms	(* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))
54.0ms	(+ x (* (/ (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))

simplify67.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1414	5018
1	5001	4777

prune350.0ms

Filtered

204 candidates to 245 candidates (-20.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	241	4	245
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	242	17	259

Merged error: 5.4b

Counts

259 → 17

localize26.0ms

Local error

Found 4 expressions with local error:

0.9b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
0.9b	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
1.1b	(* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))
9.4b	(+ x (* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

114×	`add-exp-log`
55×	`prod-exp`
45×	`add-cbrt-cube`
40×	`div-exp`
34×	`cbrt-prod`
32×	`cbrt-unprod`
26×	`cbrt-div`
22×	`cbrt-undiv`
16×	`associate-/r/`
14×	`add-sqr-sqrt` `*-un-lft-identity`
13×	`frac-times` `times-frac`
12×	`flip3--` `flip--`
10×	`add-cube-cbrt` `1-exp`
9×	`pow1` `associate-*r/`
7×	`associate-l` `associate-*l/`
6×	`add-log-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow1/3` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 128

Calls

4 calls:

12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
12.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
47.0ms	(* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))
3.0ms	(+ x (* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

series305.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
101.0ms	(cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))
57.0ms	(* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z))))))
55.0ms	(+ x (* (/ (* (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))))) 1) (* (/ (cbrt (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z))))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))) (/ (- t x) (cbrt (cbrt (- a z)))))))

simplify105.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	868	4675
1	3589	3599
2	5001	3076

prune139.0ms

Filtered

79 candidates to 140 candidates (-77.2%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	137	3	140
Fresh	2	13	15
Picked	1	0	1
Done	0	1	1
Total	140	17	157

Merged error: 5.4b

Counts

157 → 17

regimes711.0ms

Accuracy

18.7% (6.8b remaining)

Error of 11.2b against oracle of 4.4b and baseline of 12.8b

bsearch58.0ms

Steps

Iters	Range		Point
7	7.045185189784851e-112	3.910278412756505e-110	8.963349915107015e-112
9	-7.103448313937228e-86	-3.854185619732895e-94	-4.629200930946342e-92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	27
1	37	27

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 87.5%

Results

316.0ms	7728×	body	80	valid
76.0ms	491×	body	640	valid
55.0ms	278×	body	1280	valid
50.0ms	421×	body	320	valid
25.0ms	293×	body	160	valid
3.0ms	14×	body	2560	valid

Details

sample891.0ms

simplify63.0ms

prune4.0ms

localize9.0ms

rewrite33.0ms

series96.0ms

simplify53.0ms

prune154.0ms

localize13.0ms

rewrite54.0ms

series162.0ms

simplify90.0ms

prune201.0ms

localize17.0ms

rewrite120.0ms

series162.0ms

simplify67.0ms

prune350.0ms

localize26.0ms

rewrite81.0ms

series305.0ms

simplify105.0ms

prune139.0ms

regimes711.0ms

bsearch58.0ms

simplify2.0ms

end0.0ms

sample1.8s

Profiling