Details

analyze1.0s

Algorithm: search

sample35.0ms

Algorithm

intervals

Results

13.0ms	215×	body	80	valid
2.0ms	10×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	34×	body	80	invalid
1.0ms	10×	body	320	valid
1.0ms	8×	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

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: 23.1b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.5b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.4b	(/ (* (- y z) (- t x)) (- a z))

rewrite31.0ms

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:

9.0ms	(* (- y z) (- t x))
7.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series98.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(* (- y z) (- t x))
49.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
39.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (14.0ms)

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

prune156.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	12	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	12	91

Merged error: 3.3b

Counts

91 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
2.1b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
5.9b	(+ 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))
38.0ms	(* (/ (- 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))))
54.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify88.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (71.0ms)

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

prune191.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	144	14	158

Merged error: 3.3b

Counts

158 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
1.2b	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.7b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

73×	`add-exp-log`
35×	`add-cbrt-cube`
32×	`prod-exp` `cbrt-unprod`
22×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 103

Calls

4 calls:

3.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
35.0ms	(* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series161.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify76.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	660	2073
1	2511	1620
2	5001	1460

prune156.0ms

Filtered

68 candidates to 115 candidates (-69.1%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	114	15	129

Merged error: 3.3b

Counts

129 → 15

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- y z))
0.6b	(cbrt (- y z))
1.2b	(* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
6.9b	(+ x (* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

144×	`add-exp-log`
75×	`prod-exp` `cbrt-unprod`
59×	`add-cbrt-cube`
40×	`cbrt-undiv` `div-exp`
15×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity`
14×	`associate-l`
9×	`pow1` `add-cube-cbrt`
8×	`times-frac`
6×	`cbrt-div` `add-log-exp`
5×	`frac-times` `associate-*r/`
3×	`flip3--` `pow-prod-down` `associate-*l/` `flip--` `distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `associate-/r/`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 123

Calls

4 calls:

3.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
49.0ms	(* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
3.0ms	(+ x (* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

series165.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt (- y z))
26.0ms	(cbrt (- y z))
58.0ms	(* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z)))))
55.0ms	(+ x (* (/ (* (cbrt (- y z)) (* (* (cbrt (cbrt (- y z))) (cbrt (cbrt (- y z)))) (cbrt (cbrt (- y z))))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify106.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	840	3804
1	3429	2634
2	5001	2370

prune105.0ms

Filtered

70 candidates to 135 candidates (-92.9%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	12	12
Picked	0	1	1
Done	0	2	2
Total	135	15	150

Merged error: 3.3b

Counts

150 → 15

regimes655.0ms

Accuracy

13.2% (6.9b remaining)

Error of 11.1b against oracle of 4.2b and baseline of 12.1b

bsearch3.1s

Steps

Iters	Range		Point
10	4.277475726627804e-180	1.0071747384695459e-166	1.0834295989137173e-174
8	-3.059442713782889e-74	-3.195136720024306e-77	-3.295126587692333e-77

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	40
1	39	40

end0.0ms

analyze1.0s

Algorithm: search

sample804.0ms

Algorithm

intervals

Results

265.0ms	6572×	body	80	valid
76.0ms	480×	body	640	valid
54.0ms	269×	body	1280	valid
51.0ms	1232×	body	80	invalid
45.0ms	407×	body	320	valid
19.0ms	253×	body	160	valid
4.0ms	19×	body	2560	valid

Details

analyze1.0s

sample35.0ms

simplify67.0ms

prune5.0ms

localize9.0ms

rewrite31.0ms

series98.0ms

simplify59.0ms

prune156.0ms

localize13.0ms

rewrite54.0ms

series162.0ms

simplify88.0ms

prune191.0ms

localize19.0ms

rewrite49.0ms

series161.0ms

simplify76.0ms

prune156.0ms

localize22.0ms

rewrite66.0ms

series165.0ms

simplify106.0ms

prune105.0ms

regimes655.0ms

bsearch3.1s

simplify2.0ms

end0.0ms

analyze1.0s

sample804.0ms

Profiling