Details

analyze1.1s

Algorithm: search

sample37.0ms

Algorithm

intervals

Results

10.0ms	221×	body	80	valid
2.0ms	51×	body	80	invalid
2.0ms	12×	body	640	valid
1.0ms	7×	body	1280	valid
1.0ms	10×	body	320	valid
0.0ms	6×	body	160	valid

simplify69.0ms

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: 25.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.9b	(+ x (/ (* (- y z) (- t x)) (- a z)))
19.5b	(/ (* (- 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:

10.0ms	(* (- y z) (- t x))
8.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
12.0ms	(/ (* (- y z) (- t x)) (- a z))

series98.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(* (- y z) (- t x))
49.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
38.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify56.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune147.0ms

Filtered

67 candidates to 90 candidates (-34.3%)

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: 2.8b

Counts

91 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
2.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.1b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

3.0ms	(cbrt (- a z))
10.0ms	(* (cbrt (- a z)) (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))
29.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
55.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
52.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify119.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (99.0ms)

Iter	Nodes	Cost
0	872	2188
1	4156	1999
2	5003	1875

prune225.0ms

Filtered

124 candidates to 187 candidates (-50.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	181	6	187
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	184	13	197

Merged error: 2.8b

Counts

197 → 13

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.9b	(* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z)))))
1.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
7.0b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

167×	`cbrt-prod`
144×	`add-exp-log`
110×	`associate-r`
108×	`add-sqr-sqrt`
104×	`times-frac`
98×	`*-un-lft-identity`
70×	`add-cbrt-cube`
65×	`prod-exp` `cbrt-unprod`
56×	`add-cube-cbrt`
46×	`cbrt-undiv` `div-exp`
38×	`cbrt-div`
21×	`distribute-lft-out--` `difference-of-squares`
18×	`associate-l` `associate-/r/`
14×	`frac-times` `flip3--` `flip--`
11×	`pow1`
10×	`associate-*l/`
8×	`associate-*r/`
6×	`add-log-exp` `unswap-sqr`
4×	`pow-prod-down`
3×	`div-inv`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `pow1/3` `sum-log` `flip-+`

Counts

4 → 247

Calls

4 calls:

3.0ms	(cbrt (- t x))
49.0ms	(* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z)))))
31.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt (- t x))
57.0ms	(* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z)))))
119.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
49.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z)))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

259 → 259

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1672	7303
1	5001	6394

prune331.0ms

Filtered

182 candidates to 259 candidates (-42.3%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	255	4	259
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	256	16	272

Merged error: 2.8b

Counts

272 → 16

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(cbrt (/ (- t x) (cbrt (- a z))))
1.5b	(cbrt (/ (- t x) (cbrt (- a z))))
1.6b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
6.8b	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

142×	`cbrt-prod`
100×	`add-sqr-sqrt`
98×	`*-un-lft-identity`
86×	`times-frac`
44×	`add-cube-cbrt`
27×	`distribute-lft-out--` `difference-of-squares`
26×	`cbrt-div`
25×	`add-exp-log`
17×	`associate-l`
15×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`prod-exp` `cbrt-unprod`
9×	`pow1` `frac-times`
8×	`flip3--` `flip--`
7×	`associate-*r/`
6×	`add-log-exp`
5×	`associate-*l/`
4×	`cbrt-undiv` `div-exp`
3×	`pow-prod-down` `div-inv`
2×	`pow1/3` `unswap-sqr`
1×	`+-commutative` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+`

Counts

4 → 170

Calls

4 calls:

8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
39.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
3.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

series294.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
61.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
118.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z))))))
56.0ms	(+ x (* (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (* (cbrt (/ (- t x) (cbrt (- a z)))) (cbrt (/ (- t x) (cbrt (- a z)))))) (cbrt (/ (- t x) (cbrt (- a z))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	917	3105
1	2688	2765
2	5003	2755

prune195.0ms

Filtered

133 candidates to 182 candidates (-36.8%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	15	15
Picked	0	1	1
Done	0	0	0
Total	182	16	198

Merged error: 2.8b

Counts

198 → 16

regimes709.0ms

Accuracy

23% (6.4b remaining)

Error of 11.0b against oracle of 4.7b and baseline of 12.9b

bsearch1.6s

Steps

Iters	Range		Point
8	1.8120069763927198e-114	1.0856639325883653e-109	8.18560712222055e-112
1	-1.5675819501968987e-115	-1.4908251174598294e-115	-1.5100143256440967e-115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	32
1	38	32

end0.0ms

analyze1.1s

Algorithm: search

sample841.0ms

Algorithm

intervals

Results

289.0ms	6530×	body	80	valid
87.0ms	505×	body	640	valid
54.0ms	258×	body	1280	valid
51.0ms	1237×	body	80	invalid
50.0ms	426×	body	320	valid
22.0ms	269×	body	160	valid
3.0ms	12×	body	2560	valid

Details

analyze1.1s

sample37.0ms

simplify69.0ms

prune5.0ms

localize10.0ms

rewrite32.0ms

series98.0ms

simplify56.0ms

prune147.0ms

localize14.0ms

rewrite62.0ms

series162.0ms

simplify119.0ms

prune225.0ms

localize26.0ms

rewrite102.0ms

series250.0ms

simplify93.0ms

prune331.0ms

localize20.0ms

rewrite68.0ms

series294.0ms

simplify90.0ms

prune195.0ms

regimes709.0ms

bsearch1.6s

simplify2.0ms

end0.0ms

analyze1.1s

sample841.0ms

Profiling