Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	248×	body	80	valid
2.0ms	18×	body	320	valid
2.0ms	13×	body	640	valid
2.0ms	10×	body	1280	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	2560	valid

simplify64.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 22.8b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
1.6b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.1b	(/ (* (- 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:

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

series309.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(* (- y z) (- t x))
143.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
128.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify54.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (12.0ms)

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

prune390.0ms

Filtered

90 candidates to 67 candidates (74.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	8	91

Merged error: 4.3b

Counts

91 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.2b	(+ 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))
35.0ms	(* (/ (- 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)))))

series750.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
142.0ms	(cbrt (- a z))
311.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
152.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify87.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	744	1831
1	3287	1663
2	5001	1576

prune388.0ms

Filtered

146 candidates to 103 candidates (70.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	140	6	146
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	141	13	154

Merged error: 4.2b

Counts

154 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(cbrt (/ (- t x) (cbrt (- a z))))
1.4b	(cbrt (/ (- t x) (cbrt (- a z))))
1.4b	(cbrt (/ (- t x) (cbrt (- a z))))
9.0b	(+ 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))))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

213×	`cbrt-prod`
139×	`add-sqr-sqrt` `*-un-lft-identity`
120×	`times-frac`
61×	`add-cube-cbrt`
39×	`distribute-lft-out--` `difference-of-squares`
9×	`cbrt-div`
6×	`associate-/r/` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 176

Calls

4 calls:

8.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
9.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
8.0ms	(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))))))

series945.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
255.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
297.0ms	(cbrt (/ (- t x) (cbrt (- a z))))
150.0ms	(+ 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))))))

simplify65.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	474	2666
1	1142	2535
2	5001	2502

prune718.0ms

Filtered

188 candidates to 144 candidates (76.6%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	9	10
Picked	0	1	1
Done	1	1	2
Total	188	13	201

Merged error: 3.5b

Counts

201 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
8.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

146×	`cbrt-div`
83×	`cbrt-prod`
60×	`add-exp-log`
57×	`add-sqr-sqrt`
46×	`associate-r`
41×	`*-un-lft-identity`
40×	`flip3--` `flip--`
38×	`add-cbrt-cube`
37×	`frac-times`
34×	`associate-/r/`
28×	`associate-l`
26×	`prod-exp` `cbrt-unprod`
21×	`add-cube-cbrt`
19×	`associate-*l/`
17×	`cbrt-undiv` `div-exp`
13×	`pow1` `associate-*r/` `swap-sqr`
11×	`times-frac` `unswap-sqr`
9×	`distribute-lft-out--`
7×	`pow1/3` `difference-of-squares`
6×	`add-log-exp`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 186

Calls

4 calls:

3.0ms	(cbrt (- a z))
13.0ms	(* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))
49.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
3.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

series753.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(cbrt (- a z))
141.0ms	(* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z))))
308.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
151.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify128.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (96.0ms)

Iter	Nodes	Cost
0	1129	3641
1	4693	2904
2	5002	2848

prune615.0ms

Filtered

198 candidates to 135 candidates (68.2%)

Pruning

14 alts after pruning (11 fresh and 3 done)

	Pruned	Kept	Total
New	197	1	198
Fresh	0	10	10
Picked	0	1	1
Done	0	2	2
Total	197	14	211

Merged error: 3.5b

Counts

211 → 14

regimes400.0ms

Accuracy

23% (7.4b remaining)

Error of 10.6b against oracle of 3.2b and baseline of 12.9b

bsearch122.0ms

Steps

Iters	Range		Point
8	2.7754957924394407e-157	4.426179654126689e-153	4.1983362121842287e-156
10	-3.607687969514871e-118	-2.2872698318815147e-131	-2.948566510705687e-127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	53
1	42	53

end0.0ms

sample816.0ms

Algorithm

intervals

Results

318.0ms	7757×	body	80	valid
77.0ms	487×	body	640	valid
52.0ms	443×	body	320	valid
49.0ms	265×	body	1280	valid
20.0ms	267×	body	160	valid
3.0ms	11×	body	2560	valid

Details

sample32.0ms

simplify64.0ms

prune2.0ms

localize9.0ms

rewrite29.0ms

series309.0ms

simplify54.0ms

prune390.0ms

localize16.0ms

rewrite51.0ms

series750.0ms

simplify87.0ms

prune388.0ms

localize18.0ms

rewrite37.0ms

series945.0ms

simplify65.0ms

prune718.0ms

localize17.0ms

rewrite80.0ms

series753.0ms

simplify128.0ms

prune615.0ms

regimes400.0ms

bsearch122.0ms

simplify2.0ms

end0.0ms

sample816.0ms

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