Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	249×	body	80	valid
3.0ms	12×	body	1280	valid
3.0ms	19×	body	320	valid
3.0ms	13×	body	640	valid
1.0ms	8×	body	160	valid
1.0ms	2×	body	2560	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.9b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.2b	(+ x (/ (* (- y z) (- t x)) (- a z)))
17.9b	(/ (* (- y z) (- t x)) (- a z))

rewrite46.0ms

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:

17.0ms	(* (- y z) (- t x))
10.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.0ms	(/ (* (- y z) (- t x)) (- a z))

series310.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* (- y z) (- t x))
149.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
127.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify61.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (14.0ms)

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

prune245.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
10.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite92.0ms

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:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
79.0ms	(* (/ (- 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)))))

series767.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(cbrt (- a z))
150.0ms	(cbrt (- a z))
307.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify93.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (77.0ms)

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

prune466.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
3.9b	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

2.0ms	(cbrt (- a z))
2.0ms	(cbrt (- a z))
2.0ms	(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))))))

series607.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt (- a z))
148.0ms	(cbrt (- a z))
154.0ms	(cbrt (- a z))
154.0ms	(+ x (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))))

simplify134.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 3 (126.0ms)

Iter	Nodes	Cost
0	262	689
1	810	633
2	4502	622
3	5003	616

prune339.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt (- a z)))
0.6b	(cbrt (cbrt (- a z)))
1.7b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
10.0b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

128×	`cbrt-div`
58×	`add-exp-log`
38×	`add-cbrt-cube`
35×	`flip3--` `associate-r` `flip--`
34×	`associate-/r/`
33×	`frac-times`
26×	`cbrt-prod`
25×	`prod-exp` `cbrt-unprod`
24×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp` `associate-l` `associate-*l/`
12×	`add-cube-cbrt`
11×	`times-frac` `associate-*r/`
6×	`pow1` `add-log-exp`
4×	`distribute-lft-out--` `difference-of-squares`
2×	`pow1/3` `div-inv` `unswap-sqr`
1×	`+-commutative` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 137

Calls

4 calls:

2.0ms	(cbrt (cbrt (- a z)))
2.0ms	(cbrt (cbrt (- a z)))
178.0ms	(* (/ (- 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)))))))

series776.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(cbrt (cbrt (- a z)))
153.0ms	(cbrt (cbrt (- a z)))
312.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z))))))
154.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (* (* (cbrt (cbrt (- a z))) (cbrt (cbrt (- a z)))) (cbrt (cbrt (- a z)))))))

simplify103.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	1015	3080
1	3968	2364
2	5002	2261

prune505.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.8b

regimes433.0ms

Accuracy

24.2% (6.6b remaining)

Error of 10.0b against oracle of 3.4b and baseline of 12.1b

bsearch121.0ms

Steps

Iters	Range		Point
9	2.271139247461068e+213	2.3771349098410096e+218	7.373442601062735e+217
7	-1.8002041532192927e+157	-1.5931363873182533e+155	-6.829204697610091e+155

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	36	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

489.0ms	7842×	body	80	valid
106.0ms	469×	body	640	valid
74.0ms	262×	body	1280	valid
73.0ms	411×	body	320	valid
31.0ms	267×	body	160	valid
6.0ms	18×	body	2560	valid