Details

sample29.0ms

Algorithm

intervals

Results

7.0ms	251×	body	80	valid
4.0ms	17×	body	640	valid
1.0ms	16×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	5×	body	160	valid

simplify65.0ms

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: 23.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- y z) (- t x))
2.1b	(+ x (/ (* (- y z) (- t x)) (- a z)))
16.0b	(/ (* (- y z) (- t x)) (- a z))

rewrite94.0ms

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:

37.0ms	(* (- y z) (- t x))
24.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
31.0ms	(/ (* (- y z) (- t x)) (- a z))

series308.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (- y z) (- t x))
143.0ms	(+ x (/ (* (- y z) (- t x)) (- a z)))
129.0ms	(/ (* (- y z) (- t x)) (- a z))

simplify55.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (13.0ms)

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

prune251.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.8b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
8.5b	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

rewrite160.0ms

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:

5.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
136.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

series721.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(cbrt (- a z))
143.0ms	(cbrt (- a z))
292.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
144.0ms	(+ x (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))))

simplify97.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (76.0ms)

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

prune509.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.5b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
8.7b	(+ 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))))))

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
146.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
12.0ms	(+ 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))))))

series726.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(cbrt (- a z))
136.0ms	(cbrt (- a z))
294.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))
150.0ms	(+ 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))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	810	2470
1	3241	2130
2	5002	2090

prune583.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
4.0ms	(cbrt (- a z))
9.0ms	(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

series582.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(cbrt (- a z))
145.0ms	(cbrt (- a z))
139.0ms	(cbrt (- a z))
155.0ms	(+ x (* (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (* (cbrt (- t x)) (cbrt (- t x))) (cbrt (* (cbrt (- a z)) (cbrt (- a z))))))) (/ (cbrt (- t x)) (cbrt (cbrt (- a z))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	270	944
1	858	858
2	5001	849

prune397.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.8b

regimes429.0ms

Accuracy

13.9% (6.5b remaining)

Error of 11.0b against oracle of 4.5b and baseline of 12.1b

bsearch105.0ms

Steps

Iters	Range		Point
7	3.4988562344822614e-109	8.773359074032879e-108	1.2567640666857569e-108
10	-1.1939950611604269e-111	-4.619021105644525e-127	-7.943644488630814e-127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	56
1	53	56

end0.0ms

sample763.0ms

Algorithm

intervals

Results

233.0ms	7839×	body	80	valid
61.0ms	482×	body	640	valid
37.0ms	428×	body	320	valid
35.0ms	263×	body	1280	valid
13.0ms	245×	body	160	valid
1.0ms	9×	body	2560	valid