Details

sample28.0ms

Algorithm

intervals

Results

8.0ms	249×	body	80	valid
2.0ms	16×	body	640	valid
2.0ms	18×	body	320	valid
1.0ms	7×	body	1280	valid
1.0ms	3×	body	2560	valid
0.0ms	7×	body	160	valid

simplify86.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1912	5
6	4581	5
7	5001	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.0b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

13.0ms	(/ (- y z) (- a z))
1.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series170.0ms

Counts

2 → 6

Calls

2 calls:

50.0ms	(/ (- y z) (- a z))
120.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify68.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (58.0ms)

Iter	Nodes	Cost
0	265	450
1	729	425
2	2562	423
3	5002	421

prune211.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
1.7b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.0b	(* (/ (- y z) (- a z)) (- t x))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

9.0ms	(/ (- y z) (- a z))
15.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
21.0ms	(* (/ (- y z) (- a z)) (- t x))

series554.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- y z) (- a z))
176.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
326.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify77.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	682	1497
1	2657	1254
2	5002	1252

prune456.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
7.4b	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`cbrt-prod`
13×	`add-sqr-sqrt` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
3.0ms	(cbrt (- a z))
1.0ms	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

series604.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (- a z))
157.0ms	(cbrt (- a z))
157.0ms	(cbrt (- a z))
131.0ms	(fma (* (/ 1 (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) (- t x) x)

simplify63.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (56.0ms)

Iter	Nodes	Cost
0	203	532
1	492	489
2	1845	471
3	5003	446

prune316.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- y z))
0.5b	(cbrt (- y z))
0.5b	(* (cbrt (- y z)) (cbrt (- y z)))
7.9b	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

38×	`cbrt-prod`
34×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
16×	`cbrt-div`
14×	`add-cube-cbrt`
11×	`pow1`
10×	`swap-sqr`
8×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `difference-of-squares`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 102

Calls

4 calls:

3.0ms	(cbrt (- y z))
3.0ms	(cbrt (- y z))
11.0ms	(* (cbrt (- y z)) (cbrt (- y z)))
1.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

series575.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(cbrt (- y z))
160.0ms	(cbrt (- y z))
134.0ms	(* (cbrt (- y z)) (cbrt (- y z)))
122.0ms	(fma (/ (* (cbrt (- y z)) (cbrt (- y z))) (/ (- a z) (cbrt (- y z)))) (- t x) x)

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	319	857
1	1120	800
2	5001	740

prune361.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

regimes284.0ms

Accuracy

29.1% (5.8b remaining)

Error of 9.6b against oracle of 3.8b and baseline of 12.0b

bsearch116.0ms

Steps

Iters	Range		Point
10	1.176759372882819e+209	3.6666096121381543e+223	1.0645799767702823e+217
9	-8.938305822997549e+218	-9.629133914723889e+209	-3.7669650291386463e+211

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	10
1	26	10

end0.0ms

sample720.0ms

Algorithm

intervals

Results

265.0ms	7715×	body	80	valid
70.0ms	544×	body	640	valid
42.0ms	254×	body	1280	valid
42.0ms	415×	body	320	valid
17.0ms	266×	body	160	valid
3.0ms	13×	body	2560	valid