Details

sample47.0ms

Algorithm

intervals

Results

22.0ms	247×	body	80	valid
5.0ms	17×	body	640	valid
3.0ms	9×	body	1280	valid
3.0ms	13×	body	320	valid
1.0ms	9×	body	160	valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

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: 11.4b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.9b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite15.0ms

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:

12.0ms	(/ (- y z) (- a z))
0.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

series177.0ms

Counts

2 → 6

Calls

2 calls:

53.0ms	(/ (- y z) (- a z))
124.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (63.0ms)

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

prune235.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.1b	(+ (* (/ (- y z) (- a z)) (- t x)) x)
2.4b	(* (/ (- y z) (- a z)) (- t x))

rewrite71.0ms

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:

12.0ms	(/ (- y z) (- a z))
14.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
38.0ms	(* (/ (- y z) (- a z)) (- t x))

series569.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(/ (- y z) (- a z))
191.0ms	(+ (* (/ (- y z) (- a z)) (- t x)) x)
327.0ms	(* (/ (- y z) (- a z)) (- t x))

simplify92.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (70.0ms)

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

prune539.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 4.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- y z) (- a z))
0.0b	(+ (* (/ (- y z) (- a z)) t) (fma (- x) (/ (- y z) (- a z)) x))
1.7b	(* (/ (- y z) (- a z)) t)
3.9b	(fma (- x) (/ (- y z) (- a z)) x)

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

12.0ms	(/ (- y z) (- a z))
12.0ms	(+ (* (/ (- y z) (- a z)) t) (fma (- x) (/ (- y z) (- a z)) x))
25.0ms	(* (/ (- y z) (- a z)) t)
0.0ms	(fma (- x) (/ (- y z) (- a z)) x)

series420.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- y z) (- a z))
175.0ms	(+ (* (/ (- y z) (- a z)) t) (fma (- x) (/ (- y z) (- a z)) x))
105.0ms	(* (/ (- y z) (- a z)) t)
83.0ms	(fma (- x) (/ (- y z) (- a z)) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	470	961
1	1512	902
2	5001	892

prune520.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt t)
0.9b	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
1.1b	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
3.9b	(fma (- x) (/ (- y z) (- a z)) x)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
34×	`add-exp-log`
32×	`associate-l`
26×	`times-frac`
21×	`add-cbrt-cube`
18×	`pow1` `add-cube-cbrt`
17×	`prod-exp` `cbrt-unprod`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow-prod-down`
7×	`associate-r`
6×	`cbrt-prod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`associate-*l/`
2×	`associate-/r/` `*-commutative` `unswap-sqr`
1×	`flip3--` `pow1/3` `flip--` `fma-udef` `div-inv`

Counts

4 → 109

Calls

4 calls:

1.0ms	(cbrt t)
58.0ms	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
36.0ms	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
0.0ms	(fma (- x) (/ (- y z) (- a z)) x)

series676.0ms

Counts

4 → 12

Calls

4 calls:

201.0ms	(cbrt t)
137.0ms	(* (* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t))) (cbrt t))
257.0ms	(* (/ (- y z) (- a z)) (* (cbrt t) (cbrt t)))
82.0ms	(fma (- x) (/ (- y z) (- a z)) x)

simplify70.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	443	1000
1	1813	740
2	5001	699

prune408.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 3.7b

regimes412.0ms

Accuracy

0.6% (4.8b remaining)

Error of 8.1b against oracle of 3.4b and baseline of 8.2b

bsearch154.0ms

Steps

Iters	Range		Point
9	2.183162487484932e-93	3.7249818277460274e-84	3.1595740263796063e-93
8	-1.0796147249493712e-202	-5.477954589394554e-207	-2.5046416024944056e-203

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms

sample1.3s

Algorithm

intervals

Results

691.0ms	7805×	body	80	valid
142.0ms	489×	body	640	valid
86.0ms	415×	body	320	valid
76.0ms	225×	body	1280	valid
43.0ms	288×	body	160	valid
6.0ms	16×	body	2560	valid