Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	251×	body	80	valid
2.0ms	20×	body	640	valid
2.0ms	12×	body	1280	valid
1.0ms	8×	body	320	valid
0.0ms	7×	body	160	valid
0.0ms	1×	body	2560	valid

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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: 12.0b

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y z) (- a z))
3.8b	(fma (/ (- y z) (- a z)) (- t x) x)

rewrite14.0ms

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)

series180.0ms

Counts

2 → 6

Calls

2 calls:

55.0ms	(/ (- y z) (- a z))
125.0ms	(fma (/ (- y z) (- a z)) (- t x) x)

simplify76.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (69.0ms)

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

prune242.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.1b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- y z) (/ 1 (- a z)))
6.5b	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

5.0ms	(/ 1 (- a z))
23.0ms	(* (- y z) (/ 1 (- a z)))
0.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

series230.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(/ 1 (- a z))
60.0ms	(* (- y z) (/ 1 (- a z)))
132.0ms	(fma (* (- y z) (/ 1 (- a z))) (- t x) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	340	602
1	1472	525
2	5002	481

prune323.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y z) (- a z))
2.5b	(+ (* (- t x) (/ (- y z) (- a z))) x)
3.1b	(* (- t x) (/ (- y z) (- a z)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 126

Calls

3 calls:

12.0ms	(/ (- y z) (- a z))
11.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
34.0ms	(* (- t x) (/ (- y z) (- a z)))

series357.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- y z) (- a z))
170.0ms	(+ (* (- t x) (/ (- y z) (- a z))) x)
131.0ms	(* (- t x) (/ (- y z) (- a z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	490	904
1	2053	854
2	5001	852

prune413.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- a z))
0.5b	(* (cbrt (- a z)) (cbrt (- a z)))
1.5b	(* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z))))
8.4b	(+ (* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) x)

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

96×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
60×	`cbrt-prod`
54×	`associate-r`
52×	`times-frac`
34×	`add-cube-cbrt`
28×	`cbrt-div`
27×	`add-exp-log`
25×	`associate-l`
21×	`distribute-lft-out--`
19×	`difference-of-squares`
18×	`add-cbrt-cube`
14×	`flip3--` `flip--`
13×	`pow1`
10×	`swap-sqr` `associate-/r/` `unswap-sqr`
9×	`frac-times` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `pow1/3` `div-exp`
6×	`add-log-exp`
5×	`associate-r/` `associate-l/`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-prod-down`
2×	`pow-sqr` `*-commutative` `pow-prod-up` `div-inv`
1×	`+-commutative` `pow2` `fma-def` `flip3-+` `pow-plus` `sum-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

2.0ms	(cbrt (- a z))
19.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
80.0ms	(* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z))))
35.0ms	(+ (* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) x)

series679.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(cbrt (- a z))
134.0ms	(* (cbrt (- a z)) (cbrt (- a z)))
217.0ms	(* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z))))
163.0ms	(+ (* (/ (- t x) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- y z) (cbrt (- a z)))) x)

simplify145.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	863	2256
1	4235	2059
2	5001	1993

prune719.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.0b

regimes431.0ms

Accuracy

-4.7% (8.8b remaining)

Error of 12.5b against oracle of 3.7b and baseline of 12.1b

bsearch83.0ms

Steps

Iters	Range		Point
6	2.01645319072261e+30	2.864590415848179e+31	2.8040339380969858e+31
7	-1.9594404634135636e+187	-1.3995413679850284e+185	-1.0538724122977772e+187

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	16
1	26	16

end0.0ms

sample703.0ms

Algorithm

intervals

Results

264.0ms	7714×	body	80	valid
60.0ms	478×	body	640	valid
47.0ms	286×	body	1280	valid
38.0ms	417×	body	320	valid
18.0ms	287×	body	160	valid
3.0ms	14×	body	2560	valid