Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	261×	body	80	valid
1.0ms	7×	body	1280	valid
1.0ms	8×	body	640	valid
1.0ms	13×	body	160	valid
1.0ms	9×	body	320	valid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	23	6
1	46	5
2	128	5
3	362	5
4	1024	5
5	2296	5
6	5001	5

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
12.5b	(fma (- y z) (/ (- t x) (- a z)) 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	(/ (- t x) (- a z))
0.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

series141.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(/ (- t x) (- a z))
90.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (49.0ms)

Iter	Nodes	Cost
0	268	450
1	733	425
2	2490	423
3	5001	421

prune194.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.1b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
12.5b	(fma (- y z) (* (- t x) (/ 1 (- a z))) 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))
24.0ms	(* (- t x) (/ 1 (- a z)))
0.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

series172.0ms

Counts

3 → 9

Calls

3 calls:

33.0ms	(/ 1 (- a z))
50.0ms	(* (- t x) (/ 1 (- a z)))
89.0ms	(fma (- y z) (* (- t x) (/ 1 (- a z))) x)

simplify41.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	350	602
1	1497	525
2	5001	481

prune253.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
3.5b	(+ (* (- y z) (/ (- t x) (- a z))) x)
6.3b	(* (- y z) (/ (- t x) (- a z)))

rewrite61.0ms

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

series325.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(/ (- t x) (- a z))
143.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
129.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify54.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	489	904
1	2048	854
2	5001	852

prune319.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (- a z))
0.2b	(* (- t x) (/ 1 (- a z)))
4.7b	(+ (* (- y z) (* (- t x) (/ 1 (- a z)))) x)
6.3b	(* (- y z) (* (- t x) (/ 1 (- a z))))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
32×	`add-exp-log` `times-frac`
25×	`add-cube-cbrt`
22×	`associate-r`
20×	`frac-times` `add-cbrt-cube`
17×	`flip3--` `flip--`
13×	`prod-exp`
12×	`pow1`
10×	`associate-r/` `associate-l` `associate-l/`
9×	`distribute-lft-out--` `difference-of-squares`
7×	`cbrt-unprod`
6×	`div-exp` `add-log-exp`
5×	`associate-/r*`
4×	`expm1-log1p-u` `pow-prod-down` `associate-/r/` `un-div-inv` `log1p-expm1-u`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/l*` `unswap-sqr`
2×	`*-commutative` `div-inv`
1×	`+-commutative` `pow-flip` `fma-def` `frac-2neg` `flip3-+` `clear-num` `sum-log` `flip-+` `inv-pow`

Counts

4 → 155

Calls

4 calls:

6.0ms	(/ 1 (- a z))
24.0ms	(* (- t x) (/ 1 (- a z)))
30.0ms	(+ (* (- y z) (* (- t x) (/ 1 (- a z)))) x)
33.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

series360.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ 1 (- a z))
52.0ms	(* (- t x) (/ 1 (- a z)))
144.0ms	(+ (* (- y z) (* (- t x) (/ 1 (- a z)))) x)
131.0ms	(* (- y z) (* (- t x) (/ 1 (- a z))))

simplify76.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	603	1066
1	2849	944
2	5001	896

prune361.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 1.8b

regimes289.0ms

Accuracy

29.4% (7.9b remaining)

Error of 11.5b against oracle of 3.6b and baseline of 14.8b

bsearch85.0ms

Steps

Iters	Range		Point
7	4.7984808710320545e-62	9.016433913032716e-60	5.374092198457196e-62
8	-6.189772840165046e-111	-1.035467125624471e-113	-1.0923027359928953e-112

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	17
1	31	17

end0.0ms

sample693.0ms

Algorithm

intervals

Results

251.0ms	7822×	body	80	valid
58.0ms	477×	body	640	valid
39.0ms	449×	body	320	valid
38.0ms	223×	body	1280	valid
17.0ms	290×	body	160	valid
4.0ms	20×	body	2560	valid