Details

sample28.0ms

Algorithm

intervals

Results

7.0ms	248×	body	80	valid
2.0ms	23×	body	640	valid
1.0ms	11×	body	320	valid
1.0ms	6×	body	1280	valid
0.0ms	5×	body	160	valid

simplify52.0ms

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: 14.9b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- t x) (- a z))
15.0b	(fma (- y z) (/ (- t x) (- a z)) x)

rewrite27.0ms

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:

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

series127.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(/ (- t x) (- a z))
83.0ms	(fma (- y z) (/ (- t x) (- a z)) x)

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (52.0ms)

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

prune201.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.3b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- t x) (- a z))
1.6b	(+ (* (- y z) (/ (- t x) (- a z))) x)
5.7b	(* (- y z) (/ (- t x) (- a z)))

rewrite108.0ms

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:

24.0ms	(/ (- t x) (- a z))
22.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
57.0ms	(* (- y z) (/ (- t x) (- a z)))

series293.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(/ (- t x) (- a z))
133.0ms	(+ (* (- y z) (/ (- t x) (- a z))) x)
114.0ms	(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (46.0ms)

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

prune313.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- t x))
0.6b	(cbrt (- t x))
1.1b	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
7.3b	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

rewrite394.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`cbrt-div`
14×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-r`
10×	`cbrt-prod` `flip3--` `flip--`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `associate-/r/`
6×	`pow1` `frac-times` `add-log-exp`
5×	`associate-l`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-*l/` `log1p-expm1-u`
3×	`associate-*r/` `distribute-lft-out--` `difference-of-squares`
2×	`times-frac` `pow1/3` `unswap-sqr`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+` `div-inv`

Counts

4 → 94

Calls

4 calls:

4.0ms	(cbrt (- t x))
4.0ms	(cbrt (- t x))
98.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
286.0ms	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

series659.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(cbrt (- t x))
136.0ms	(cbrt (- t x))
258.0ms	(* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z)))))
133.0ms	(+ (* (* (- y z) (/ (* (cbrt (- t x)) (cbrt (- t x))) (* (cbrt (- a z)) (cbrt (- a z))))) (/ (cbrt (- t x)) (cbrt (- a z)))) x)

simplify75.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	704	1461
1	2717	1229
2	5001	1155

prune404.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a z))
0.6b	(cbrt (- a z))
1.9b	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
6.8b	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

rewrite205.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r/` `associate-l/`
2×	`pow1/3` `div-inv`
1×	`+-commutative` `fma-def` `flip3-+` `pow-prod-down` `sum-log` `*-commutative` `flip-+`

Counts

4 → 143

Calls

4 calls:

4.0ms	(cbrt (- a z))
5.0ms	(cbrt (- a z))
124.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
66.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

series700.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (- a z))
132.0ms	(cbrt (- a z))
275.0ms	(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
153.0ms	(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

simplify89.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	758	1907
1	3316	1731
2	5001	1632

prune444.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.0b

regimes240.0ms

Accuracy

-5.3% (9.3b remaining)

Error of 12.8b against oracle of 3.5b and baseline of 12.3b

bsearch87.0ms

Steps

Iters	Range		Point
9	2.4178810551420217e+40	2.2223676827457423e+47	2.4670226099090405e+40
7	-5.781079580069761e-276	-7.092039131285206e-278	-1.7965648978181715e-276

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	24
1	33	24

end0.0ms

sample797.0ms

Algorithm

intervals

Results

238.0ms	7739×	body	80	valid
52.0ms	500×	body	640	valid
37.0ms	427×	body	320	valid
35.0ms	268×	body	1280	valid
16.0ms	255×	body	160	valid
3.0ms	16×	body	2560	valid