Details

sample39.0ms

Algorithm

intervals

Results

14.0ms	224×	body	80	valid
4.0ms	17×	body	640	valid
4.0ms	12×	body	1280	valid
3.0ms	14×	body	320	valid
1.0ms	7×	body	160	valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (15.0ms)

Iter	Nodes	Cost
0	22	6
1	52	6
2	111	6
3	213	6
4	517	5
5	1051	5
6	2055	5
7	3280	5
8	5002	5

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.1b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
13.6b	(fma (/ y (- a t)) (- t z) (+ x y))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 49

Calls

2 calls:

5.0ms	(/ y (- a t))
0.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

series113.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(/ y (- a t))
83.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify50.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	170	278
1	468	257
2	1400	257
3	5002	257

prune192.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ y (- a t))
3.7b	(+ (* (/ y (- a t)) (- t z)) (+ x y))
9.9b	(* (/ y (- a t)) (- t z))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 157

Calls

3 calls:

5.0ms	(/ y (- a t))
18.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
29.0ms	(* (/ y (- a t)) (- t z))

series298.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ y (- a t))
105.0ms	(+ (* (/ y (- a t)) (- t z)) (+ x y))
164.0ms	(* (/ y (- a t)) (- t z))

simplify108.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	859	1392
1	4016	1146
2	5001	1146

prune598.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
1.7b	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
2.5b	(* (/ (cbrt y) (- a t)) (- t z))
10.0b	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

rewrite153.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-sqr-sqrt`
99×	`distribute-rgt-in` `*-un-lft-identity` `distribute-lft-in`
90×	`prod-diff`
85×	`add-cube-cbrt`
66×	`add-exp-log`
44×	`associate-+l+`
43×	`associate-l`
35×	`times-frac` `add-cbrt-cube`
33×	`prod-exp`
29×	`frac-times` `associate-*r/`
22×	`frac-add`
20×	`cbrt-unprod`
19×	`cbrt-prod`
18×	`div-exp`
15×	`flip3--` `flip--`
12×	`flip3-+` `flip-+`
11×	`pow1`
10×	`cbrt-undiv` `sub-neg` `associate-*l/`
9×	`add-log-exp`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`1-exp` `associate-r`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u`
3×	`sum-log` `unswap-sqr`
2×	`associate-/r/` `*-commutative` `div-inv`
1×	`+-commutative` `associate-+r+` `fma-def` `pow1/3`

Counts

4 → 280

Calls

4 calls:

1.0ms	(cbrt y)
49.0ms	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
32.0ms	(* (/ (cbrt y) (- a t)) (- t z))
55.0ms	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

192.0ms	(cbrt y)
188.0ms	(* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)))
510.0ms	(* (/ (cbrt y) (- a t)) (- t z))
168.0ms	(+ (* (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z))) (+ x y))

simplify76.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (41.0ms)

Iter	Nodes	Cost
0	1731	4253
1	5002	3476

prune929.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 6.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt y)
0.5b	(cbrt y)
2.5b	(* (/ (cbrt y) (- a t)) (- t z))
13.0b	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
50×	`*-un-lft-identity`
36×	`add-cube-cbrt` `associate-l`
32×	`times-frac`
22×	`cbrt-prod`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
9×	`add-exp-log`
8×	`add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `sub-neg` `pow1/3` `associate-*r/` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `fma-udef` `div-inv`

Counts

4 → 122

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
31.0ms	(* (/ (cbrt y) (- a t)) (- t z))
1.0ms	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

series1.1s

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt y)
183.0ms	(cbrt y)
518.0ms	(* (/ (cbrt y) (- a t)) (- t z))
181.0ms	(fma (/ (* (cbrt y) (cbrt y)) 1) (* (/ (cbrt y) (- a t)) (- t z)) (+ x y))

simplify68.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	516	1106
1	2119	918
2	5002	906

prune492.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 6.8b

regimes450.0ms

Accuracy

-20.9% (6.4b remaining)

Error of 12.6b against oracle of 6.2b and baseline of 11.5b

bsearch138.0ms

Steps

Iters	Range		Point
9	-3.886584170193121e-264	-1.5055688256259804e-271	-1.7634254942085058e-264
9	-3.218864969602556e-138	-1.3035949753897318e-145	-6.35321437481323e-142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	24
1	32	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

493.0ms	7331×	body	80	valid
125.0ms	503×	body	640	valid
83.0ms	266×	body	1280	valid
71.0ms	388×	body	320	valid
30.0ms	224×	body	160	valid
10.0ms	28×	body	2560	valid