Details

sample24.0ms

Algorithm

intervals

Results

8.0ms	247×	body	80	valid
2.0ms	12×	body	1280	valid
1.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 4 (12.0ms)

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

prune8.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.4b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ y (- a t))
10.0b	(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))

series118.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(/ y (- a t))
83.0ms	(fma (/ y (- a t)) (- t z) (+ x y))

simplify43.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 1 (6.0ms)

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

prune181.0ms

Filtered

55 candidates to 43 candidates (78.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
0.6b	(/ 1 (/ (- a t) y))
9.9b	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

132×	`times-frac`
101×	`add-sqr-sqrt` `*-un-lft-identity`
69×	`add-cube-cbrt`
22×	`associate-/r*`
16×	`add-exp-log` `distribute-lft-out--` `difference-of-squares`
10×	`add-cbrt-cube`
8×	`div-exp` `associate-/l*`
6×	`div-inv`
4×	`pow1` `cbrt-undiv`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-/r/` `flip--` `fma-udef` `inv-pow`

Counts

3 → 152

Calls

3 calls:

9.0ms	(/ (- a t) y)
9.0ms	(/ 1 (/ (- a t) y))
0.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

series191.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ (- a t) y)
75.0ms	(/ 1 (/ (- a t) y))
89.0ms	(fma (/ 1 (/ (- a t) y)) (- t z) (+ x y))

simplify49.0ms

Algorithm

egg-herbie

Counts

161 → 161

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	466	1086
1	1950	958
2	5001	852

prune345.0ms

Filtered

161 candidates to 85 candidates (52.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.5b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- a t) y)
2.4b	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
8.9b	(/ (- t z) (/ (- a t) y))

rewrite144.0ms

Algorithm

rewrite-expression-head

Rules

370×	`times-frac`
309×	`*-un-lft-identity`
304×	`add-sqr-sqrt`
152×	`add-cube-cbrt`
100×	`fma-def`
76×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
14×	`div-inv`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
8×	`add-log-exp`
4×	`cbrt-undiv` `div-exp` `associate-/l/`
3×	`pow1` `expm1-log1p-u` `div-sub` `sum-log` `log1p-expm1-u` `distribute-lft-out`
2×	`flip3--` `frac-2neg` `flip3-+` `frac-add` `clear-num` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `associate-+l-` `associate-+r+`

Counts

3 → 299

Calls

3 calls:

10.0ms	(/ (- a t) y)
98.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
16.0ms	(/ (- t z) (/ (- a t) y))

series340.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(/ (- a t) y)
210.0ms	(+ (/ (- t z) (/ (- a t) y)) (+ x y))
102.0ms	(/ (- t z) (/ (- a t) y))

simplify95.0ms

Algorithm

egg-herbie

Counts

308 → 308

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	892	1815
1	3565	1754
2	5001	1752

prune844.0ms

Filtered

308 candidates to 212 candidates (68.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (- a t))
0.6b	(cbrt (- a t))
3.8b	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
8.4b	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
19×	`add-cbrt-cube`
18×	`cbrt-undiv` `div-exp`
16×	`cbrt-div`
13×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`cbrt-prod`
8×	`add-cube-cbrt` `flip3--` `flip--` `associate-/l/`
7×	`times-frac`
5×	`associate-/r*`
4×	`pow1` `expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp`
3×	`div-inv`
2×	`pow1/3` `associate-r/` `associate-l/` `distribute-lft-out--` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r/` `fma-udef` `associate-/l*`

Counts

4 → 96

Calls

4 calls:

2.0ms	(cbrt (- a t))
2.0ms	(cbrt (- a t))
23.0ms	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
0.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

series1.5s

Counts

4 → 12

Calls

4 calls:

163.0ms	(cbrt (- a t))
183.0ms	(cbrt (- a t))
336.0ms	(/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y))))
769.0ms	(fma (/ (* (cbrt (- t z)) (cbrt (- t z))) (/ (* (cbrt (- a t)) (cbrt (- a t))) (* (cbrt y) (cbrt y)))) (/ (cbrt (- t z)) (/ (cbrt (- a t)) (cbrt y))) (+ x y))

simplify66.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	565	1566
1	2424	1280
2	5002	1181

prune462.0ms

Filtered

108 candidates to 82 candidates (75.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 1.4b

regimes212.0ms

Accuracy

42.2% (4.2b remaining)

Error of 7.4b against oracle of 3.2b and baseline of 10.5b

bsearch103.0ms

Steps

Iters	Range		Point
4	2.3437436495179523e+76	3.325624108380948e+76	2.7030262370830962e+76
12	-2.845756183556343e+125	-1.394422923917771e+85	-2.1012034468767935e+108

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	26
1	31	26

end0.0ms

sample659.0ms

Algorithm

intervals

Results

246.0ms	7394×	body	80	valid
53.0ms	454×	body	640	valid
37.0ms	378×	body	320	valid
36.0ms	225×	body	1280	valid
15.0ms	250×	body	160	valid
4.0ms	22×	body	2560	valid