Details

sample119.0ms

Algorithm

intervals

Results

39.0ms	790×	body	80	nan
11.0ms	27×	body	640	valid
10.0ms	189×	body	80	valid
6.0ms	8×	body	1280	valid
4.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify67.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	27	9
1	57	8
2	136	8
3	312	8
4	709	8
5	1629	8
6	3564	8
7	5001	8

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- z 1.0) (log (- 1.0 y)))
0.1b	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.6b	(log (- 1.0 y))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`log-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`add-exp-log`
5×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `add-cbrt-cube`
4×	`associate-r` `distribute-lft-out--` `difference-of-squares`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`log-div` `flip3--` `associate-*l/` `log-pow` `flip--`
1×	`rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 63

Calls

3 calls:

31.0ms	(* (- z 1.0) (log (- 1.0 y)))
0.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
6.0ms	(log (- 1.0 y))

series272.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* (- z 1.0) (log (- 1.0 y)))
190.0ms	(fma (log y) (- x 1.0) (- (* (- z 1.0) (log (- 1.0 y))) t))
40.0ms	(log (- 1.0 y))

simplify37.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	364	521
1	1204	461
2	5001	449

prune229.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

0.0b

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

0.1b

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

88×	`add-sqr-sqrt`
80×	`times-frac`
68×	`associate-r`
56×	`unpow-prod-down`
54×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate--l+`
27×	`prod-diff`
26×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`
11×	`pow1`
10×	`prod-exp`
9×	`div-exp`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `log-prod` `pow-exp` `log-pow`
5×	`add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `associate-l` `log1p-expm1-u`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `flip3--` `fma-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative` `flip--` `fma-udef` `div-inv`

Counts

3 → 174

Calls

3 calls:

39.0ms

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

49.0ms

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

0.0ms

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

series385.0ms

Counts

3 → 9

Calls

3 calls:

50.0ms

(* 1/2 (/ (pow y 2) (pow 1.0 2)))

132.0ms

(- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)

203.0ms

(fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))

simplify89.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	810	2097
1	3303	1478
2	5001	1476

prune700.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.1b	(fma (log y) (- x 1.0) (fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

80×	`times-frac`
70×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
36×	`add-cube-cbrt` `*-un-lft-identity`
25×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`prod-exp`
9×	`div-exp`
7×	`add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
4×	`pow1`
3×	`associate-l`
2×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
1×	`cbrt-undiv` `associate-r/` `pow-prod-down` `-commutative` `fma-udef` `div-inv`

Counts

2 → 122

Calls

2 calls:

38.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
0.0ms	(fma (log y) (- x 1.0) (fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

series207.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(* 1/2 (/ (pow y 2) (pow 1.0 2)))
161.0ms	(fma (log y) (- x 1.0) (fma (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2))))) (- t)))

simplify63.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	613	925
1	3000	712
2	5002	710

prune468.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
0.5b	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

13.0ms	(* (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
1.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

series1.6s

Counts

4 → 12

Calls

4 calls:

660.0ms	(* (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))) (cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t))))
328.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
330.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))
330.0ms	(cbrt (fma (log y) (- x 1.0) (- (* (- z 1.0) (- (log 1.0) (+ (* 1.0 y) (* 1/2 (/ (pow y 2) (pow 1.0 2)))))) t)))

simplify58.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	408	2733
1	1367	2487
2	5001	2281

prune430.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes359.0ms

Accuracy

0% (0.0b remaining)

Error of 0.3b against oracle of 0.3b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	14
1	24	14

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	24302×	body	80	nan
338.0ms	5868×	body	80	valid
236.0ms	766×	body	640	valid
164.0ms	264×	body	1280	valid
130.0ms	695×	body	320	valid
52.0ms	440×	body	160	valid