Details

sample112.0ms

Algorithm

intervals

Results

29.0ms	60×	body	10240	exit
19.0ms	55×	body	640	valid
16.0ms	33×	body	1280	valid
10.0ms	5×	body	2560	valid
7.0ms	117×	body	80	valid
6.0ms	34×	body	320	valid
2.0ms	62×	body	80	nan
2.0ms	11×	body	640	nan
2.0ms	15×	body	160	valid
1.0ms	3×	body	1280	nan
1.0ms	7×	body	320	nan
0.0ms	2×	body	160	nan

simplify220.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	35	7
2	53	7
3	81	7
4	121	7
5	250	7
6	314	7
7	532	7
8	908	7
9	1397	7
10	1553	7
11	1892	7
12	4682	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* y (exp z))
0.0b	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
1.4b	(log (+ (- 1.0 y) (* y (exp z))))
4.1b	(+ (- 1.0 y) (* y (exp z)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
25×	`*-un-lft-identity`
23×	`add-cube-cbrt`
12×	`times-frac`
11×	`pow1` `associate-+l+`
9×	`prod-diff` `add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`fma-def` `log-pow`
4×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`div-sub` `sum-log`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 102

Calls

4 calls:

5.0ms	(* y (exp z))
8.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
6.0ms	(log (+ (- 1.0 y) (* y (exp z))))
7.0ms	(+ (- 1.0 y) (* y (exp z)))

series409.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* y (exp z))
277.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
71.0ms	(log (+ (- 1.0 y) (* y (exp z))))
40.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	499	918
1	2002	785
2	5001	761

prune389.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.3b	(/ (* z y) t)
6.3b	(* (pow z 2) y)
6.6b	(/ (* (pow z 2) y) t)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

1.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.0ms	(/ (* z y) t)
5.0ms	(* (pow z 2) y)
6.0ms	(/ (* (pow z 2) y) t)

series211.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(fma (/ (* z y) t) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
31.0ms	(/ (* z y) t)
20.0ms	(* (pow z 2) y)
18.0ms	(/ (* (pow z 2) y) t)

simplify45.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	301	473
1	1345	406
2	5001	406

prune348.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.3b	(/ t (* z y))
6.3b	(* (pow z 2) y)
6.6b	(/ (* (pow z 2) y) t)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `unpow-prod-down` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp` `unswap-sqr`
3×	`associate-r` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef`

Counts

4 → 87

Calls

4 calls:

1.0ms	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
4.0ms	(/ t (* z y))
5.0ms	(* (pow z 2) y)
6.0ms	(/ (* (pow z 2) y) t)

series188.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(fma (/ 1 (/ t (* z y))) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
20.0ms	(/ t (* z y))
20.0ms	(* (pow z 2) y)
19.0ms	(/ (* (pow z 2) y) t)

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	305	486
1	1301	414
2	5001	412

prune359.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

3.7b	(/ (/ t z) y)
3.8b	(fma (/ 1 (/ (/ t z) y)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
6.3b	(* (pow z 2) y)
6.6b	(/ (* (pow z 2) y) t)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac`
57×	`add-sqr-sqrt`
51×	`add-cube-cbrt` `*-un-lft-identity`
24×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`associate-/l*`
8×	`associate-l`
7×	`div-exp`
6×	`prod-exp` `associate-/r*` `div-inv`
5×	`cbrt-undiv`
4×	`pow1` `expm1-log1p-u` `unpow-prod-down` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`associate-r`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod` `unpow2` `sqr-pow`
1×	`*-commutative` `fma-udef` `associate-/l/`

Counts

4 → 136

Calls

4 calls:

6.0ms	(/ (/ t z) y)
1.0ms	(fma (/ 1 (/ (/ t z) y)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
5.0ms	(* (pow z 2) y)
5.0ms	(/ (* (pow z 2) y) t)

series197.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ t z) y)
131.0ms	(fma (/ 1 (/ (/ t z) y)) 1.0 (fma 0.5 (/ (* (pow z 2) y) t) (/ (log 1.0) t)))
17.0ms	(* (pow z 2) y)
23.0ms	(/ (* (pow z 2) y) t)

simplify63.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	525	844
1	2254	767
2	5001	765

prune553.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.6b

regimes630.0ms

Accuracy

73.2% (4.4b remaining)

Error of 8.1b against oracle of 3.7b and baseline of 20.1b

bsearch131.0ms

Steps

Iters	Range		Point
8	2.5548096550536154e-78	5.333502830476792e-74	2.802488273816828e-74
6	-5.8829093822384e-14	-7.856438118040365e-15	-5.458414998494592e-14

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	45	26

end0.0ms

sample3.2s

Algorithm

intervals

Results

770.0ms	1518×	body	10240	exit
744.0ms	1352×	body	1280	valid
464.0ms	1531×	body	640	valid
224.0ms	3637×	body	80	valid
172.0ms	911×	body	320	valid
126.0ms	97×	body	2560	valid
96.0ms	2422×	body	80	nan
60.0ms	505×	body	160	valid
54.0ms	265×	body	640	nan
32.0ms	99×	body	1280	nan
30.0ms	190×	body	320	nan
9.0ms	106×	body	160	nan