Details

sample108.0ms

Algorithm

intervals

Results

26.0ms	52×	body	1280	valid
21.0ms	46×	body	10240	exit
13.0ms	47×	body	640	valid
9.0ms	118×	body	80	valid
4.0ms	3×	body	2560	valid
4.0ms	22×	body	320	valid
3.0ms	93×	body	80	nan
2.0ms	7×	body	1280	nan
2.0ms	16×	body	160	valid
1.0ms	5×	body	640	nan
1.0ms	8×	body	320	nan
0.0ms	4×	body	160	nan

simplify205.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	7
1	33	7
2	49	7
3	71	7
4	93	7
5	180	7
6	232	7
7	411	7
8	710	7
9	1092	7
10	1240	7
11	1558	7
12	4191	7
13	5001	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.7b

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)
1.5b	(log (+ (- 1.0 y) (* y (exp z))))
2.0b	(+ (- 1.0 y) (* y (exp z)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
12×	`times-frac`
11×	`pow1`
9×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
5×	`log-pow`
4×	`log-div` `associate-/l*`
3×	`log-prod` `flip3-+` `associate-r` `associate-l` `associate-/r*` `flip-+`
2×	`associate-+l+` `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` `unswap-sqr`

Counts

4 → 80

Calls

4 calls:

12.0ms	(* y (exp z))
55.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
20.0ms	(log (+ (- 1.0 y) (* y (exp z))))
31.0ms	(+ (- 1.0 y) (* y (exp z)))

series256.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(* y (exp z))
139.0ms	(/ (log (+ (- 1.0 y) (* y (exp z)))) t)
66.0ms	(log (+ (- 1.0 y) (* y (exp z))))
32.0ms	(+ (- 1.0 y) (* y (exp z)))

simplify50.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	452	795
1	1740	733
2	5001	726

prune285.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 3.6b

localize17.0ms

Local error

Found 4 expressions with local error:

3.7b	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
5.7b	(/ (* z y) t)
7.5b	(/ (* (pow z 2) y) t)
7.9b	(* (pow z 2) y)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`add-cbrt-cube`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`add-log-exp`
8×	`associate-l`
7×	`prod-exp`
6×	`times-frac` `div-exp` `associate-/r*`
4×	`pow1` `cbrt-undiv` `unpow-prod-down` `associate-*r/` `frac-add` `unswap-sqr`
3×	`associate-r` `sum-log` `cbrt-unprod`
2×	`pow-to-exp` `frac-2neg` `flip3-+` `pow-exp` `clear-num` `flip-+` `div-inv` `associate-/l*` `unpow2` `sqr-pow`
1×	`+-commutative` `associate-+r+` `*-commutative`

Counts

4 → 87

Calls

4 calls:

57.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
10.0ms	(/ (* z y) t)
15.0ms	(/ (* (pow z 2) y) t)
12.0ms	(* (pow z 2) y)

series147.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(+ (* 1.0 (/ (* z y) t)) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
17.0ms	(/ (* z y) t)
22.0ms	(/ (* (pow z 2) y) t)
22.0ms	(* (pow z 2) y)

simplify64.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	492	659
1	2299	586
2	5001	586

prune297.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.1b

localize21.0ms

Local error

Found 4 expressions with local error:

3.7b	(+ (* 1.0 (* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
4.4b	(* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))
7.5b	(/ (* (pow z 2) y) t)
7.9b	(* (pow z 2) y)

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`add-exp-log`
31×	`times-frac`
25×	`associate-r` `add-cbrt-cube`
24×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-*r/`
15×	`associate-l`
14×	`prod-exp`
12×	`frac-add`
11×	`cbrt-prod` `div-exp`
10×	`cbrt-unprod` `unswap-sqr`
9×	`cbrt-undiv` `add-log-exp`
6×	`pow1`
4×	`frac-times` `unpow-prod-down` `flip3-+` `associate-*l/` `flip-+`
3×	`associate-/r*` `sum-log` `div-inv`
2×	`pow-to-exp` `pow-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `associate-+r+` `frac-2neg` `pow-prod-down` `clear-num` `associate-/l*`

Counts

4 → 131

Calls

4 calls:

120.0ms	(+ (* 1.0 (* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
47.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))
11.0ms	(/ (* (pow z 2) y) t)
12.0ms	(* (pow z 2) y)

series191.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (* 1.0 (* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
46.0ms	(* (/ z (* (cbrt t) (cbrt t))) (/ y (cbrt t)))
16.0ms	(/ (* (pow z 2) y) t)
16.0ms	(* (pow z 2) y)

simplify124.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 2 (110.0ms)

Iter	Nodes	Cost
0	929	1557
1	4839	1399
2	5001	1385

prune589.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize25.0ms

Local error

Found 4 expressions with local error:

3.7b	(+ (* 1.0 (* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
5.6b	(* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))
7.5b	(/ (* (pow z 2) y) t)
7.9b	(* (pow z 2) y)

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

113×	`add-sqr-sqrt`
109×	`times-frac`
57×	`cbrt-prod`
51×	`add-exp-log`
44×	`add-cube-cbrt` `*-un-lft-identity`
40×	`associate-l`
34×	`associate-r`
29×	`add-cbrt-cube`
24×	`unswap-sqr`
18×	`div-exp`
16×	`cbrt-undiv` `associate-*r/` `prod-exp`
12×	`frac-add` `cbrt-unprod`
9×	`add-log-exp`
7×	`div-inv`
6×	`pow1`
4×	`frac-times` `unpow-prod-down` `flip3-+` `associate-*l/` `flip-+`
3×	`associate-/r*` `sum-log`
2×	`pow-to-exp` `pow-exp` `*-commutative` `unpow2` `sqr-pow`
1×	`+-commutative` `associate-+r+` `frac-2neg` `pow-prod-down` `clear-num` `associate-/l*`

Counts

4 → 183

Calls

4 calls:

141.0ms	(+ (* 1.0 (* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
81.0ms	(* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))
12.0ms	(/ (* (pow z 2) y) t)
13.0ms	(* (pow z 2) y)

series201.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(+ (* 1.0 (* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))) (+ (/ (log 1.0) t) (* 0.5 (/ (* (pow z 2) y) t))))
44.0ms	(* (/ (/ z (* (cbrt t) (cbrt t))) (cbrt (* (cbrt t) (cbrt t)))) (/ y (cbrt (cbrt t))))
21.0ms	(/ (* (pow z 2) y) t)
16.0ms	(* (pow z 2) y)

simplify60.0ms

Algorithm

egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1306	3106
1	5001	2891

prune967.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

regimes660.0ms

Accuracy

72.8% (4.6b remaining)

Error of 8.1b against oracle of 3.5b and baseline of 20.4b

bsearch150.0ms

Steps

Iters	Range		Point
7	-4.7047821553969426e-126	-6.045525225535021e-128	-2.0531339008743572e-126
8	-91081.84287867452	-1.7357868943924353	-1.7663611360594609

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	53
1	72	53

end0.0ms

sample3.2s

Algorithm

intervals

Results

764.0ms	1578×	body	10240	exit
749.0ms	1476×	body	1280	valid
424.0ms	1499×	body	640	valid
209.0ms	3611×	body	80	valid
160.0ms	898×	body	320	valid
113.0ms	88×	body	2560	valid
95.0ms	2592×	body	80	nan
51.0ms	263×	body	640	nan
50.0ms	470×	body	160	valid
31.0ms	110×	body	1280	nan
24.0ms	190×	body	320	nan
10.0ms	122×	body	160	nan